TSTP Solution File: LAT304+3 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT304+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 11:27:37 EDT 2023
% Result : Theorem 137.22s 31.58s
% Output : Refutation 138.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1430
% Syntax : Number of formulae : 2622 ( 158 unt; 293 typ; 0 def)
% Number of atoms : 16806 (1710 equ; 0 cnn)
% Maximal formula atoms : 47 ( 7 avg)
% Number of connectives : 63171 (2679 ~; 232 |;7468 &;46021 @)
% ( 276 <=>;6495 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 643 ( 643 >; 0 *; 0 +; 0 <<)
% Number of symbols : 296 ( 293 usr; 17 con; 0-9 aty)
% Number of variables : 7607 ( 0 ^;7250 !; 357 ?;7607 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_type,type,
v10_lattices: $i > $o ).
thf(l3_lattices_type,type,
l3_lattices: $i > $o ).
thf(m2_filter_2_type,type,
m2_filter_2: $i > $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(v17_lattices_type,type,
v17_lattices: $i > $o ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(k8_lopclset_type,type,
k8_lopclset: $i > $i ).
thf(m1_filter_0_type,type,
m1_filter_0: $i > $i > $o ).
thf(v1_filter_0_type,type,
v1_filter_0: $i > $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
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(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k14_funct_3_type,type,
k14_funct_3: $i > $i > $i > $i > $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v4_lattice3_type,type,
v4_lattice3: $i > $o ).
thf(v3_filter_0_type,type,
v3_filter_0: $i > $o ).
thf(v5_lattice3_type,type,
v5_lattice3: $i > $o ).
thf(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
thf(k9_setwiseo_type,type,
k9_setwiseo: $i > $i ).
thf(k5_finsub_1_type,type,
k5_finsub_1: $i > $i ).
thf(r5_binop_1_type,type,
r5_binop_1: $i > $i > $i > $o ).
thf(k7_filter_1_type,type,
k7_filter_1: $i > $i > $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k6_partfun1_type,type,
k6_partfun1: $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k4_relset_1_type,type,
k4_relset_1: $i > $i > $i > $i ).
thf(r3_binop_1_type,type,
r3_binop_1: $i > $i > $i > $o ).
thf(k3_binop_1_type,type,
k3_binop_1: $i > $i > $i ).
thf(k6_relat_1_type,type,
k6_relat_1: $i > $i ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(k10_setwiseo_type,type,
k10_setwiseo: $i > $i > $i > $i > $i ).
thf(k8_setwiseo_type,type,
k8_setwiseo: $i > $i > $i > $i > $i ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(r1_binop_1_type,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_binop_1_type,type,
k1_binop_1: $i > $i > $i > $i ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(v5_monoid_0_type,type,
v5_monoid_0: $i > $i > $o ).
thf(v3_monoid_0_type,type,
v3_monoid_0: $i > $i > $o ).
thf(v4_monoid_0_type,type,
v4_monoid_0: $i > $i > $o ).
thf(k7_lopclset_type,type,
k7_lopclset: $i > $i ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k10_lopclset_type,type,
k10_lopclset: $i > $i ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(k6_funcop_1_type,type,
k6_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(k7_ens_1_type,type,
k7_ens_1: $i > $i > $i > $i ).
thf(k2_ens_1_type,type,
k2_ens_1: $i > $i ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(k5_setwiseo_type,type,
k5_setwiseo: $i > $i > $i > $i ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(r4_binop_1_type,type,
r4_binop_1: $i > $i > $i > $o ).
thf(k1_lattice3_type,type,
k1_lattice3: $i > $i ).
thf(r1_lattices_type,type,
r1_lattices: $i > $i > $i > $o ).
thf(r4_lattice3_type,type,
r4_lattice3: $i > $i > $i > $o ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(v2_orders_2_type,type,
v2_orders_2: $i > $o ).
thf(l1_orders_2_type,type,
l1_orders_2: $i > $o ).
thf(r1_orders_2_type,type,
r1_orders_2: $i > $i > $i > $o ).
thf(k9_lopclset_type,type,
k9_lopclset: $i > $i ).
thf(k7_lattices_type,type,
k7_lattices: $i > $i > $i ).
thf(m1_filter_1_type,type,
m1_filter_1: $i > $i > $i > $o ).
thf(r3_orders_2_type,type,
r3_orders_2: $i > $i > $i > $o ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(v6_lattice3_type,type,
v6_lattice3: $i > $o ).
thf(m2_realset1_type,type,
m2_realset1: $i > $i > $i > $o ).
thf(k11_setwiseo_type,type,
k11_setwiseo: $i > $i ).
thf(k7_setwiseo_type,type,
k7_setwiseo: $i > $i > $i > $i > $i > $i ).
thf(k7_funcop_1_type,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(r2_binop_1_type,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k1_setwiseo_type,type,
k1_setwiseo: $i > $i ).
thf(k6_setwiseo_type,type,
k6_setwiseo: $i > $i > $i > $i ).
thf(g1_orders_2_type,type,
g1_orders_2: $i > $i > $i ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k4_lattices_type,type,
k4_lattices: $i > $i > $i > $i ).
thf(k7_relset_1_type,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(r3_lattice3_type,type,
r3_lattice3: $i > $i > $i > $o ).
thf(k11_relset_1_type,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(k8_funcop_1_type,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k5_relset_1_type,type,
k5_relset_1: $i > $i > $i > $i ).
thf(k10_relset_1_type,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(a_3_0_ens_1_type,type,
a_3_0_ens_1: $i > $i > $i > $i ).
thf(v5_orders_2_type,type,
v5_orders_2: $i > $i > $o ).
thf(k1_struct_0_type,type,
k1_struct_0: $i > $i > $i ).
thf(r6_binop_1_type,type,
r6_binop_1: $i > $i > $i > $o ).
thf(v8_monoid_0_type,type,
v8_monoid_0: $i > $i > $o ).
thf(v6_monoid_0_type,type,
v6_monoid_0: $i > $i > $o ).
thf(v7_monoid_0_type,type,
v7_monoid_0: $i > $i > $o ).
thf(v1_setwiseo_type,type,
v1_setwiseo: $i > $i > $o ).
thf(r1_relat_2_type,type,
r1_relat_2: $i > $i > $o ).
thf(r3_relat_2_type,type,
r3_relat_2: $i > $i > $o ).
thf(r8_relat_2_type,type,
r8_relat_2: $i > $i > $o ).
thf(a_1_1_ens_1_type,type,
a_1_1_ens_1: $i > $i ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(k7_grcat_1_type,type,
k7_grcat_1: $i > $i ).
thf(r7_binop_1_type,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(k15_lattice3_type,type,
k15_lattice3: $i > $i > $i ).
thf(v11_lattices_type,type,
v11_lattices: $i > $o ).
thf(v13_lattices_type,type,
v13_lattices: $i > $o ).
thf(u1_lattices_type,type,
u1_lattices: $i > $i ).
thf(k2_lattice2_type,type,
k2_lattice2: $i > $i > $i > $i > $i ).
thf(k1_orders_1_type,type,
k1_orders_1: $i > $i ).
thf(a_3_5_quantal1_type,type,
a_3_5_quantal1: $i > $i > $i > $i ).
thf(k3_setwiseo_type,type,
k3_setwiseo: $i > $i > $i > $i ).
thf(k3_relat_1_type,type,
k3_relat_1: $i > $i ).
thf(k5_lattices_type,type,
k5_lattices: $i > $i ).
thf(a_3_4_quantal1_type,type,
a_3_4_quantal1: $i > $i > $i > $i ).
thf(a_2_0_lattice3_type,type,
a_2_0_lattice3: $i > $i > $i ).
thf(k3_lattice2_type,type,
k3_lattice2: $i > $i > $i > $i > $i ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(k2_setwiseo_type,type,
k2_setwiseo: $i > $i > $i ).
thf(a_2_5_lattice3_type,type,
a_2_5_lattice3: $i > $i > $i ).
thf(k16_lattice3_type,type,
k16_lattice3: $i > $i > $i ).
thf(a_2_6_lattice3_type,type,
a_2_6_lattice3: $i > $i > $i ).
thf(r3_lattices_type,type,
r3_lattices: $i > $i > $i > $o ).
thf(r2_lattice3_type,type,
r2_lattice3: $i > $i > $i > $o ).
thf(k4_setwiseo_type,type,
k4_setwiseo: $i > $i > $i > $i > $i ).
thf(k5_lattice4_type,type,
k5_lattice4: $i > $i ).
thf(a_2_0_lopclset_type,type,
a_2_0_lopclset: $i > $i > $i ).
thf(m2_card_fil_type,type,
m2_card_fil: $i > $i > $o ).
thf(v14_lattices_type,type,
v14_lattices: $i > $o ).
thf(k3_lattices_type,type,
k3_lattices: $i > $i > $i > $i ).
thf(k8_lattice3_type,type,
k8_lattice3: $i > $i > $i ).
thf(k7_lattice3_type,type,
k7_lattice3: $i > $i ).
thf(a_2_2_lattice3_type,type,
a_2_2_lattice3: $i > $i > $i ).
thf(a_3_5_lattice3_type,type,
a_3_5_lattice3: $i > $i > $i > $i ).
thf(k6_lattices_type,type,
k6_lattices: $i > $i ).
thf(m1_lattice4_type,type,
m1_lattice4: $i > $i > $i > $o ).
thf(l1_lattices_type,type,
l1_lattices: $i > $o ).
thf(a_2_1_lattice3_type,type,
a_2_1_lattice3: $i > $i > $i ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $i > $i > $i ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(k1_lattice2_type,type,
k1_lattice2: $i > $i ).
thf(k3_borsuk_1_type,type,
k3_borsuk_1: $i > $i > $i > $i ).
thf(a_2_2_domain_1_type,type,
a_2_2_domain_1: $i > $i > $i ).
thf(l2_lattices_type,type,
l2_lattices: $i > $o ).
thf(u2_lattices_type,type,
u2_lattices: $i > $i ).
thf(k4_filter_2_type,type,
k4_filter_2: $i > $i > $i > $i ).
thf(k5_filter_0_type,type,
k5_filter_0: $i > $i > $i > $i ).
thf(r7_relat_2_type,type,
r7_relat_2: $i > $i > $o ).
thf(m2_filter_1_type,type,
m2_filter_1: $i > $i > $i > $o ).
thf(k1_ens_1_type,type,
k1_ens_1: $i > $i ).
thf(k2_struct_0_type,type,
k2_struct_0: $i > $i > $i > $i ).
thf(v3_lattice3_type,type,
v3_lattice3: $i > $o ).
thf(r1_lattice3_type,type,
r1_lattice3: $i > $i > $i > $o ).
thf(a_1_1_lopclset_type,type,
a_1_1_lopclset: $i > $i ).
thf(v1_lattice4_type,type,
v1_lattice4: $i > $i > $i > $o ).
thf(a_3_3_lattice3_type,type,
a_3_3_lattice3: $i > $i > $i > $i ).
thf(r1_lattice2_type,type,
r1_lattice2: $i > $i > $i > $o ).
thf(k6_filter_1_type,type,
k6_filter_1: $i > $i > $i > $i ).
thf(k5_filter_1_type,type,
k5_filter_1: $i > $i > $i ).
thf(k8_filter_0_type,type,
k8_filter_0: $i > $i > $i ).
thf(v2_lattice4_type,type,
v2_lattice4: $i > $i > $i > $o ).
thf(v16_lattices_type,type,
v16_lattices: $i > $o ).
thf(r2_lattices_type,type,
r2_lattices: $i > $i > $i > $o ).
thf(v9_monoid_0_type,type,
v9_monoid_0: $i > $i > $o ).
thf(a_2_7_lattice3_type,type,
a_2_7_lattice3: $i > $i > $i ).
thf(a_1_0_domain_1_type,type,
a_1_0_domain_1: $i > $i ).
thf(a_2_3_lattice3_type,type,
a_2_3_lattice3: $i > $i > $i ).
thf(a_2_4_lattice3_type,type,
a_2_4_lattice3: $i > $i > $i ).
thf(r5_relat_2_type,type,
r5_relat_2: $i > $i > $o ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $i > $i > $i ).
thf(m2_nat_lat_type,type,
m2_nat_lat: $i > $i > $o ).
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(r2_lattice4_type,type,
r2_lattice4: $i > $i > $i > $o ).
thf(k3_lattice3_type,type,
k3_lattice3: $i > $i ).
thf(m1_filter_2_type,type,
m1_filter_2: $i > $i > $o ).
thf(k2_filter_0_type,type,
k2_filter_0: $i > $i > $i ).
thf(a_3_0_filter_0_type,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(v15_lattices_type,type,
v15_lattices: $i > $o ).
thf(m2_lattice4_type,type,
m2_lattice4: $i > $i > $o ).
thf(a_2_1_lattice4_type,type,
a_2_1_lattice4: $i > $i > $i ).
thf(k3_lattice4_type,type,
k3_lattice4: $i > $i > $i ).
thf(a_2_0_filter_0_type,type,
a_2_0_filter_0: $i > $i > $i ).
thf(r4_lattice4_type,type,
r4_lattice4: $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(k4_filter_0_type,type,
k4_filter_0: $i > $i > $i > $i ).
thf(k4_lattice3_type,type,
k4_lattice3: $i > $i > $i ).
thf(a_2_1_domain_1_type,type,
a_2_1_domain_1: $i > $i > $i ).
thf(l1_funcsdom_type,type,
l1_funcsdom: $i > $o ).
thf(k5_filter_2_type,type,
k5_filter_2: $i > $i > $i ).
thf(k6_filter_2_type,type,
k6_filter_2: $i > $i > $i ).
thf(m3_lattice4_type,type,
m3_lattice4: $i > $i > $o ).
thf(k10_filter_2_type,type,
k10_filter_2: $i > $i > $i ).
thf(k12_filter_2_type,type,
k12_filter_2: $i > $i > $i ).
thf(k8_filter_2_type,type,
k8_filter_2: $i > $i > $i ).
thf(k3_filter_0_type,type,
k3_filter_0: $i > $i > $i ).
thf(v1_lattice2_type,type,
v1_lattice2: $i > $o ).
thf(v1_lattice3_type,type,
v1_lattice3: $i > $o ).
thf(v2_lattice3_type,type,
v2_lattice3: $i > $o ).
thf(k1_lattice4_type,type,
k1_lattice4: $i > $i > $i ).
thf(k7_filter_0_type,type,
k7_filter_0: $i > $i > $i > $i ).
thf(a_1_0_filter_1_type,type,
a_1_0_filter_1: $i > $i ).
thf(k1_filter_1_type,type,
k1_filter_1: $i > $i > $i > $i ).
thf(r2_relat_2_type,type,
r2_relat_2: $i > $i > $o ).
thf(k3_filter_2_type,type,
k3_filter_2: $i > $i > $i ).
thf(k5_lattice3_type,type,
k5_lattice3: $i > $i > $i ).
thf(k9_filter_0_type,type,
k9_filter_0: $i > $i > $i > $i ).
thf(a_3_4_lattice3_type,type,
a_3_4_lattice3: $i > $i > $i > $i ).
thf(r1_filter_2_type,type,
r1_filter_2: $i > $i > $i > $o ).
thf(r1_lattice4_type,type,
r1_lattice4: $i > $i > $i > $o ).
thf(k7_filter_2_type,type,
k7_filter_2: $i > $i > $i ).
thf(k4_lattice4_type,type,
k4_lattice4: $i > $i > $i ).
thf(k2_lattice4_type,type,
k2_lattice4: $i > $i > $i ).
thf(k14_filter_2_type,type,
k14_filter_2: $i > $i > $i ).
thf(a_3_6_lattice3_type,type,
a_3_6_lattice3: $i > $i > $i > $i ).
thf(k10_domain_1_type,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_3_2_lattice3_type,type,
a_3_2_lattice3: $i > $i > $i > $i ).
thf(k4_card_fil_type,type,
k4_card_fil: $i > $i ).
thf(r3_lattice4_type,type,
r3_lattice4: $i > $i > $i > $o ).
thf(k11_filter_0_type,type,
k11_filter_0: $i > $i > $i ).
thf(a_3_2_domain_1_type,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(a_2_0_lattice4_type,type,
a_2_0_lattice4: $i > $i > $i ).
thf(v12_lattices_type,type,
v12_lattices: $i > $o ).
thf(k18_group_2_type,type,
k18_group_2: $i > $i > $i ).
thf(k12_domain_1_type,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k24_filter_2_type,type,
k24_filter_2: $i > $i > $i ).
thf(k11_lattice3_type,type,
k11_lattice3: $i > $i > $i > $i ).
thf(k1_filter_0_type,type,
k1_filter_0: $i > $i ).
thf(a_1_2_domain_1_type,type,
a_1_2_domain_1: $i > $i ).
thf(k6_filter_0_type,type,
k6_filter_0: $i > $i > $i > $i ).
thf(v1_quantal1_type,type,
v1_quantal1: $i > $i > $o ).
thf(a_3_1_domain_1_type,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(a_3_6_domain_1_type,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(r4_wellord1_type,type,
r4_wellord1: $i > $i > $o ).
thf(k1_finsub_1_type,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(a_3_5_domain_1_type,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(v3_lattice4_type,type,
v3_lattice4: $i > $i > $i > $o ).
thf(a_3_4_domain_1_type,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(r1_filter_1_type,type,
r1_filter_1: $i > $i > $o ).
thf(k9_domain_1_type,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(v2_filter_0_type,type,
v2_filter_0: $i > $i > $o ).
thf(k2_filter_1_type,type,
k2_filter_1: $i > $i > $i > $i ).
thf(k13_nat_lat_type,type,
k13_nat_lat: $i ).
thf(k6_nat_lat_type,type,
k6_nat_lat: $i ).
thf(a_3_3_domain_1_type,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(k11_domain_1_type,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k20_filter_2_type,type,
k20_filter_2: $i > $i > $i > $i ).
thf(k8_domain_1_type,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(k13_domain_1_type,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k6_lattice3_type,type,
k6_lattice3: $i > $i > $i ).
thf(k2_lattice3_type,type,
k2_lattice3: $i > $i ).
thf(k11_filter_2_type,type,
k11_filter_2: $i > $i > $i ).
thf(k12_filter_0_type,type,
k12_filter_0: $i > $i > $i ).
thf(k9_filter_1_type,type,
k9_filter_1: $i > $i ).
thf(k10_lattice3_type,type,
k10_lattice3: $i > $i > $i > $i ).
thf(a_3_1_filter_0_type,type,
a_3_1_filter_0: $i > $i > $i > $i ).
thf(l2_quantal1_type,type,
l2_quantal1: $i > $o ).
thf(a_3_7_domain_1_type,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(k19_filter_2_type,type,
k19_filter_2: $i > $i > $i ).
thf(k21_filter_2_type,type,
k21_filter_2: $i > $i > $i > $i ).
thf(k22_filter_2_type,type,
k22_filter_2: $i > $i > $i > $i ).
thf(v6_group_1_type,type,
v6_group_1: $i > $o ).
thf(k2_filter_2_type,type,
k2_filter_2: $i > $i > $i ).
thf(k13_filter_2_type,type,
k13_filter_2: $i > $i > $i ).
thf(k16_filter_2_type,type,
k16_filter_2: $i > $i > $i ).
thf(k9_filter_2_type,type,
k9_filter_2: $i > $i > $i ).
thf(k14_lattice3_type,type,
k14_lattice3: $i > $i ).
thf(k15_filter_2_type,type,
k15_filter_2: $i > $i > $i ).
thf(k2_pcomps_1_type,type,
k2_pcomps_1: $i > $i ).
thf(k18_filter_2_type,type,
k18_filter_2: $i > $i > $i ).
thf(k1_filter_2_type,type,
k1_filter_2: $i > $i ).
thf(k23_filter_2_type,type,
k23_filter_2: $i > $i > $i ).
thf(k17_filter_2_type,type,
k17_filter_2: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i > $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk35_type,type,
sk35: $i ).
thf(sk149_type,type,
sk149: $i ).
thf(sk182_type,type,
sk182: $i ).
thf(sk183_type,type,
sk183: $i ).
thf(sk253_type,type,
sk253: $i ).
thf(sk267_type,type,
sk267: $i ).
thf(sk461_type,type,
sk461: $i ).
thf(sk468_type,type,
sk468: $i ).
thf(sk489_type,type,
sk489: $i ).
thf(sk492_type,type,
sk492: $i ).
thf(901,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/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(5509,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)],[901]) ).
thf(887,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/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(5422,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)],[887]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r7_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r7_relat_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_orders_1) ).
thf(2778,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r7_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r7_relat_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(514,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r1_lattice2 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice2) ).
thf(3666,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r1_lattice2 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= D ) ) )
=> ( r1_lattice2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).
thf(3167,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)],[418]) ).
thf(522,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funcop_1) ).
thf(3698,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_sysrel) ).
thf(3581,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(938,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/sandbox/benchmark/theBenchmark.p',redefinition_k12_filter_0) ).
thf(5654,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)],[938]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k10_filter_2 @ A @ B ) )
& ( m2_lattice4 @ ( k10_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_2) ).
thf(3969,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k10_filter_2 @ A @ B ) )
& ( m2_lattice4 @ ( k10_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1036,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/sandbox/benchmark/theBenchmark.p',t2_filter_1) ).
thf(6042,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)],[1036]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k4_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_setwiseo) ).
thf(5028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k4_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1028,axiom,
? [A: $i] :
( ( l1_funcsdom @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funcsdom) ).
thf(6014,plain,
? [A: $i] :
( ( l1_funcsdom @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(5582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(940,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/sandbox/benchmark/theBenchmark.p',t31_lattices) ).
thf(5659,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)],[940]) ).
thf(398,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v7_monoid_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_monoid_0) ).
thf(3021,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v7_monoid_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) )
=> ( D = E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) )
=> ( D = E ) ) ) ) )
=> ( v7_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(611,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/sandbox/benchmark/theBenchmark.p',t15_filter_1) ).
thf(4094,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)],[611]) ).
thf(997,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_setwiseo @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_lattice2) ).
thf(5918,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_setwiseo @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1127,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_nat_lat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_nat_lat) ).
thf(6355,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_nat_lat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(1823,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)],[165]) ).
thf(705,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( C = D )
=> ( ( k7_lattices @ A @ C )
= ( k7_lattices @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_2) ).
thf(4571,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( C = D )
=> ( ( k7_lattices @ A @ C )
= ( k7_lattices @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(452,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/sandbox/benchmark/theBenchmark.p',t33_partfun1) ).
thf(3345,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)],[452]) ).
thf(257,axiom,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(2341,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(218,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).
thf(2072,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(646,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/sandbox/benchmark/theBenchmark.p',d6_lattice4) ).
thf(4262,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)],[646]) ).
thf(604,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( u1_struct_0 @ ( k8_filter_0 @ A @ B ) )
= B )
& ( ( u2_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( ( u1_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_0) ).
thf(4062,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( u1_struct_0 @ ( k8_filter_0 @ A @ B ) )
= B )
& ( ( u2_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( ( u1_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',t28_lopclset) ).
thf(2412,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)],[275]) ).
thf(873,axiom,
m2_nat_lat @ k13_nat_lat @ k6_nat_lat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_nat_lat) ).
thf(5320,plain,
m2_nat_lat @ k13_nat_lat @ k6_nat_lat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1104,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k5_filter_2 @ A @ B ) @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).
thf(6283,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k5_filter_2 @ A @ B ) @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(1105,axiom,
( ~ ( v3_struct_0 @ k13_nat_lat )
& ( v10_lattices @ k13_nat_lat )
& ( l3_lattices @ k13_nat_lat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_nat_lat) ).
thf(6285,plain,
( ~ ( v3_struct_0 @ k13_nat_lat )
& ( v10_lattices @ k13_nat_lat )
& ( l3_lattices @ k13_nat_lat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(2463,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)],[290]) ).
thf(183,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funcop_1) ).
thf(1899,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(594,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( k16_lattice3 @ A @ B )
= ( k15_lattice3 @ A @ ( a_2_1_lattice3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d22_lattice3) ).
thf(4015,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( k16_lattice3 @ A @ B )
= ( k15_lattice3 @ A @ ( a_2_1_lattice3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1046,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
thf(6074,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(245,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(2280,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(96,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 ) )
=> ! [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,G: $i] :
( ( ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ B ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_2) ).
thf(1554,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 ) )
=> ! [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,G: $i] :
( ( ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ B ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(990,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 ) ) ) )
=> ( m2_filter_2 @ ( k19_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_filter_2) ).
thf(5898,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 ) ) ) )
=> ( m2_filter_2 @ ( k19_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1031,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/sandbox/benchmark/theBenchmark.p',t35_filter_1) ).
thf(6022,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)],[1031]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',t70_setwiseo) ).
thf(2309,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)],[251]) ).
thf(244,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B ) )
=> ( ( ( D = k1_xboole_0 )
& ~ ( v1_setwiseo @ C @ B ) )
| ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( F
= ( k7_setwiseo @ A @ B @ C @ D @ E ) )
<=> ? [G: $i] :
( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( F
= ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ( ( r3_binop_1 @ B @ H @ C )
=> ( ( k1_funct_1 @ G @ k1_xboole_0 )
= H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
= ( k8_funct_2 @ A @ B @ E @ H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( r1_tarski @ H @ D )
=> ( ( H = k1_xboole_0 )
| ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( r2_hidden @ I @ ( k6_setwiseo @ A @ D @ H ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_setwiseo) ).
thf(2210,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B ) )
=> ( ( ( D = k1_xboole_0 )
& ~ ( v1_setwiseo @ C @ B ) )
| ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( ( F
= ( k7_setwiseo @ A @ B @ C @ D @ E ) )
=> ? [G: $i] :
( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( F
= ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ( ( r3_binop_1 @ B @ H @ C )
=> ( ( k1_funct_1 @ G @ k1_xboole_0 )
= H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
= ( k8_funct_2 @ A @ B @ E @ H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( r1_tarski @ H @ D )
=> ( ( H = k1_xboole_0 )
| ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( r2_hidden @ I @ ( k6_setwiseo @ A @ D @ H ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( F
= ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ( ( r3_binop_1 @ B @ H @ C )
=> ( ( k1_funct_1 @ G @ k1_xboole_0 )
= H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
= ( k8_funct_2 @ A @ B @ E @ H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( r1_tarski @ H @ D )
=> ( ( H = k1_xboole_0 )
| ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( r2_hidden @ I @ ( k6_setwiseo @ A @ D @ H ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) )
=> ( F
= ( k7_setwiseo @ A @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(5069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ~ ( r2_hidden @ E @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ~ ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ~ ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(413,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 @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ D @ A )
& ( v1_binop_1 @ D @ A )
& ( v2_binop_1 @ D @ A )
& ( v1_setwiseo @ D @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ C @ A )
& ( m2_relset_1 @ G @ C @ A ) )
=> ( ( k7_setwiseo @ C @ A @ D @ ( k8_setwiseo @ B @ C @ F @ E ) @ G )
= ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ C @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setwiseo) ).
thf(3153,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 @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ D @ A )
& ( v1_binop_1 @ D @ A )
& ( v2_binop_1 @ D @ A )
& ( v1_setwiseo @ D @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ C @ A )
& ( m2_relset_1 @ G @ C @ A ) )
=> ( ( k7_setwiseo @ C @ A @ D @ ( k8_setwiseo @ B @ C @ F @ E ) @ G )
= ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ C @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',dt_m1_filter_1) ).
thf(2014,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)],[202]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',t17_funct_2) ).
thf(1728,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)],[138]) ).
thf(1016,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_lattice3 @ A )
= ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( k2_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
thf(5982,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_lattice3 @ A )
= ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( k2_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( u1_struct_0 @ A ) @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1139,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1142,plain,
v10_lattices @ sk1,
inference(cnf,[status(esa)],[1139]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',t18_funct_2) ).
thf(1793,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)],[156]) ).
thf(1029,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/sandbox/benchmark/theBenchmark.p',t2_filter_0) ).
thf(6017,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)],[1029]) ).
thf(931,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 ) ) ) )
=> ~ ( v1_xboole_0 @ ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_filter_2) ).
thf(5614,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 ) ) ) )
=> ~ ( v1_xboole_0 @ ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(709,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/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(4592,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)],[709]) ).
thf(9,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(1171,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)],[9]) ).
thf(1173,plain,
v2_funct_1 @ sk3,
inference(cnf,[status(esa)],[1171]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [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] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ C )
& ( m2_relset_1 @ F @ A @ C ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ A @ C )
& ( m2_relset_1 @ G @ A @ C ) )
=> ( ( ( k14_funct_3 @ A @ B @ C @ D @ F )
= ( k14_funct_3 @ A @ B @ C @ E @ G ) )
=> ( ( D = E )
& ( F = G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funct_3) ).
thf(1855,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [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] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ C )
& ( m2_relset_1 @ F @ A @ C ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ A @ C )
& ( m2_relset_1 @ G @ A @ C ) )
=> ( ( ( k14_funct_3 @ A @ B @ C @ D @ F )
= ( k14_funct_3 @ A @ B @ C @ E @ G ) )
=> ( ( D = E )
& ( F = G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r2_hidden @ ( k8_funct_2 @ A @ B @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_isocat_2) ).
thf(1200,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r2_hidden @ ( k8_funct_2 @ A @ B @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(834,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( k1_lattice2 @ A )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice2) ).
thf(5141,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( k1_lattice2 @ A )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(67,axiom,
! [A: $i] : ( v6_lattice3 @ ( k1_lattice3 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_lattice3) ).
thf(1406,plain,
! [A: $i] : ( v6_lattice3 @ ( k1_lattice3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(636,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/sandbox/benchmark/theBenchmark.p',t79_lattice2) ).
thf(4226,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)],[636]) ).
thf(693,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 ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice2) ).
thf(4500,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 ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(659,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/sandbox/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(4339,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)],[659]) ).
thf(951,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(5716,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(5718,plain,
~ ( v1_xboole_0 @ sk468 ),
inference(cnf,[status(esa)],[5716]) ).
thf(654,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v15_lattices @ A )
<=> ( ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_lattices) ).
thf(4311,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)],[654]) ).
thf(331,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ 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 ) ) )
=> ( ( C = D )
<=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_tops_3) ).
thf(2644,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ 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 ) ) )
=> ( ( ( C = D )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) )
=> ( C = D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',t51_lattice2) ).
thf(2659,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)],[335]) ).
thf(465,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(3412,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)],[465]) ).
thf(3413,plain,
( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(miniscope,[status(thm)],[3412]) ).
thf(3414,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[3413]) ).
thf(3416,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[3414]) ).
thf(3417,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[3416]) ).
thf(854,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_tops_2) ).
thf(5242,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(442,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(3285,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)],[442]) ).
thf(860,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/sandbox/benchmark/theBenchmark.p',t55_filter_0) ).
thf(5265,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)],[860]) ).
thf(479,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(3498,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(4215,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(268,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(2380,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(5425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
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 ) )
=> ( ( k1_lattice4 @ A @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_lattice4) ).
thf(6278,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)],[1102]) ).
thf(123,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 @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funcop_1) ).
thf(1655,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 @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(537,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B )
& ( v1_setwiseo @ C @ B ) )
=> ! [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 @ ( k5_finsub_1 @ A ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
=> ( ( ( k8_setwiseo @ A @ B @ D @ F )
= ( k8_setwiseo @ A @ B @ E @ G ) )
=> ( ( k7_setwiseo @ A @ B @ C @ F @ D )
= ( k7_setwiseo @ A @ B @ C @ G @ E ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_setwiseo) ).
thf(3745,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B )
& ( v1_setwiseo @ C @ B ) )
=> ! [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 @ ( k5_finsub_1 @ A ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
=> ( ( ( k8_setwiseo @ A @ B @ D @ F )
= ( k8_setwiseo @ A @ B @ E @ G ) )
=> ( ( k7_setwiseo @ A @ B @ C @ F @ D )
= ( k7_setwiseo @ A @ B @ C @ G @ E ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(342,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ( r1_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_binop_1) ).
thf(2686,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ( r1_binop_1 @ A @ C @ B ) )
& ( ( r1_binop_1 @ A @ C @ B )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(706,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( a_3_2_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_domain_1) ).
thf(4575,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( a_3_2_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(864,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( r1_tarski @ B @ C )
=> ( ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ ( k16_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_lattice3) ).
thf(5288,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( r1_tarski @ B @ C )
=> ( ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ ( k16_lattice3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(616,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/sandbox/benchmark/theBenchmark.p',t4_relset_1) ).
thf(4110,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)],[616]) ).
thf(252,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) )
& ! [B: $i,C: $i] :
~ ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_4) ).
thf(2316,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) )
& ! [B: $i,C: $i] :
~ ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(287,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v1_setwiseo @ B @ A )
<=> ( r3_binop_1 @ A @ ( k3_binop_1 @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_setwiseo) ).
thf(2448,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v1_setwiseo @ B @ A )
=> ( r3_binop_1 @ A @ ( k3_binop_1 @ A @ B ) @ B ) )
& ( ( r3_binop_1 @ A @ ( k3_binop_1 @ A @ B ) @ B )
=> ( v1_setwiseo @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(872,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ 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 ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k15_lattice3 @ A @ ( a_3_6_lattice3 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_lattice3) ).
thf(5316,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ 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 ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k15_lattice3 @ A @ ( a_3_6_lattice3 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k10_lattice3 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_lattice3) ).
thf(5701,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k10_lattice3 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(680,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k6_lattices @ A )
= ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_lattice2) ).
thf(4440,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k6_lattices @ A )
= ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(520,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/sandbox/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(3693,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)],[520]) ).
thf(1121,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 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k6_filter_2 @ A @ ( k5_filter_2 @ A @ B ) )
= B )
& ( ( k5_filter_2 @ A @ ( k6_filter_2 @ A @ C ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_filter_2) ).
thf(6336,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 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k6_filter_2 @ A @ ( k5_filter_2 @ A @ B ) )
= B )
& ( ( k5_filter_2 @ A @ ( k6_filter_2 @ A @ C ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1134,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattice3 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
thf(6370,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattice3 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_4_quantal1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ E ) )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_quantal1) ).
thf(2146,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_4_quantal1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ E ) )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ E ) )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_4_quantal1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',d17_lattice4) ).
thf(2360,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)],[262]) ).
thf(317,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funcop_1) ).
thf(2575,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
= ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(449,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/sandbox/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(3332,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)],[449]) ).
thf(460,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/sandbox/benchmark/theBenchmark.p',dt_k6_filter_1) ).
thf(3367,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)],[460]) ).
thf(775,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/sandbox/benchmark/theBenchmark.p',t44_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 ) )
=> ! [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)],[775]) ).
thf(770,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v2_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(4870,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v2_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(352,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/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
thf(2740,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)],[352]) ).
thf(1129,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_setwiseo @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_lattice2) ).
thf(6359,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_setwiseo @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(1342,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)],[49]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_zfmisc_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(3121,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_zfmisc_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) ) )
& ( ? [E: $i,F: $i] :
( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B )
& ( D
= ( k4_tarski @ E @ F ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_partfun1) ).
thf(3481,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)],[474]) ).
thf(641,axiom,
? [A: $i] : ( l1_orders_2 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(4247,plain,
? [A: $i] : ( l1_orders_2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(318,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(2578,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(2580,plain,
l1_struct_0 @ sk149,
inference(cnf,[status(esa)],[2578]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',t21_lopclset) ).
thf(1196,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)],[14]) ).
thf(407,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ( v3_realset2 @ A ) )
=> ( v3_realset2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_tex_2) ).
thf(3088,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ( v3_realset2 @ A ) )
=> ( v3_realset2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(785,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/sandbox/benchmark/theBenchmark.p',d9_lattice4) ).
thf(4916,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)],[785]) ).
thf(869,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/sandbox/benchmark/theBenchmark.p',t21_filter_1) ).
thf(5301,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)],[869]) ).
thf(630,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/sandbox/benchmark/theBenchmark.p',t52_filter_1) ).
thf(4198,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)],[630]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',t47_lattice2) ).
thf(2531,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)],[307]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(1254,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)],[29]) ).
thf(743,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_setwiseo @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ A )
= ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice2) ).
thf(4775,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_setwiseo @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ A )
= ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_filter_2 @ A @ B @ C )
=> ( r1_filter_2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
thf(4249,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_filter_2 @ A @ B @ C )
=> ( r1_filter_2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(554,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/sandbox/benchmark/theBenchmark.p',t25_lattice4) ).
thf(3836,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)],[554]) ).
thf(432,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/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(3236,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)],[432]) ).
thf(506,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/sandbox/benchmark/theBenchmark.p',t25_lopclset) ).
thf(3634,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)],[506]) ).
thf(857,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lopclset) ).
thf(5252,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)],[857]) ).
thf(1092,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_2 @ ( k2_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_filter_2) ).
thf(6251,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_2 @ ( k2_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(187,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k1_binop_1 @ A @ B @ C )
= ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).
thf(1914,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k1_binop_1 @ A @ B @ C )
= ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(357,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( ( k2_funct_2 @ A @ B @ E @ D )
= ( k2_setwiseo @ B @ F ) )
=> ( ( k7_setwiseo @ A @ B @ C @ D @ E )
= F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_setwiseo) ).
thf(2763,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( ( k2_funct_2 @ A @ B @ E @ D )
= ( k2_setwiseo @ B @ F ) )
=> ( ( k7_setwiseo @ A @ B @ C @ D @ E )
= F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(896,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/sandbox/benchmark/theBenchmark.p',t16_setwiseo) ).
thf(5486,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)],[896]) ).
thf(692,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/sandbox/benchmark/theBenchmark.p',t9_lattice4) ).
thf(4496,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)],[692]) ).
thf(1004,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/sandbox/benchmark/theBenchmark.p',t85_lattice2) ).
thf(5935,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)],[1004]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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 @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funcop_1) ).
thf(1391,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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 @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(974,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
=> ( r3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice3) ).
thf(5825,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
=> ( r3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1005,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/sandbox/benchmark/theBenchmark.p',d9_filter_1) ).
thf(5938,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)],[1005]) ).
thf(549,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r5_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_2) ).
thf(3809,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r5_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r5_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(237,axiom,
! [A: $i] :
( ( k1_setwiseo @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setwiseo) ).
thf(2173,plain,
! [A: $i] :
( ( k1_setwiseo @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m1_filter_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_1) ).
thf(1366,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)],[57]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_nat_lat @ B @ A ) )
=> ( ( v3_lattices @ ( k24_filter_2 @ A @ B ) )
& ( m2_nat_lat @ ( k24_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k24_filter_2) ).
thf(4760,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_nat_lat @ B @ A ) )
=> ( ( v3_lattices @ ( k24_filter_2 @ A @ B ) )
& ( m2_nat_lat @ ( k24_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(2067,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)],[216]) ).
thf(374,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_ens_1 @ A ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ( B
= ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_ens_1 @ A ) @ ( k1_domain_1 @ A @ A @ D @ E ) @ C ) )
& ( ( E = k1_xboole_0 )
=> ( D = k1_xboole_0 ) )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ D @ E )
& ( m2_relset_1 @ C @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ens_1) ).
thf(2825,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_ens_1 @ A ) )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ( B
= ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_ens_1 @ A ) @ ( k1_domain_1 @ A @ A @ D @ E ) @ C ) )
& ( ( E = k1_xboole_0 )
=> ( D = k1_xboole_0 ) )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ D @ E )
& ( m2_relset_1 @ C @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_lattice3 @ B ) ) )
=> ( ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ C )
<=> ( r3_lattice3 @ B @ ( k5_lattice3 @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattice3) ).
thf(4156,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_lattice3 @ B ) ) )
=> ( ( ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ C )
=> ( r3_lattice3 @ B @ ( k5_lattice3 @ B @ C ) @ A ) )
& ( ( r3_lattice3 @ B @ ( k5_lattice3 @ B @ C ) @ A )
=> ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(566,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(3880,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)],[566]) ).
thf(1107,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) )
=> ( ( k5_lattice3 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).
thf(6291,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) )
=> ( ( k5_lattice3 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(88,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(1517,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1518,plain,
v2_funct_1 @ sk35,
inference(cnf,[status(esa)],[1517]) ).
thf(713,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/sandbox/benchmark/theBenchmark.p',t50_filter_0) ).
thf(4610,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)],[713]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',t29_partfun1) ).
thf(1709,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)],[131]) ).
thf(351,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
=> ( D
= ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funcop_1) ).
thf(2735,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
=> ( D
= ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(519,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(3689,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(819,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/sandbox/benchmark/theBenchmark.p',t47_lattice4) ).
thf(5064,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)],[819]) ).
thf(502,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/sandbox/benchmark/theBenchmark.p',t34_relat_1) ).
thf(3612,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)],[502]) ).
thf(475,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r6_binop_1 @ A @ C @ D )
& ( r6_binop_1 @ B @ E @ F ) )
<=> ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_filter_1) ).
thf(3485,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r6_binop_1 @ A @ C @ D )
& ( r6_binop_1 @ B @ E @ F ) )
=> ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r6_binop_1 @ A @ C @ D )
& ( r6_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(744,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/sandbox/benchmark/theBenchmark.p',t23_lattice4) ).
thf(4778,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)],[744]) ).
thf(1115,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(6315,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(314,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funcop_1) ).
thf(2562,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(455,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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 ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v1_setwiseo @ C @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k1_setwiseo @ B ) @ D )
= ( k3_binop_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_setwiseo) ).
thf(3353,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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 ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v1_setwiseo @ C @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k1_setwiseo @ B ) @ D )
= ( k3_binop_1 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(862,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/sandbox/benchmark/theBenchmark.p',t58_filter_0) ).
thf(5279,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)],[862]) ).
thf(550,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/sandbox/benchmark/theBenchmark.p',t30_subset_1) ).
thf(3820,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)],[550]) ).
thf(911,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 @ ( k20_filter_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k20_filter_2) ).
thf(5553,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 @ ( k20_filter_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_struct_0 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(3204,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_struct_0 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(701,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
thf(4539,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)],[701]) ).
thf(961,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/sandbox/benchmark/theBenchmark.p',d13_filter_0) ).
thf(5765,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)],[961]) ).
thf(429,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 @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_binop_1) ).
thf(3221,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 @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k1_binop_1 @ B @ C @ D )
= D )
& ( ( k1_binop_1 @ B @ D @ C )
= D ) ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(870,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( k8_filter_1 @ A @ B )
= ( g3_lattices @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k7_filter_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u2_lattices @ A ) @ ( u2_lattices @ B ) ) @ ( k7_filter_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_lattices @ A ) @ ( u1_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_filter_1) ).
thf(5306,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( k8_filter_1 @ A @ B )
= ( g3_lattices @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k7_filter_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u2_lattices @ A ) @ ( u2_lattices @ B ) ) @ ( k7_filter_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ ( u1_lattices @ A ) @ ( u1_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(4896,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',t77_funct_2) ).
thf(1430,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)],[73]) ).
thf(439,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/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).
thf(3275,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)],[439]) ).
thf(1033,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_2) ).
thf(6034,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k4_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(1660,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k4_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(42,axiom,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
thf(1298,plain,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(478,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
=> ~ ( ( E != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ E @ F ) @ D )
!= ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_setwiseo) ).
thf(3495,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
=> ~ ( ( E != k1_xboole_0 )
& ( F != k1_xboole_0 )
& ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ E @ F ) @ D )
!= ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(995,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/sandbox/benchmark/theBenchmark.p',t11_filter_0) ).
thf(5910,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)],[995]) ).
thf(721,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v5_orders_2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_orders_2) ).
thf(4654,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v5_orders_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(1860,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)],[175]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',dt_k3_borsuk_1) ).
thf(2682,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)],[341]) ).
thf(166,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funcop_1) ).
thf(1826,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',t48_lattice2) ).
thf(2897,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)],[387]) ).
thf(1025,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_filter_2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_2) ).
thf(6006,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_filter_2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(316,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/sandbox/benchmark/theBenchmark.p',idempotence_k5_setwiseo) ).
thf(2571,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)],[316]) ).
thf(527,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/sandbox/benchmark/theBenchmark.p',t49_lattice2) ).
thf(3713,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)],[527]) ).
thf(1027,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/sandbox/benchmark/theBenchmark.p',t41_filter_1) ).
thf(6010,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)],[1027]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
<=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(1379,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)],[61]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k4_tarski @ D @ E )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(2169,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( k4_tarski @ D @ E )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',t20_lopclset) ).
thf(1144,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)],[3]) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v17_lattices @ B )
| ( v3_realset2 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
| ( r2_hidden @ C @ ( sk2 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[1144]) ).
thf(6385,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ B )
| ~ ( v17_lattices @ B )
| ( v3_realset2 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
| ( r2_hidden @ C @ ( sk2 @ C @ B @ A ) )
| ( ( v10_lattices @ sk1 )
!= ( v10_lattices @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1142,1146]) ).
thf(6386,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( l3_lattices @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( r2_hidden @ B @ ( sk2 @ B @ sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[6385:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(6390,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( l3_lattices @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( r2_hidden @ B @ ( sk2 @ B @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[6386]) ).
thf(1141,plain,
l3_lattices @ sk1,
inference(cnf,[status(esa)],[1139]) ).
thf(1143,plain,
~ ( v3_struct_0 @ sk1 ),
inference(cnf,[status(esa)],[1139]) ).
thf(6395,plain,
! [B: $i,A: $i] :
( $false
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ $true
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( r2_hidden @ B @ ( sk2 @ B @ sk1 @ A ) ) ),
inference(rewrite,[status(thm)],[6390,1141,1143]) ).
thf(6396,plain,
! [B: $i,A: $i] :
( ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( r2_hidden @ B @ ( sk2 @ B @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[6395]) ).
thf(830,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/sandbox/benchmark/theBenchmark.p',t47_filter_0) ).
thf(5127,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)],[830]) ).
thf(1114,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/sandbox/benchmark/theBenchmark.p',d7_lattice4) ).
thf(6310,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)],[1114]) ).
thf(1132,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_filter_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_filter_2) ).
thf(6365,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_filter_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(815,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_lattice4 @ A @ B )
= ( k7_setwiseo @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ B @ ( k7_grcat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_lattice4) ).
thf(5052,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_lattice4 @ A @ B )
= ( k7_setwiseo @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ B @ ( k7_grcat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
thf(1931,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)],[192]) ).
thf(959,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/sandbox/benchmark/theBenchmark.p',t61_filter_1) ).
thf(5746,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)],[959]) ).
thf(684,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/sandbox/benchmark/theBenchmark.p',t44_lattice4) ).
thf(4460,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)],[684]) ).
thf(420,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v2_binop_1 @ C @ A )
& ( v2_binop_1 @ D @ B ) )
<=> ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_1) ).
thf(3180,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( v2_binop_1 @ C @ A )
& ( v2_binop_1 @ D @ B ) )
=> ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( v2_binop_1 @ C @ A )
& ( v2_binop_1 @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(877,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(5338,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)],[877]) ).
thf(1093,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/sandbox/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(6253,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)],[1093]) ).
thf(381,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_ens_1 @ A ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ C @ D )
& ( m2_relset_1 @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_ens_1) ).
thf(2857,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( r2_hidden @ B @ ( k1_ens_1 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ C @ D )
& ( m2_relset_1 @ B @ C @ D ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ C @ D )
& ( m2_relset_1 @ B @ C @ D ) ) )
=> ( r2_hidden @ B @ ( k1_ens_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(747,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/sandbox/benchmark/theBenchmark.p',dt_k8_filter_1) ).
thf(4788,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)],[747]) ).
thf(265,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m2_card_fil @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_card_fil) ).
thf(2373,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m2_card_fil @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(574,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/sandbox/benchmark/theBenchmark.p',t41_filter_0) ).
thf(3919,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)],[574]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(1347,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)],[51]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',t40_funct_2) ).
thf(1572,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)],[101]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(1741,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)],[140]) ).
thf(656,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/sandbox/benchmark/theBenchmark.p',t66_filter_0) ).
thf(4317,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)],[656]) ).
thf(533,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(3734,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(397,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/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(3014,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)],[397]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(2024,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)],[204]) ).
thf(715,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/sandbox/benchmark/theBenchmark.p',d21_lattices) ).
thf(4632,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)],[715]) ).
thf(749,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/sandbox/benchmark/theBenchmark.p',t27_lopclset) ).
thf(4793,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)],[749]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',t1_group_6) ).
thf(1875,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)],[178]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(1232,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)],[23]) ).
thf(797,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/sandbox/benchmark/theBenchmark.p',t65_filter_0) ).
thf(4967,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)],[797]) ).
thf(710,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/sandbox/benchmark/theBenchmark.p',t48_lattices) ).
thf(4595,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)],[710]) ).
thf(1013,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( m2_filter_2 @ ( k13_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_filter_2) ).
thf(5974,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( m2_filter_2 @ ( k13_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).
thf(2451,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)],[288]) ).
thf(1061,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice2) ).
thf(6135,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(1040,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ~ ( v3_struct_0 @ ( k14_lattice3 @ A ) )
& ( v3_lattices @ ( k14_lattice3 @ A ) )
& ( v10_lattices @ ( k14_lattice3 @ A ) )
& ( l3_lattices @ ( k14_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_lattice3) ).
thf(6054,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ~ ( v3_struct_0 @ ( k14_lattice3 @ A ) )
& ( v3_lattices @ ( k14_lattice3 @ A ) )
& ( v10_lattices @ ( k14_lattice3 @ A ) )
& ( l3_lattices @ ( k14_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(936,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5648,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(5649,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(miniscope,[status(thm)],[5648]) ).
thf(5650,plain,
~ ( v1_xboole_0 @ sk461 ),
inference(cnf,[status(esa)],[5649]) ).
thf(36,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r1_tarski @ ( k7_ens_1 @ A @ B @ C ) @ ( k2_ens_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_ens_1) ).
thf(1283,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r1_tarski @ ( k7_ens_1 @ A @ B @ C ) @ ( k2_ens_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(289,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B ) )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D ) )
=> ( ( ( v1_binop_1 @ E @ D )
& ( v2_binop_1 @ E @ D )
& ( v3_binop_1 @ E @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ B @ D )
& ( m2_relset_1 @ G @ B @ D ) )
=> ( ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ B )
=> ( ( k8_funct_2 @ B @ D @ G @ ( k2_binop_1 @ B @ B @ B @ C @ H @ I ) )
= ( k2_binop_1 @ D @ D @ D @ E @ ( k8_funct_2 @ B @ D @ G @ H ) @ ( k8_funct_2 @ B @ D @ G @ I ) ) ) ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( H != k1_xboole_0 )
=> ( ( k8_funct_2 @ B @ D @ G @ ( k7_setwiseo @ A @ B @ C @ H @ F ) )
= ( k7_setwiseo @ A @ D @ E @ H @ ( k7_funct_2 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_setwiseo) ).
thf(2456,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B ) )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D ) )
=> ( ( ( v1_binop_1 @ E @ D )
& ( v2_binop_1 @ E @ D )
& ( v3_binop_1 @ E @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ B @ D )
& ( m2_relset_1 @ G @ B @ D ) )
=> ( ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ B )
=> ( ( k8_funct_2 @ B @ D @ G @ ( k2_binop_1 @ B @ B @ B @ C @ H @ I ) )
= ( k2_binop_1 @ D @ D @ D @ E @ ( k8_funct_2 @ B @ D @ G @ H ) @ ( k8_funct_2 @ B @ D @ G @ I ) ) ) ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( H != k1_xboole_0 )
=> ( ( k8_funct_2 @ B @ D @ G @ ( k7_setwiseo @ A @ B @ C @ H @ F ) )
= ( k7_setwiseo @ A @ D @ E @ H @ ( k7_funct_2 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funcop_1) ).
thf(2007,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_subset_1 @ D @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v17_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice3) ).
thf(5682,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v17_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(1049,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/sandbox/benchmark/theBenchmark.p',t65_lattice2) ).
thf(6081,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)],[1049]) ).
thf(672,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 ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_filter_2 @ C @ A )
=> ( m1_filter_2 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_filter_2) ).
thf(4411,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 ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_filter_2 @ C @ A )
=> ( m1_filter_2 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1095,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/sandbox/benchmark/theBenchmark.p',t54_filter_1) ).
thf(6259,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)],[1095]) ).
thf(800,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r3_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_2) ).
thf(4988,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r3_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r3_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_partfun1) ).
thf(2616,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)],[326]) ).
thf(670,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
& ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) )
=> ( v10_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_lattice2) ).
thf(4396,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
& ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) )
=> ( v10_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relat_1) ).
thf(1465,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)],[75]) ).
thf(586,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/sandbox/benchmark/theBenchmark.p',t17_filter_1) ).
thf(3966,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)],[586]) ).
thf(254,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_lattice3 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ B )
=> ( r1_orders_2 @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
thf(2324,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ B )
=> ( r1_orders_2 @ A @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ B )
=> ( r1_orders_2 @ A @ D @ C ) ) )
=> ( r2_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(1714,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 ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ E ) )
& ! [F: $i,G: $i] :
( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_partfun1) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
= ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ E ) )
& ! [F: $i,G: $i] :
( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D ) )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(781,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_lattice2) ).
thf(4903,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_4_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_4_lattice3) ).
thf(4443,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_4_lattice3 @ 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_4_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(707,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(4578,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)],[707]) ).
thf(404,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_setwiseo @ A ) )
& ( m1_subset_1 @ ( k1_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setwiseo) ).
thf(3075,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)],[404]) ).
thf(926,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v3_lattice3 @ A )
=> ( ( v1_lattice3 @ A )
& ( v2_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_lattice3) ).
thf(5597,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_orders_2 @ A ) )
=> ( ( v3_lattice3 @ A )
=> ( ( v1_lattice3 @ A )
& ( v2_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(595,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_lattice3 @ A )
<=> ( v2_lattice3 @ ( k7_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice3) ).
thf(4018,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v1_lattice3 @ A )
=> ( v2_lattice3 @ ( k7_lattice3 @ A ) ) )
& ( ( v2_lattice3 @ ( k7_lattice3 @ A ) )
=> ( v1_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(220,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r6_binop_1 @ A @ C @ B )
<=> ( r4_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_binop_1) ).
thf(2090,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r6_binop_1 @ A @ C @ B )
=> ( r4_binop_1 @ A @ C @ B ) )
& ( ( r4_binop_1 @ A @ C @ B )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(768,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/sandbox/benchmark/theBenchmark.p',d1_filter_0) ).
thf(4857,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)],[768]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relat_1) ).
thf(4258,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)],[644]) ).
thf(386,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/sandbox/benchmark/theBenchmark.p',dt_k9_lopclset) ).
thf(2893,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)],[386]) ).
thf(116,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(1632,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)],[116]) ).
thf(758,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/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(4820,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)],[758]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ k1_xboole_0 @ B )
=> ( ( k8_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_mssubfam) ).
thf(2650,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ k1_xboole_0 @ B )
=> ( ( k8_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(484,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_binop_1) ).
thf(3527,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ D @ C )
= D ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1082,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/sandbox/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(6189,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)],[1082]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r8_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r8_relat_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_orders_1) ).
thf(3525,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r8_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r8_relat_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(226,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_orders_1) ).
thf(2122,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(471,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v9_monoid_0 @ B @ A )
<=> ( ( v1_setwiseo @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k3_binop_1 @ A @ B ) )
=> ( ( C = D )
& ( D
= ( k3_binop_1 @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_monoid_0) ).
thf(3438,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v9_monoid_0 @ B @ A )
=> ( ( v1_setwiseo @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k3_binop_1 @ A @ B ) )
=> ( ( C = D )
& ( D
= ( k3_binop_1 @ A @ B ) ) ) ) ) ) ) )
& ( ( ( v1_setwiseo @ B @ A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k3_binop_1 @ A @ B ) )
=> ( ( C = D )
& ( D
= ( k3_binop_1 @ A @ B ) ) ) ) ) ) )
=> ( v9_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1081,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/sandbox/benchmark/theBenchmark.p',t89_filter_0) ).
thf(6187,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)],[1081]) ).
thf(756,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/sandbox/benchmark/theBenchmark.p',t21_lattice4) ).
thf(4815,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)],[756]) ).
thf(1076,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattice2) ).
thf(6176,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(970,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/sandbox/benchmark/theBenchmark.p',d16_lattice4) ).
thf(5804,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)],[970]) ).
thf(197,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1978,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(5541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(810,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/sandbox/benchmark/theBenchmark.p',t39_lattices) ).
thf(5032,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)],[810]) ).
thf(492,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(3567,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(3569,plain,
v1_relat_1 @ sk267,
inference(cnf,[status(esa)],[3567]) ).
thf(1017,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/sandbox/benchmark/theBenchmark.p',t53_filter_1) ).
thf(5985,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)],[1017]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r3_lattice3 @ B @ C @ A )
<=> ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice3) ).
thf(3923,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r3_lattice3 @ B @ C @ A )
=> ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) ) )
& ( ( r1_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) )
=> ( r3_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(832,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattice2) ).
thf(5135,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)],[832]) ).
thf(445,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) ) )
=> ( ( B
= ( k9_setwiseo @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ( ( k2_binop_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ B @ C @ D )
= ( k5_setwiseo @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_setwiseo) ).
thf(3300,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) ) )
=> ( ( ( B
= ( k9_setwiseo @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ( ( k2_binop_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ B @ C @ D )
= ( k5_setwiseo @ A @ C @ D ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ( ( k2_binop_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ B @ C @ D )
= ( k5_setwiseo @ A @ C @ D ) ) ) )
=> ( B
= ( k9_setwiseo @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(618,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/sandbox/benchmark/theBenchmark.p',t42_filter_0) ).
thf(4115,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)],[618]) ).
thf(728,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/sandbox/benchmark/theBenchmark.p',t69_filter_0) ).
thf(4686,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)],[728]) ).
thf(895,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/sandbox/benchmark/theBenchmark.p',t9_filter_0) ).
thf(5457,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)],[895]) ).
thf(746,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/sandbox/benchmark/theBenchmark.p',t52_lattices) ).
thf(4783,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)],[746]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(1843,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)],[170]) ).
thf(734,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(4718,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(602,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( m1_subset_1 @ ( k8_filter_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_2) ).
thf(4055,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( m1_subset_1 @ ( k8_filter_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(5379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(18,axiom,
! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) ) @ ( k9_setwiseo @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_setwiseo) ).
thf(1215,plain,
! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) ) @ ( k9_setwiseo @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(240,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ C )
& ( m2_relset_1 @ D @ B @ C ) )
=> ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
=> ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k1_domain_1 @ A @ A @ B @ C ) @ D ) @ ( k7_ens_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_ens_1) ).
thf(2190,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ C )
& ( m2_relset_1 @ D @ B @ C ) )
=> ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
=> ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k1_domain_1 @ A @ A @ B @ C ) @ D ) @ ( k7_ens_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(400,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v8_monoid_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
| ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_monoid_0) ).
thf(3036,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v8_monoid_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
| ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) ) )
=> ( D = E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
| ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) ) )
=> ( D = E ) ) ) ) )
=> ( v8_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ B )
& ( m1_subset_1 @ D @ B ) )
=> ( ( r2_hidden @ A @ ( a_3_0_ens_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
& ( A
= ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
& ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) @ ( k2_ens_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_ens_1) ).
thf(2809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ B )
& ( m1_subset_1 @ D @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_ens_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
& ( A
= ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
& ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) @ ( k2_ens_1 @ B ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
& ( A
= ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
& ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) @ ( k2_ens_1 @ B ) ) )
=> ( r2_hidden @ A @ ( a_3_0_ens_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(2103,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)],[223]) ).
thf(1069,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/sandbox/benchmark/theBenchmark.p',t1_filter_1) ).
thf(6156,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)],[1069]) ).
thf(491,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 ) )
=> ( ( v2_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_binop_1) ).
thf(3559,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 ) )
=> ( ( ( v2_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
= ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) )
=> ( v2_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(633,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(4211,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(916,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_filter_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_1) ).
thf(5572,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_filter_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(5059,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)],[817]) ).
thf(486,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 ) )
=> ( ( v1_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_binop_1) ).
thf(3537,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 ) )
=> ( ( ( v1_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= ( k1_binop_1 @ B @ D @ C ) ) ) )
=> ( v1_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(191,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 @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
& ( r2_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_binop_1) ).
thf(1928,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 @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
& ( r2_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) )
=> ( v2_funct_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_partfun1) ).
thf(1886,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) )
=> ( v2_funct_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(279,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(2424,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1124,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattice3 @ A @ B ) @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(6347,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattice3 @ A @ B ) @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(65,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r4_lattice3 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattice3) ).
thf(1394,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r4_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) )
=> ( r4_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(867,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_orders_1) ).
thf(5296,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) )
& ( ( r2_hidden @ A @ ( k1_orders_1 @ B ) )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(516,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/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(3676,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)],[516]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k3_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k3_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(2137,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k3_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k3_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(874,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/sandbox/benchmark/theBenchmark.p',t48_lattice4) ).
thf(5321,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)],[874]) ).
thf(653,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 )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_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 ) )
=> ( ( ( C = E )
& ( D = F )
& ( r2_lattices @ A @ C @ D ) )
=> ( r2_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_filter_2) ).
thf(4307,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 )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_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 ) )
=> ( ( ( C = E )
& ( D = F )
& ( r2_lattices @ A @ C @ D ) )
=> ( r2_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(787,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/sandbox/benchmark/theBenchmark.p',t10_filter_0) ).
thf(4924,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)],[787]) ).
thf(840,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/sandbox/benchmark/theBenchmark.p',t31_filter_0) ).
thf(5169,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)],[840]) ).
thf(50,axiom,
! [A: $i] : ( v3_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_setwiseo) ).
thf(1345,plain,
! [A: $i] : ( v3_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(247,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( k15_lattice3 @ A @ B )
= ( k15_lattice3 @ A @ ( a_2_5_lattice3 @ A @ B ) ) )
& ( ( k16_lattice3 @ A @ B )
= ( k16_lattice3 @ A @ ( a_2_6_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_lattice3) ).
thf(2286,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( k15_lattice3 @ A @ B )
= ( k15_lattice3 @ A @ ( a_2_5_lattice3 @ A @ B ) ) )
& ( ( k16_lattice3 @ A @ B )
= ( k16_lattice3 @ A @ ( a_2_6_lattice3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
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 ) )
=> ( ( ~ ( 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/sandbox/benchmark/theBenchmark.p',t45_filter_1) ).
thf(4038,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)],[599]) ).
thf(233,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(2154,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1053,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/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_1) ).
thf(6103,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)],[1053]) ).
thf(89,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 @ ( k6_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setwiseo) ).
thf(1521,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 @ ( k6_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_partfun1) ).
thf(3492,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(242,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2205,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(421,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(3184,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(320,axiom,
! [A: $i] :
( ( v3_lattices @ ( k1_lattice3 @ A ) )
& ( l3_lattices @ ( k1_lattice3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
thf(2586,plain,
! [A: $i] :
( ( v3_lattices @ ( k1_lattice3 @ A ) )
& ( l3_lattices @ ( k1_lattice3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(606,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/sandbox/benchmark/theBenchmark.p',t35_lopclset) ).
thf(4082,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)],[606]) ).
thf(689,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/sandbox/benchmark/theBenchmark.p',dt_k2_setwiseo) ).
thf(4483,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)],[689]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(1564,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)],[98]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(1604,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(2011,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)],[201]) ).
thf(472,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/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(3450,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)],[472]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( B
= ( k6_relat_1 @ A ) )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(2910,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( B
= ( k6_relat_1 @ A ) )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) )
& ( ( ( r2_hidden @ C @ A )
& ( C = D ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ A )
& ( C = D ) ) )
& ( ( ( r2_hidden @ C @ A )
& ( C = D ) )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( B
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(6015,plain,
~ ( v3_struct_0 @ sk492 ),
inference(cnf,[status(esa)],[6014]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ C )
& ( m1_relset_1 @ E @ A @ C ) )
=> ( ( v1_funct_1 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_funct_3) ).
thf(1153,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ C )
& ( m1_relset_1 @ E @ A @ C ) )
=> ( ( v1_funct_1 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( m2_relset_1 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1011,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 ) ) )
=> ( ( k10_filter_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_filter_1) ).
thf(5968,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 ) ) )
=> ( ( k10_filter_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(865,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/sandbox/benchmark/theBenchmark.p',t44_lattice2) ).
thf(5291,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)],[865]) ).
thf(210,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v3_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_binop_1) ).
thf(2047,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v3_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
= C ) )
=> ( v3_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(665,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/sandbox/benchmark/theBenchmark.p',t38_filter_0) ).
thf(4370,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)],[665]) ).
thf(330,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/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(2641,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)],[330]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',t113_funct_2) ).
thf(1736,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)],[139]) ).
thf(517,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r1_relat_2 @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
thf(3679,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r1_relat_2 @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) )
=> ( r1_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(767,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/sandbox/benchmark/theBenchmark.p',t76_lattice2) ).
thf(4853,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)],[767]) ).
thf(430,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/sandbox/benchmark/theBenchmark.p',d2_lattice4) ).
thf(3229,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)],[430]) ).
thf(1030,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/sandbox/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(6020,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)],[1030]) ).
thf(1079,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/sandbox/benchmark/theBenchmark.p',t7_filter_0) ).
thf(6183,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)],[1079]) ).
thf(708,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/sandbox/benchmark/theBenchmark.p',t72_filter_0) ).
thf(4589,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)],[708]) ).
thf(128,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 ) )
=> ( ( k10_setwiseo @ A @ B @ D @ C )
= ( k3_tarski @ ( k8_setwiseo @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_setwiseo) ).
thf(1691,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 ) )
=> ( ( k10_setwiseo @ A @ B @ D @ C )
= ( k3_tarski @ ( k8_setwiseo @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1109,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A ) )
=> ( ( k15_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
thf(6296,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A ) )
=> ( ( k15_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(688,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( a_2_1_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_domain_1) ).
thf(4480,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( a_2_1_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(698,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/sandbox/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).
thf(4531,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)],[698]) ).
thf(804,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/sandbox/benchmark/theBenchmark.p',t14_filter_0) ).
thf(5017,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)],[804]) ).
thf(1043,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_lattice3 @ A )
= ( k9_filter_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
thf(6064,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_lattice3 @ A )
= ( k9_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(839,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/sandbox/benchmark/theBenchmark.p',t55_lattice2) ).
thf(5167,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)],[839]) ).
thf(77,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r5_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d19_binop_1) ).
thf(1470,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r5_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) )
=> ( r5_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(2093,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)],[221]) ).
thf(1113,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 ) ) )
=> ( ( k7_filter_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_filter_2) ).
thf(6307,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 ) ) )
=> ( ( k7_filter_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(2307,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)],[250]) ).
thf(149,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v8_monoid_0 @ B @ A )
<=> ( ( v6_monoid_0 @ B @ A )
& ( v7_monoid_0 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_monoid_0) ).
thf(1768,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v8_monoid_0 @ B @ A )
=> ( ( v6_monoid_0 @ B @ A )
& ( v7_monoid_0 @ B @ A ) ) )
& ( ( ( v6_monoid_0 @ B @ A )
& ( v7_monoid_0 @ B @ A ) )
=> ( v8_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(2382,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)],[269]) ).
thf(214,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 @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
& ( r3_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_binop_1) ).
thf(2061,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 @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
& ( r3_binop_1 @ A @ D @ B ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(4999,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
& ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_realset1) ).
thf(2673,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
& ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(534,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k15_lattice3 @ A @ ( a_2_3_lattice3 @ A @ B ) ) )
& ( B
= ( k16_lattice3 @ A @ ( a_2_4_lattice3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_lattice3) ).
thf(3735,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k15_lattice3 @ A @ ( a_2_3_lattice3 @ A @ B ) ) )
& ( B
= ( k16_lattice3 @ A @ ( a_2_4_lattice3 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',t20_lattice4) ).
thf(2409,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)],[274]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m1_relset_1 @ E @ A @ B ) )
=> ( m1_subset_1 @ ( k7_setwiseo @ A @ B @ C @ D @ E ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setwiseo) ).
thf(1723,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m1_relset_1 @ E @ A @ B ) )
=> ( m1_subset_1 @ ( k7_setwiseo @ A @ B @ C @ D @ E ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ ( k5_finsub_1 @ C ) )
& ( m2_relset_1 @ F @ B @ ( k5_finsub_1 @ C ) ) )
=> ( ( k10_setwiseo @ B @ C @ ( k8_setwiseo @ A @ B @ E @ D ) @ F )
= ( k10_setwiseo @ A @ C @ D @ ( k7_funct_2 @ A @ B @ ( k5_finsub_1 @ C ) @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_setwiseo) ).
thf(1223,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ ( k5_finsub_1 @ C ) )
& ( m2_relset_1 @ F @ B @ ( k5_finsub_1 @ C ) ) )
=> ( ( k10_setwiseo @ B @ C @ ( k8_setwiseo @ A @ B @ E @ D ) @ F )
= ( k10_setwiseo @ A @ C @ D @ ( k7_funct_2 @ A @ B @ ( k5_finsub_1 @ C ) @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(955,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_filter_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_1) ).
thf(5734,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_filter_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1519,plain,
v1_funct_1 @ sk35,
inference(cnf,[status(esa)],[1517]) ).
thf(53,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_orders_2 @ A @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_orders_2) ).
thf(1355,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_orders_2 @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(19,axiom,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(1217,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(393,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( r2_hidden @ k1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_card_fil) ).
thf(2937,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( r2_hidden @ k1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(691,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r3_lattice3 @ A @ B @ C ) )
=> ( ( k16_lattice3 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_lattice3) ).
thf(4493,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r3_lattice3 @ A @ B @ C ) )
=> ( ( k16_lattice3 @ A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1055,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_nat_lat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_nat_lat) ).
thf(6107,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_nat_lat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',t27_relset_1) ).
thf(2528,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)],[306]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(1238,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)],[25]) ).
thf(1000,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/sandbox/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(5924,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)],[1000]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A ) )
=> ( m1_filter_2 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_filter_2) ).
thf(6079,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A ) )
=> ( m1_filter_2 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(2428,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)],[281]) ).
thf(369,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r2_binop_1 @ A @ C @ E )
& ( r2_binop_1 @ B @ D @ F ) )
<=> ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_1) ).
thf(2805,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r2_binop_1 @ A @ C @ E )
& ( r2_binop_1 @ B @ D @ F ) )
=> ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
& ( ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
=> ( ( r2_binop_1 @ A @ C @ E )
& ( r2_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(588,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/sandbox/benchmark/theBenchmark.p',d20_lattices) ).
thf(3972,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)],[588]) ).
thf(967,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/sandbox/benchmark/theBenchmark.p',t71_lattice2) ).
thf(5794,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)],[967]) ).
thf(678,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k4_card_fil @ A ) )
& ( m1_subset_1 @ ( k4_card_fil @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_card_fil) ).
thf(4434,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k4_card_fil @ A ) )
& ( m1_subset_1 @ ( k4_card_fil @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(773,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/sandbox/benchmark/theBenchmark.p',t32_lattices) ).
thf(4878,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)],[773]) ).
thf(919,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/sandbox/benchmark/theBenchmark.p',t59_filter_1) ).
thf(5579,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)],[919]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(1570,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)],[100]) ).
thf(1174,plain,
v1_funct_1 @ sk3,
inference(cnf,[status(esa)],[1171]) ).
thf(878,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( C = D )
=> ( ( ( r3_lattice3 @ A @ C @ E )
=> ( r3_lattice3 @ B @ D @ E ) )
& ( ( r3_lattice3 @ B @ D @ E )
=> ( r3_lattice3 @ A @ C @ E ) )
& ( ( r4_lattice3 @ A @ C @ E )
=> ( r4_lattice3 @ B @ D @ E ) )
& ( ( r4_lattice3 @ B @ D @ E )
=> ( r4_lattice3 @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_quantal1) ).
thf(5349,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( C = D )
=> ( ( ( r3_lattice3 @ A @ C @ E )
=> ( r3_lattice3 @ B @ D @ E ) )
& ( ( r3_lattice3 @ B @ D @ E )
=> ( r3_lattice3 @ A @ C @ E ) )
& ( ( r4_lattice3 @ A @ C @ E )
=> ( r4_lattice3 @ B @ D @ E ) )
& ( ( r4_lattice3 @ B @ D @ E )
=> ( r4_lattice3 @ A @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(894,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/sandbox/benchmark/theBenchmark.p',t33_lattice4) ).
thf(5455,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)],[894]) ).
thf(143,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k7_ens_1 @ A @ B @ C )
= ( a_3_0_ens_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ens_1) ).
thf(1751,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k7_ens_1 @ A @ B @ C )
= ( a_3_0_ens_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(952,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/sandbox/benchmark/theBenchmark.p',d1_lattice4) ).
thf(5719,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)],[952]) ).
thf(80,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
=> ( ( k10_setwiseo @ A @ B @ C @ D )
= ( k7_setwiseo @ A @ ( k5_finsub_1 @ B ) @ ( k9_setwiseo @ B ) @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_setwiseo) ).
thf(1487,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
=> ( ( k10_setwiseo @ A @ B @ C @ D )
= ( k7_setwiseo @ A @ ( k5_finsub_1 @ B ) @ ( k9_setwiseo @ B ) @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(536,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funcop_1) ).
thf(3742,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(610,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/sandbox/benchmark/theBenchmark.p',t40_lattices) ).
thf(4091,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)],[610]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(2032,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m1_relset_1 @ D @ A @ B )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ C )
& ( m1_relset_1 @ E @ B @ C ) )
=> ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
& ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(989,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 @ A @ B @ C )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ C ) @ ( k5_filter_2 @ A @ B ) ) )
& ( ( r3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ C ) @ ( k5_filter_2 @ A @ B ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
=> ( r3_lattices @ A @ ( k6_filter_2 @ A @ E ) @ ( k6_filter_2 @ A @ D ) ) )
& ( ( r3_lattices @ A @ ( k6_filter_2 @ A @ E ) @ ( k6_filter_2 @ A @ D ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_2) ).
thf(5893,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 @ A @ B @ C )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ C ) @ ( k5_filter_2 @ A @ B ) ) )
& ( ( r3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ C ) @ ( k5_filter_2 @ A @ B ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
=> ( r3_lattices @ A @ ( k6_filter_2 @ A @ E ) @ ( k6_filter_2 @ A @ D ) ) )
& ( ( r3_lattices @ A @ ( k6_filter_2 @ A @ E ) @ ( k6_filter_2 @ A @ D ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1077,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/sandbox/benchmark/theBenchmark.p',t34_filter_1) ).
thf(6178,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)],[1077]) ).
thf(228,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 @ A )
=> ( ( k10_setwiseo @ A @ B @ ( k3_setwiseo @ A @ D @ E ) @ C )
= ( k5_setwiseo @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_setwiseo) ).
thf(2132,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 @ A )
=> ( ( k10_setwiseo @ A @ B @ ( k3_setwiseo @ A @ D @ E ) @ C )
= ( k5_setwiseo @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(762,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/sandbox/benchmark/theBenchmark.p',t78_filter_0) ).
thf(4836,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)],[762]) ).
thf(925,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/sandbox/benchmark/theBenchmark.p',t29_subset_1) ).
thf(5594,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)],[925]) ).
thf(427,axiom,
! [A: $i] :
( ( v1_funct_1 @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).
thf(3207,plain,
! [A: $i] :
( ( ( v1_funct_1 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) )
=> ( v1_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(4021,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)],[596]) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).
thf(2445,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)],[286]) ).
thf(883,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/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(5391,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)],[883]) ).
thf(189,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( r2_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_binop_1) ).
thf(1920,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( r2_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
= D ) )
=> ( r2_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(5690,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ~ ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_realset1) ).
thf(2872,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(906,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( ( v5_orders_2 @ B @ A )
& ( 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 @ C @ B )
=> ( ( v5_orders_2 @ C @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_orders_2) ).
thf(5534,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( ( v5_orders_2 @ B @ A )
& ( 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 @ C @ B )
=> ( ( v5_orders_2 @ C @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(812,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/sandbox/benchmark/theBenchmark.p',t57_filter_1) ).
thf(5038,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)],[812]) ).
thf(914,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/sandbox/benchmark/theBenchmark.p',t30_filter_0) ).
thf(5566,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)],[914]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',t1_realset1) ).
thf(1291,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)],[39]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( k4_tarski @ F @ G ) )
& ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
& ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(2769,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( k4_tarski @ F @ G ) )
& ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
& ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(2653,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)],[333]) ).
thf(590,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/sandbox/benchmark/theBenchmark.p',t53_filter_0) ).
thf(3980,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)],[590]) ).
thf(504,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 @ A )
& ( r3_binop_1 @ A @ C @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( C
= ( k3_binop_1 @ A @ B ) )
<=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_binop_1) ).
thf(3618,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 @ A )
& ( r3_binop_1 @ A @ C @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( C
= ( k3_binop_1 @ A @ B ) )
=> ( r3_binop_1 @ A @ C @ B ) )
& ( ( r3_binop_1 @ A @ C @ B )
=> ( C
= ( k3_binop_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(601,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/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(4053,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)],[601]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k8_lattice3 @ A @ B ) @ ( u1_struct_0 @ ( k7_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_lattice3) ).
thf(2433,plain,
! [A: $i,B: $i] :
( ( ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k8_lattice3 @ A @ B ) @ ( u1_struct_0 @ ( k7_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(294,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(2477,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(315,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 ) )
=> ( ( v3_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_binop_1) ).
thf(2565,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 ) )
=> ( ( ( v3_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k1_binop_1 @ B @ C @ C )
= C ) )
=> ( v3_binop_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(424,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funcop_1) ).
thf(3198,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(447,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( C
= ( k15_lattice3 @ A @ B ) )
<=> ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattice3) ).
thf(3314,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( C
= ( k15_lattice3 @ A @ B ) )
=> ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) )
& ( ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) )
=> ( C
= ( k15_lattice3 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(372,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/sandbox/benchmark/theBenchmark.p',t27_lattice4) ).
thf(2820,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)],[372]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
<=> ~ ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(4947,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
=> ~ ( r2_hidden @ E @ D ) )
& ( ~ ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
=> ~ ( r2_hidden @ E @ D ) )
& ( ~ ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(3499,plain,
v1_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3498]) ).
thf(490,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k3_setwiseo @ B @ E @ F ) @ D )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_setwiseo) ).
thf(3556,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k3_setwiseo @ B @ E @ F ) @ D )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_setwiseo) ).
thf(1296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(565,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/sandbox/benchmark/theBenchmark.p',t50_lattice4) ).
thf(3877,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)],[565]) ).
thf(1018,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice4) ).
thf(5988,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)],[1018]) ).
thf(568,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/sandbox/benchmark/theBenchmark.p',t38_lattice4) ).
thf(3894,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)],[568]) ).
thf(965,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(5779,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)],[965]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_funcop_1) ).
thf(1819,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m1_relset_1 @ E @ B @ A ) )
=> ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
= C )
& ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_2) ).
thf(1836,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
= C )
& ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(5113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
| ( ~ ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) )
=> ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1051,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_nat_lat @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_nat_lat) ).
thf(6096,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_nat_lat @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(793,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/sandbox/benchmark/theBenchmark.p',t44_lattices) ).
thf(4942,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)],[793]) ).
thf(1073,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/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_1) ).
thf(6168,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)],[1073]) ).
thf(577,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/sandbox/benchmark/theBenchmark.p',t53_lattices) ).
thf(3926,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)],[577]) ).
thf(1097,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/sandbox/benchmark/theBenchmark.p',t50_filter_1) ).
thf(6267,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)],[1097]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',t32_partfun1) ).
thf(2344,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)],[258]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',fc2_lopclset) ).
thf(2492,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)],[298]) ).
thf(614,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/sandbox/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(4104,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)],[614]) ).
thf(579,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(3931,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',dt_k10_setwiseo) ).
thf(1910,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)],[185]) ).
thf(532,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_domain_1) ).
thf(3731,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(428,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B ) )
=> ! [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 @ ( k5_finsub_1 @ A ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
=> ( ( ( k2_funct_2 @ A @ B @ D @ F )
= ( k2_funct_2 @ A @ B @ E @ G ) )
=> ( ( F = k1_xboole_0 )
| ( ( k7_setwiseo @ A @ B @ C @ F @ D )
= ( k7_setwiseo @ A @ B @ C @ G @ E ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_setwiseo) ).
thf(3218,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B ) )
=> ! [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 @ ( k5_finsub_1 @ A ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
=> ( ( ( k2_funct_2 @ A @ B @ D @ F )
= ( k2_funct_2 @ A @ B @ E @ G ) )
=> ( ( F = k1_xboole_0 )
| ( ( k7_setwiseo @ A @ B @ C @ F @ D )
= ( k7_setwiseo @ A @ B @ C @ G @ E ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(1425,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)],[72]) ).
thf(524,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funcop_1) ).
thf(3704,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(481,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/sandbox/benchmark/theBenchmark.p',dt_k8_lopclset) ).
thf(3518,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)],[481]) ).
thf(349,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/sandbox/benchmark/theBenchmark.p',d1_filter_1) ).
thf(2726,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)],[349]) ).
thf(789,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/sandbox/benchmark/theBenchmark.p',t16_filter_1) ).
thf(4930,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)],[789]) ).
thf(898,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/sandbox/benchmark/theBenchmark.p',t28_lattice4) ).
thf(5497,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)],[898]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice3 @ A ) ) )
=> ( ( k7_lattices @ ( k1_lattice3 @ A ) @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_lattice3) ).
thf(1360,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice3 @ A ) ) )
=> ( ( k7_lattices @ ( k1_lattice3 @ A ) @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k2_relat_1 @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_partfun1) ).
thf(1350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ ( k2_relat_1 @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
& ( C
= ( k1_funct_1 @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(843,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/sandbox/benchmark/theBenchmark.p',t70_filter_0) ).
thf(5189,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)],[843]) ).
thf(249,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( ( k5_lattices @ A )
= ( k15_lattice3 @ A @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice3) ).
thf(2300,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( ( k5_lattices @ A )
= ( k15_lattice3 @ A @ k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(544,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k5_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relset_1) ).
thf(3784,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k5_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(993,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A )
& ( m2_filter_2 @ C @ A ) )
=> ( ( k21_filter_2 @ A @ B @ C )
= ( k20_filter_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k21_filter_2) ).
thf(5904,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A )
& ( m2_filter_2 @ C @ A ) )
=> ( ( k21_filter_2 @ A @ B @ C )
= ( k20_filter_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v5_monoid_0 @ B @ A )
<=> ( ( v3_monoid_0 @ B @ A )
& ( v4_monoid_0 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_monoid_0) ).
thf(1234,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v5_monoid_0 @ B @ A )
=> ( ( v3_monoid_0 @ B @ A )
& ( v4_monoid_0 @ B @ A ) ) )
& ( ( ( v3_monoid_0 @ B @ A )
& ( v4_monoid_0 @ B @ A ) )
=> ( v5_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',t29_lopclset) ).
thf(1541,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)],[94]) ).
thf(552,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/sandbox/benchmark/theBenchmark.p',t87_filter_0) ).
thf(3831,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)],[552]) ).
thf(929,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/sandbox/benchmark/theBenchmark.p',t36_lattice4) ).
thf(5609,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)],[929]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(1762,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_relset_1 @ E @ A @ B )
& ( m1_relset_1 @ F @ C @ D ) )
=> ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(222,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] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( k2_binop_1 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ C ) @ ( u1_lattices @ C ) @ E @ ( k2_lattice2 @ A @ C @ B @ D ) )
= ( k2_lattice2 @ A @ C @ B @ ( k8_funcop_1 @ ( u1_struct_0 @ C ) @ A @ ( u1_lattices @ C ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_lattice2) ).
thf(2100,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] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( k2_binop_1 @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ C ) @ ( u1_struct_0 @ C ) @ ( u1_lattices @ C ) @ E @ ( k2_lattice2 @ A @ C @ B @ D ) )
= ( k2_lattice2 @ A @ C @ B @ ( k8_funcop_1 @ ( u1_struct_0 @ C ) @ A @ ( u1_lattices @ C ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funcop_1) ).
thf(1772,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(825,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/sandbox/benchmark/theBenchmark.p',t58_filter_1) ).
thf(5098,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)],[825]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funcop_1) ).
thf(1259,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ A )
& ( m2_relset_1 @ D @ A @ A ) )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(92,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(1534,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(802,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/sandbox/benchmark/theBenchmark.p',t30_lattice4) ).
thf(5006,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)],[802]) ).
thf(798,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/sandbox/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(4974,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)],[798]) ).
thf(562,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/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(3862,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)],[562]) ).
thf(918,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/sandbox/benchmark/theBenchmark.p',t31_lattice4) ).
thf(5577,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)],[918]) ).
thf(968,axiom,
? [A: $i] : ( l2_quantal1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_quantal1) ).
thf(5798,plain,
? [A: $i] : ( l2_quantal1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(344,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( a_2_2_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_domain_1) ).
thf(2692,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( a_2_2_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(84,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 ) )
=> ( m1_subset_1 @ ( k3_binop_1 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(1498,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 ) )
=> ( m1_subset_1 @ ( k3_binop_1 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',t7_funct_2) ).
thf(1587,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)],[105]) ).
thf(979,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(5847,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)],[979]) ).
thf(593,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(4012,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(573,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/sandbox/benchmark/theBenchmark.p',t13_filter_0) ).
thf(3916,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)],[573]) ).
thf(581,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 ) ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) @ ( k5_filter_2 @ A @ C ) ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) @ ( k5_filter_2 @ A @ C ) ) )
& ( ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E )
= ( k3_lattices @ A @ ( k6_filter_2 @ A @ D ) @ ( k6_filter_2 @ A @ E ) ) )
& ( ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
= ( k4_lattices @ A @ ( k6_filter_2 @ A @ D ) @ ( k6_filter_2 @ A @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_filter_2) ).
thf(3941,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 ) ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) @ ( k5_filter_2 @ A @ C ) ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) @ ( k5_filter_2 @ A @ C ) ) )
& ( ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E )
= ( k3_lattices @ A @ ( k6_filter_2 @ A @ D ) @ ( k6_filter_2 @ A @ E ) ) )
& ( ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
= ( k4_lattices @ A @ ( k6_filter_2 @ A @ D ) @ ( k6_filter_2 @ A @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1087,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/sandbox/benchmark/theBenchmark.p',t40_filter_1) ).
thf(6218,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)],[1087]) ).
thf(780,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ 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 )
= ( k15_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k16_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattice3) ).
thf(4898,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ 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 )
= ( k15_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k16_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(1493,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)],[82]) ).
thf(6,axiom,
! [A: $i] : ( v1_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_setwiseo) ).
thf(1160,plain,
! [A: $i] : ( v1_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(1942,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)],[194]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(1182,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)],[11]) ).
thf(628,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 ) ) ) )
=> ( ( m2_filter_2 @ 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 @ ( 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 )
& ( r3_lattices @ A @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_2) ).
thf(4167,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 ) ) ) )
=> ( ( ( m2_filter_2 @ 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 @ ( 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 )
& ( r3_lattices @ A @ D @ C ) )
=> ( 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 @ ( 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 )
& ( r3_lattices @ A @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) )
=> ( m2_filter_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(1112,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/sandbox/benchmark/theBenchmark.p',d3_filter_0) ).
thf(6304,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)],[1112]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( ( v3_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( B
= ( k1_lattice3 @ A ) )
<=> ( ( ( u1_struct_0 @ 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 ) )
=> ( ( ( k1_binop_1 @ ( u2_lattices @ B ) @ C @ D )
= ( k4_subset_1 @ A @ C @ D ) )
& ( ( k1_binop_1 @ ( u1_lattices @ B ) @ C @ D )
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice3) ).
thf(4545,plain,
! [A: $i,B: $i] :
( ( ( v3_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( B
= ( k1_lattice3 @ A ) )
=> ( ( ( u1_struct_0 @ 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 ) )
=> ( ( ( k1_binop_1 @ ( u2_lattices @ B ) @ C @ D )
= ( k4_subset_1 @ A @ C @ D ) )
& ( ( k1_binop_1 @ ( u1_lattices @ B ) @ C @ D )
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ) )
& ( ( ( ( u1_struct_0 @ 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 ) )
=> ( ( ( k1_binop_1 @ ( u2_lattices @ B ) @ C @ D )
= ( k4_subset_1 @ A @ C @ D ) )
& ( ( k1_binop_1 @ ( u1_lattices @ B ) @ C @ D )
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) )
=> ( B
= ( k1_lattice3 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(923,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/sandbox/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(5588,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)],[923]) ).
thf(941,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/sandbox/benchmark/theBenchmark.p',t60_filter_0) ).
thf(5662,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)],[941]) ).
thf(310,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t180_orders_1) ).
thf(2551,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',t23_lopclset) ).
thf(1567,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)],[99]) ).
thf(725,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/sandbox/benchmark/theBenchmark.p',t56_filter_1) ).
thf(4676,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)],[725]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( m2_nat_lat @ ( k23_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k23_filter_2) ).
thf(6299,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( m2_nat_lat @ ( k23_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(1006,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(5941,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)],[1006]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice3 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_lattice3 @ A ) ) )
=> ( ( r1_lattices @ ( k1_lattice3 @ A ) @ B @ C )
<=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
thf(1329,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice3 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_lattice3 @ A ) ) )
=> ( ( ( r1_lattices @ ( k1_lattice3 @ A ) @ B @ C )
=> ( r1_tarski @ B @ C ) )
& ( ( r1_tarski @ B @ C )
=> ( r1_lattices @ ( k1_lattice3 @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(463,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/sandbox/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(3407,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)],[463]) ).
thf(949,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/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(5705,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)],[949]) ).
thf(937,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k11_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_filter_2) ).
thf(5651,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k11_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(1020,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/sandbox/benchmark/theBenchmark.p',d5_lattice4) ).
thf(5992,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)],[1020]) ).
thf(966,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_setwiseo @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( k6_lattices @ A )
= ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_lattice2) ).
thf(5791,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_setwiseo @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
=> ( ( k6_lattices @ A )
= ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1131,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/sandbox/benchmark/theBenchmark.p',dt_k2_lattice4) ).
thf(6363,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)],[1131]) ).
thf(676,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] : ( r3_lattices @ A @ ( k15_lattice3 @ A @ ( a_3_2_lattice3 @ A @ B @ C ) ) @ ( k4_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lattice3) ).
thf(4421,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] : ( r3_lattices @ A @ ( k15_lattice3 @ A @ ( a_3_2_lattice3 @ A @ B @ C ) ) @ ( k4_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(655,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(4315,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_realset1) ).
thf(2053,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ C @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(241,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v3_monoid_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ E @ C )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_monoid_0) ).
thf(2196,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v3_monoid_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ E @ C )
= D ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ E @ C )
= D ) ) ) )
=> ( v3_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(1072,axiom,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_nat_lat) ).
thf(6164,plain,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(850,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 @ A ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ C @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_mssubfam) ).
thf(5213,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 @ A ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ C @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(325,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k7_grcat_1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_grcat_1) ).
thf(2613,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k7_grcat_1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(3723,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',commutativity_k5_setwiseo) ).
thf(2666,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)],[336]) ).
thf(1099,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/sandbox/benchmark/theBenchmark.p',t41_lattice4) ).
thf(6271,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)],[1099]) ).
thf(736,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/sandbox/benchmark/theBenchmark.p',d15_lattice4) ).
thf(4736,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)],[736]) ).
thf(512,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ C )
& ( m2_relset_1 @ D @ B @ C ) )
=> ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
=> ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k1_domain_1 @ A @ A @ B @ C ) @ D ) @ ( k2_ens_1 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ens_1) ).
thf(3654,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ C )
& ( m2_relset_1 @ D @ B @ C ) )
=> ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
=> ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k1_domain_1 @ A @ A @ B @ C ) @ D ) @ ( k2_ens_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',t31_relat_1) ).
thf(2845,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)],[377]) ).
thf(935,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
<=> ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(5639,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) ) )
& ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( k4_tarski @ C @ D ) ) )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(991,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice2) ).
thf(5900,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(319,axiom,
! [A: $i] :
( ~ ( v3_struct_0 @ ( k1_lattice3 @ A ) )
& ( v3_lattices @ ( k1_lattice3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
thf(2581,plain,
! [A: $i] :
( ~ ( v3_struct_0 @ ( k1_lattice3 @ A ) )
& ( v3_lattices @ ( k1_lattice3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(964,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ ( k12_filter_2 @ A @ B ) )
& ( m2_lattice4 @ ( k12_filter_2 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_filter_2) ).
thf(5776,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ ( k12_filter_2 @ A @ B ) )
& ( m2_lattice4 @ ( k12_filter_2 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(5823,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(464,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/sandbox/benchmark/theBenchmark.p',t31_partfun1) ).
thf(3409,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)],[464]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k5_relset_1 @ A @ B @ C )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(1720,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k5_relset_1 @ A @ B @ C )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',t59_setwiseo) ).
thf(2370,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)],[264]) ).
thf(1125,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) )
=> ( m1_subset_1 @ ( k6_filter_2 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_filter_2) ).
thf(6349,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) )
=> ( m1_subset_1 @ ( k6_filter_2 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( ( k4_relset_1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_partfun1) ).
thf(1324,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( ( k4_relset_1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(300,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/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(2504,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)],[300]) ).
thf(766,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/sandbox/benchmark/theBenchmark.p',t64_filter_0) ).
thf(4846,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)],[766]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_2_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_lattice3) ).
thf(5850,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_2_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_2_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1147,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v17_lattices @ B )
| ( v3_realset2 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
| ( ( sk2 @ C @ B @ A )
= A ) ),
inference(cnf,[status(esa)],[1144]) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ C @ B @ A )
= A )
| ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v17_lattices @ B )
| ( v3_realset2 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) ) ),
inference(lifteq,[status(thm)],[1147]) ).
thf(78,axiom,
! [A: $i] :
( ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_setwiseo) ).
thf(1478,plain,
! [A: $i] :
( ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(668,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/sandbox/benchmark/theBenchmark.p',t43_lattice4) ).
thf(4384,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)],[668]) ).
thf(837,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/sandbox/benchmark/theBenchmark.p',t15_relset_1) ).
thf(5149,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)],[837]) ).
thf(1032,axiom,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( v13_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_nat_lat) ).
thf(6029,plain,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( v13_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(6033,plain,
~ ( v3_struct_0 @ k6_nat_lat ),
inference(cnf,[status(esa)],[6029]) ).
thf(545,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( 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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( D
= ( k1_realset1 @ C @ B ) )
=> ( ( ( v1_binop_1 @ C @ A )
=> ( v1_binop_1 @ D @ B ) )
& ( ( v3_binop_1 @ C @ A )
=> ( v3_binop_1 @ D @ B ) )
& ( ( v2_binop_1 @ C @ A )
=> ( v2_binop_1 @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_2) ).
thf(3787,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( 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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( D
= ( k1_realset1 @ C @ B ) )
=> ( ( ( v1_binop_1 @ C @ A )
=> ( v1_binop_1 @ D @ B ) )
& ( ( v3_binop_1 @ C @ A )
=> ( v3_binop_1 @ D @ B ) )
& ( ( v2_binop_1 @ C @ A )
=> ( v2_binop_1 @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(375,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(2836,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(696,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/sandbox/benchmark/theBenchmark.p',t46_filter_1) ).
thf(4508,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)],[696]) ).
thf(32,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(1266,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1119,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/sandbox/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(6331,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)],[1119]) ).
thf(271,axiom,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( k4_tarski @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_1) ).
thf(2387,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( k4_tarski @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( v1_funct_1 @ ( k7_filter_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( m2_relset_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_1) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( v1_funct_1 @ ( k7_filter_1 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( m2_relset_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(640,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k5_lattices @ A )
= ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_lattice2) ).
thf(4244,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k5_lattices @ A )
= ( k3_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(358,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_card_fil) ).
thf(2766,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k7_relset_1 @ A @ A @ A @ A @ B @ ( k6_partfun1 @ A ) )
= B )
& ( ( k7_relset_1 @ A @ A @ A @ A @ ( k6_partfun1 @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_2) ).
thf(1599,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( ( k7_relset_1 @ A @ A @ A @ A @ B @ ( k6_partfun1 @ A ) )
= B )
& ( ( k7_relset_1 @ A @ A @ A @ A @ ( k6_partfun1 @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(27,axiom,
! [A: $i] :
( ( m1_relset_1 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
=> ( ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 ) )
=> ( ( v1_funct_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
& ( v1_binop_1 @ A @ k1_xboole_0 )
& ( v2_binop_1 @ A @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(1246,plain,
! [A: $i] :
( ( m1_relset_1 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
=> ( ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 ) )
=> ( ( v1_funct_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
& ( v1_binop_1 @ A @ k1_xboole_0 )
& ( v2_binop_1 @ A @ k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(409,axiom,
( ( k3_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_toler_1) ).
thf(3109,plain,
( ( k3_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(1067,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/sandbox/benchmark/theBenchmark.p',dt_k1_lattice4) ).
thf(6152,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)],[1067]) ).
thf(729,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v2_lattice3 @ 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_orders_2 @ A @ D @ B )
& ( r1_orders_2 @ A @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_orders_2 @ A @ E @ B )
& ( r1_orders_2 @ A @ E @ C ) )
=> ( r1_orders_2 @ A @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_lattice3) ).
thf(4689,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v2_lattice3 @ 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_orders_2 @ A @ D @ B )
& ( r1_orders_2 @ A @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_orders_2 @ A @ E @ B )
& ( r1_orders_2 @ A @ E @ C ) )
=> ( r1_orders_2 @ 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_orders_2 @ A @ D @ B )
& ( r1_orders_2 @ A @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_orders_2 @ A @ E @ B )
& ( r1_orders_2 @ A @ E @ C ) )
=> ( r1_orders_2 @ A @ E @ D ) ) ) ) ) )
=> ( v2_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(605,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ C )
<=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_t_0topsp) ).
thf(4069,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ C )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) )
& ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ C ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(674,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/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(4416,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)],[674]) ).
thf(459,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 @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k10_setwiseo @ A @ B @ ( k4_setwiseo @ A @ D @ E @ F ) @ C )
= ( k5_setwiseo @ B @ ( k5_setwiseo @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ E ) ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_setwiseo) ).
thf(3364,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 @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k10_setwiseo @ A @ B @ ( k4_setwiseo @ A @ D @ E @ F ) @ C )
= ( k5_setwiseo @ B @ ( k5_setwiseo @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ E ) ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(231,axiom,
! [A: $i] :
( ( v13_lattices @ ( k1_lattice3 @ A ) )
& ( ( k5_lattices @ ( k1_lattice3 @ A ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice3) ).
thf(2140,plain,
! [A: $i] :
( ( v13_lattices @ ( k1_lattice3 @ A ) )
& ( ( k5_lattices @ ( k1_lattice3 @ A ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(608,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 ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lattice2) ).
thf(4086,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 ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(3162,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k3_setwiseo @ A @ B @ C )
= ( k3_setwiseo @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_setwiseo) ).
thf(3201,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k3_setwiseo @ A @ B @ C )
= ( k3_setwiseo @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(635,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/sandbox/benchmark/theBenchmark.p',t22_lattice4) ).
thf(4223,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)],[635]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',t16_lattice2) ).
thf(1759,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)],[146]) ).
thf(1074,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_2 @ ( k1_filter_2 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_2) ).
thf(6171,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_2 @ ( k1_filter_2 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(539,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/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(3755,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)],[539]) ).
thf(329,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v1_binop_1 @ D @ A )
& ( v2_binop_1 @ D @ A )
& ( v3_binop_1 @ D @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ ( k5_finsub_1 @ C ) )
& ( m2_relset_1 @ F @ B @ ( k5_finsub_1 @ C ) ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k5_finsub_1 @ C ) @ A )
& ( m2_relset_1 @ G @ ( k5_finsub_1 @ C ) @ A ) )
=> ( ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ C ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( k5_finsub_1 @ C ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ ( k5_setwiseo @ C @ H @ I ) )
= ( k2_binop_1 @ A @ A @ A @ D @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ H ) @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ I ) ) ) ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ ( k10_setwiseo @ B @ C @ E @ F ) )
= ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ ( k5_finsub_1 @ C ) @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_setwiseo) ).
thf(2634,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v1_binop_1 @ D @ A )
& ( v2_binop_1 @ D @ A )
& ( v3_binop_1 @ D @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ ( k5_finsub_1 @ C ) )
& ( m2_relset_1 @ F @ B @ ( k5_finsub_1 @ C ) ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k5_finsub_1 @ C ) @ A )
& ( m2_relset_1 @ G @ ( k5_finsub_1 @ C ) @ A ) )
=> ( ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ C ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( k5_finsub_1 @ C ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ ( k5_setwiseo @ C @ H @ I ) )
= ( k2_binop_1 @ A @ A @ A @ D @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ H ) @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ I ) ) ) ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ ( k10_setwiseo @ B @ C @ E @ F ) )
= ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ ( k5_finsub_1 @ C ) @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(3834,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)],[553]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',t38_lopclset) ).
thf(1241,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)],[26]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
<=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(2883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
& ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(560,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/sandbox/benchmark/theBenchmark.p',t71_filter_0) ).
thf(3856,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)],[560]) ).
thf(354,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v4_monoid_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_monoid_0) ).
thf(2748,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v4_monoid_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
= D ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
= D ) ) ) )
=> ( v4_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(889,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/sandbox/benchmark/theBenchmark.p',t55_filter_1) ).
thf(5434,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)],[889]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',t19_lopclset) ).
thf(2368,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)],[263]) ).
thf(1137,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( k17_filter_2 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_filter_2) ).
thf(6378,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( k17_filter_2 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(508,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v3_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
=> ( ( r1_tarski @ E @ F )
=> ( ( E = k1_xboole_0 )
| ( ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) )
= ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_setwiseo) ).
thf(3639,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v3_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
=> ( ( r1_tarski @ E @ F )
=> ( ( E = k1_xboole_0 )
| ( ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) )
= ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(977,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_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ B @ C )
= C ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lattice2) ).
thf(5840,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_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ B @ C )
= C ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(983,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r3_lattices @ A @ D @ E )
& ( r2_hidden @ E @ C ) ) ) ) )
=> ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_lattice3) ).
thf(5872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r3_lattices @ A @ D @ E )
& ( r2_hidden @ E @ C ) ) ) ) )
=> ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',t116_funct_2) ).
thf(1202,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)],[16]) ).
thf(661,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/sandbox/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(4352,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)],[661]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',t2_realset1) ).
thf(1814,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)],[162]) ).
thf(718,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/sandbox/benchmark/theBenchmark.p',t67_filter_0) ).
thf(4644,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)],[718]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(3624,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)],[505]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(5402,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)],[886]) ).
thf(208,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(2043,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(777,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_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ B @ C )
= C ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_lattice2) ).
thf(4889,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_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ B @ C )
= C ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(2057,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)],[212]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',t25_borsuk_1) ).
thf(1712,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)],[132]) ).
thf(498,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/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).
thf(3592,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)],[498]) ).
thf(171,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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 @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funcop_1) ).
thf(1846,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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 @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(987,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/sandbox/benchmark/theBenchmark.p',d4_lattice4) ).
thf(5887,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)],[987]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(1895,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)],[181]) ).
thf(902,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/sandbox/benchmark/theBenchmark.p',t75_filter_0) ).
thf(5513,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)],[902]) ).
thf(847,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/sandbox/benchmark/theBenchmark.p',t42_lattice4) ).
thf(5198,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)],[847]) ).
thf(113,axiom,
! [A: $i] :
( ~ ( ? [B: $i] :
( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) )
& ( ( k3_tarski @ A )
= k1_xboole_0 ) )
& ~ ( ( ( k3_tarski @ A )
!= k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_orders_1) ).
thf(1616,plain,
! [A: $i] :
( ~ ( ? [B: $i] :
( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) )
& ( ( k3_tarski @ A )
= k1_xboole_0 ) )
& ~ ( ( ( k3_tarski @ A )
!= k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(467,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/sandbox/benchmark/theBenchmark.p',d3_lattice4) ).
thf(3422,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)],[467]) ).
thf(1133,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(6368,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(395,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( r6_binop_1 @ A @ D @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ A )
& ( m2_relset_1 @ F @ B @ A ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ D @ G @ ( k7_setwiseo @ B @ A @ C @ E @ F ) )
= ( k7_setwiseo @ B @ A @ C @ E @ ( k8_funcop_1 @ A @ B @ D @ G @ F ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_setwiseo) ).
thf(2941,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( r6_binop_1 @ A @ D @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ A )
& ( m2_relset_1 @ F @ B @ A ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ D @ G @ ( k7_setwiseo @ B @ A @ C @ E @ F ) )
= ( k7_setwiseo @ B @ A @ C @ E @ ( k8_funcop_1 @ A @ B @ D @ G @ F ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(323,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(2602,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(1374,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)],[60]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lopclset @ B @ C ) )
<=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lopclset) ).
thf(5043,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_lopclset @ B @ C ) )
=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_lopclset @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(3660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',t115_funct_2) ).
thf(2001,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)],[199]) ).
thf(525,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [H: $i] :
( ( ( v1_funct_1 @ H )
& ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( k2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ G @ H ) @ ( k1_domain_1 @ A @ B @ C @ E ) @ ( k1_domain_1 @ A @ B @ D @ F ) )
= ( k1_domain_1 @ A @ B @ ( k2_binop_1 @ A @ A @ A @ G @ C @ D ) @ ( k2_binop_1 @ B @ B @ B @ H @ E @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_1) ).
thf(3707,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [H: $i] :
( ( ( v1_funct_1 @ H )
& ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( k2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ G @ H ) @ ( k1_domain_1 @ A @ B @ C @ E ) @ ( k1_domain_1 @ A @ B @ D @ F ) )
= ( k1_domain_1 @ A @ B @ ( k2_binop_1 @ A @ A @ A @ G @ C @ D ) @ ( k2_binop_1 @ B @ B @ B @ H @ E @ F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(876,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/sandbox/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(5327,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)],[876]) ).
thf(87,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) )
& ( m2_relset_1 @ E @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) ) )
=> ( ( ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k1_setwiseo @ B ) )
= ( k1_setwiseo @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ B ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k5_setwiseo @ B @ F @ G ) )
= ( k5_setwiseo @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ F ) @ ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ G ) ) ) ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ A ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k10_setwiseo @ A @ B @ F @ D ) )
= ( k10_setwiseo @ A @ C @ F @ ( k7_funct_2 @ A @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_setwiseo) ).
thf(1510,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) )
& ( m2_relset_1 @ E @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) ) )
=> ( ( ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k1_setwiseo @ B ) )
= ( k1_setwiseo @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ B ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k5_setwiseo @ B @ F @ G ) )
= ( k5_setwiseo @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ F ) @ ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ G ) ) ) ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ A ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k10_setwiseo @ A @ B @ F @ D ) )
= ( k10_setwiseo @ A @ C @ F @ ( k7_funct_2 @ A @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(148,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r6_binop_1 @ A @ B @ C )
<=> ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_binop_1) ).
thf(1764,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r6_binop_1 @ A @ B @ C )
=> ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) ) )
& ( ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) )
=> ( r6_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1021,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_filter_0) ).
thf(5996,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)],[1021]) ).
thf(621,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/sandbox/benchmark/theBenchmark.p',t22_filter_0) ).
thf(4131,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)],[621]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(5524,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)],[904]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).
thf(2176,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)],[238]) ).
thf(732,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/sandbox/benchmark/theBenchmark.p',d14_lattice4) ).
thf(4708,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)],[732]) ).
thf(685,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/sandbox/benchmark/theBenchmark.p',t22_lopclset) ).
thf(4470,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)],[685]) ).
thf(144,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v5_orders_2 @ ( k1_struct_0 @ A @ B ) @ A )
& ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_orders_2) ).
thf(1754,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v5_orders_2 @ ( k1_struct_0 @ A @ B ) @ A )
& ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(771,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k6_lattices @ A )
= ( k6_lattices @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_filter_2) ).
thf(4872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k6_lattices @ A )
= ( k6_lattices @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(388,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 ) ) )
=> ( ( D != k1_xboole_0 )
=> ( ( k3_lattices @ A @ B @ ( k2_lattice2 @ C @ A @ D @ E ) )
= ( k2_lattice2 @ C @ A @ D @ ( k8_funcop_1 @ ( u1_struct_0 @ A ) @ C @ ( u2_lattices @ A ) @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice2) ).
thf(2904,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 ) ) )
=> ( ( D != k1_xboole_0 )
=> ( ( k3_lattices @ A @ B @ ( k2_lattice2 @ C @ A @ D @ E ) )
= ( k2_lattice2 @ C @ A @ D @ ( k8_funcop_1 @ ( u1_struct_0 @ A ) @ C @ ( u2_lattices @ A ) @ B @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relat_1) ).
thf(2556,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)],[312]) ).
thf(662,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r3_binop_1 @ ( u1_struct_0 @ A ) @ ( k5_lattices @ A ) @ ( u2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_lattice2) ).
thf(4354,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r3_binop_1 @ ( u1_struct_0 @ A ) @ ( k5_lattices @ A ) @ ( u2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(714,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(4613,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( k4_tarski @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(833,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_lattice3 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lattice3) ).
thf(5138,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_lattice3 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(722,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/sandbox/benchmark/theBenchmark.p',t15_subset_1) ).
thf(4657,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)],[722]) ).
thf(1008,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/sandbox/benchmark/theBenchmark.p',t48_filter_0) ).
thf(5960,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)],[1008]) ).
thf(1089,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).
thf(6243,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1023,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k9_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_filter_2) ).
thf(6001,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k9_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(108,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(1595,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ~ ( ( r2_hidden @ C @ D )
& ! [E: $i,F: $i] :
~ ( ( C
= ( k4_tarski @ E @ F ) )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relset_1) ).
thf(3888,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ~ ( ( r2_hidden @ C @ D )
& ! [E: $i,F: $i] :
~ ( ( C
= ( k4_tarski @ E @ F ) )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(555,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 ) )
=> ( ( ( k3_lattice3 @ A )
= ( k3_lattice3 @ B ) )
=> ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice3) ).
thf(3839,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 ) )
=> ( ( ( k3_lattice3 @ A )
= ( k3_lattice3 @ B ) )
=> ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(1002,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/sandbox/benchmark/theBenchmark.p',t1_filter_0) ).
thf(5928,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)],[1002]) ).
thf(694,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) )
=> ( v11_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice2) ).
thf(4503,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) )
=> ( v11_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(985,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ D ) )
& ( r2_hidden @ C @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ D ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_setwiseo) ).
thf(5882,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ D ) )
& ( r2_hidden @ C @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ D ) ) )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(824,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/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(5095,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)],[824]) ).
thf(410,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B )
& ( v1_setwiseo @ C @ B ) )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D ) )
=> ( ( ( v1_binop_1 @ E @ D )
& ( v2_binop_1 @ E @ D )
& ( v3_binop_1 @ E @ D )
& ( v1_setwiseo @ E @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ B @ D )
& ( m2_relset_1 @ G @ B @ D ) )
=> ( ( ( ( k8_funct_2 @ B @ D @ G @ ( k3_binop_1 @ B @ C ) )
= ( k3_binop_1 @ D @ E ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ B )
=> ( ( k8_funct_2 @ B @ D @ G @ ( k2_binop_1 @ B @ B @ B @ C @ H @ I ) )
= ( k2_binop_1 @ D @ D @ D @ E @ ( k8_funct_2 @ B @ D @ G @ H ) @ ( k8_funct_2 @ B @ D @ G @ I ) ) ) ) ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( k8_funct_2 @ B @ D @ G @ ( k7_setwiseo @ A @ B @ C @ H @ F ) )
= ( k7_setwiseo @ A @ D @ E @ H @ ( k7_funct_2 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_setwiseo) ).
thf(3111,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v3_binop_1 @ C @ B )
& ( v1_setwiseo @ C @ B ) )
=> ! [D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D ) )
=> ( ( ( v1_binop_1 @ E @ D )
& ( v2_binop_1 @ E @ D )
& ( v3_binop_1 @ E @ D )
& ( v1_setwiseo @ E @ D ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ B @ D )
& ( m2_relset_1 @ G @ B @ D ) )
=> ( ( ( ( k8_funct_2 @ B @ D @ G @ ( k3_binop_1 @ B @ C ) )
= ( k3_binop_1 @ D @ E ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ B )
=> ( ( k8_funct_2 @ B @ D @ G @ ( k2_binop_1 @ B @ B @ B @ C @ H @ I ) )
= ( k2_binop_1 @ D @ D @ D @ E @ ( k8_funct_2 @ B @ D @ G @ H ) @ ( k8_funct_2 @ B @ D @ G @ I ) ) ) ) ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( k8_funct_2 @ B @ D @ G @ ( k7_setwiseo @ A @ B @ C @ H @ F ) )
= ( k7_setwiseo @ A @ D @ E @ H @ ( k7_funct_2 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k10_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_filter_2) ).
thf(4269,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k10_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(518,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/sandbox/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(3686,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)],[518]) ).
thf(946,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/sandbox/benchmark/theBenchmark.p',t34_lattices) ).
thf(5698,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)],[946]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
<=> ( ( k4_relset_1 @ B @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
thf(3187,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
=> ( ( k4_relset_1 @ B @ A @ C )
= B ) )
& ( ( ( k4_relset_1 @ B @ A @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(507,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k15_lattice3 @ A @ ( k3_tarski @ B ) )
= ( k15_lattice3 @ A @ ( a_2_7_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_lattice3) ).
thf(3636,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k15_lattice3 @ A @ ( k3_tarski @ B ) )
= ( k15_lattice3 @ A @ ( a_2_7_lattice3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(1884,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)],[179]) ).
thf(820,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r4_wellord1 @ A @ B )
& ( r4_wellord1 @ B @ C ) )
=> ( r4_wellord1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_wellord1) ).
thf(5067,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r4_wellord1 @ A @ B )
& ( r4_wellord1 @ B @ C ) )
=> ( r4_wellord1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( r6_binop_1 @ A @ D @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ A )
& ( m2_relset_1 @ F @ B @ A ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ D @ ( k7_setwiseo @ B @ A @ C @ E @ F ) @ G )
= ( k7_setwiseo @ B @ A @ C @ E @ ( k7_funcop_1 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_setwiseo) ).
thf(2489,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( r6_binop_1 @ A @ D @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ A )
& ( m2_relset_1 @ F @ B @ A ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ D @ ( k7_setwiseo @ B @ A @ C @ E @ F ) @ G )
= ( k7_setwiseo @ B @ A @ C @ E @ ( k7_funcop_1 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(930,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/sandbox/benchmark/theBenchmark.p',t46_lattice2) ).
thf(5612,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)],[930]) ).
thf(570,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/sandbox/benchmark/theBenchmark.p',t44_filter_1) ).
thf(3900,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)],[570]) ).
thf(667,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
thf(4381,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_5_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ D @ E )
& ( r2_hidden @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_5_lattice3) ).
thf(4341,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_5_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ D @ E )
& ( r2_hidden @ E @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ D @ E )
& ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_5_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1003,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_2) ).
thf(5933,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(1784,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_7_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k15_lattice3 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_7_lattice3) ).
thf(5488,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_7_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k15_lattice3 @ B @ D ) )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k15_lattice3 @ B @ D ) )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_7_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(435,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( v5_lattice3 @ A )
<=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ C @ ( k15_lattice3 @ A @ B ) ) @ ( k15_lattice3 @ A @ ( a_3_3_lattice3 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_lattice3) ).
thf(3255,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v5_lattice3 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ C @ ( k15_lattice3 @ A @ B ) ) @ ( k15_lattice3 @ A @ ( a_3_3_lattice3 @ A @ B @ C ) ) ) ) )
& ( ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ C @ ( k15_lattice3 @ A @ B ) ) @ ( k15_lattice3 @ A @ ( a_3_3_lattice3 @ A @ B @ C ) ) ) )
=> ( v5_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(2525,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(501,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 @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ C )
& ( m2_relset_1 @ E @ A @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k8_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ F )
= ( k4_tarski @ ( k8_funct_2 @ A @ B @ D @ F ) @ ( k8_funct_2 @ A @ C @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_3) ).
thf(3609,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 @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ C )
& ( m2_relset_1 @ E @ A @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k8_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ F )
= ( k4_tarski @ ( k8_funct_2 @ A @ B @ D @ F ) @ ( k8_funct_2 @ A @ C @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(627,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_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 @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) )
=> ( m2_filter_2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_2) ).
thf(4159,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_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 @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_filter_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(378,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v3_realset2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_realset2) ).
thf(2847,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v3_realset2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(2849,plain,
l1_struct_0 @ sk182,
inference(cnf,[status(esa)],[2847]) ).
thf(122,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r1_binop_1 @ A @ C @ B )
<=> ( r2_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_binop_1) ).
thf(1652,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r1_binop_1 @ A @ C @ B )
=> ( r2_binop_1 @ A @ C @ B ) )
& ( ( r2_binop_1 @ A @ C @ B )
=> ( r1_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(540,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ D @ B )
& ( v2_binop_1 @ D @ B )
& ( v3_binop_1 @ D @ B )
& ( v1_setwiseo @ D @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( k5_finsub_1 @ C ) )
& ( m2_relset_1 @ E @ A @ ( k5_finsub_1 @ C ) ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k5_finsub_1 @ C ) @ B )
& ( m2_relset_1 @ F @ ( k5_finsub_1 @ C ) @ B ) )
=> ( ( ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k1_setwiseo @ C ) )
= ( k3_binop_1 @ B @ D ) )
& ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ C ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ C ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k5_setwiseo @ C @ G @ H ) )
= ( k2_binop_1 @ B @ B @ B @ D @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ G ) @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ H ) ) ) ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k10_setwiseo @ A @ C @ G @ E ) )
= ( k7_setwiseo @ A @ B @ D @ G @ ( k7_funct_2 @ A @ ( k5_finsub_1 @ C ) @ B @ E @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_setwiseo) ).
thf(3758,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ D @ B )
& ( v2_binop_1 @ D @ B )
& ( v3_binop_1 @ D @ B )
& ( v1_setwiseo @ D @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( k5_finsub_1 @ C ) )
& ( m2_relset_1 @ E @ A @ ( k5_finsub_1 @ C ) ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k5_finsub_1 @ C ) @ B )
& ( m2_relset_1 @ F @ ( k5_finsub_1 @ C ) @ B ) )
=> ( ( ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k1_setwiseo @ C ) )
= ( k3_binop_1 @ B @ D ) )
& ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ C ) )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ C ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k5_setwiseo @ C @ G @ H ) )
= ( k2_binop_1 @ B @ B @ B @ D @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ G ) @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ H ) ) ) ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k10_setwiseo @ A @ C @ G @ E ) )
= ( k7_setwiseo @ A @ B @ D @ G @ ( k7_funct_2 @ A @ ( k5_finsub_1 @ C ) @ B @ E @ F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(441,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/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(3283,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)],[441]) ).
thf(437,axiom,
! [A: $i] :
( ( v14_lattices @ ( k1_lattice3 @ A ) )
& ( ( k6_lattices @ ( k1_lattice3 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_lattice3) ).
thf(3266,plain,
! [A: $i] :
( ( v14_lattices @ ( k1_lattice3 @ A ) )
& ( ( k6_lattices @ ( k1_lattice3 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',t19_setwiseo) ).
thf(1388,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)],[63]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
=> ( r1_tarski @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(3272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [E: $i,F: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
=> ( r1_tarski @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(712,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ C )
=> ( A
!= ( k4_tarski @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_domain_1) ).
thf(4605,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ C )
=> ( A
!= ( k4_tarski @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_filter_2 @ A @ B @ C )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
thf(5876,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r1_filter_2 @ A @ B @ C )
=> ( B = C ) )
& ( ( B = C )
=> ( r1_filter_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(1403,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)],[66]) ).
thf(1123,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_2 @ A )
= ( k1_filter_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).
thf(6344,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_2 @ A )
= ( k1_filter_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(130,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r5_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_binop_1) ).
thf(1701,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r5_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) )
=> ( r5_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(497,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_ens_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ens_1) ).
thf(3590,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_ens_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(1520,plain,
v1_relat_1 @ sk35,
inference(cnf,[status(esa)],[1517]) ).
thf(564,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/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(3868,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)],[564]) ).
thf(371,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ( ( D = k1_xboole_0 )
| ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ D @ ( k2_setwiseo @ B @ F ) ) @ E )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ D @ E ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_setwiseo) ).
thf(2817,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ( ( D = k1_xboole_0 )
| ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ D @ ( k2_setwiseo @ B @ F ) ) @ E )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ D @ E ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(4758,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(345,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_binop_1) ).
thf(2695,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ B @ C @ D )
= D ) )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(22,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 ) )
=> ( ( r1_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_binop_1) ).
thf(1226,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 ) )
=> ( ( ( r1_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ B @ D )
= D ) )
=> ( r1_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(695,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/sandbox/benchmark/theBenchmark.p',t19_lattice4) ).
thf(4505,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)],[695]) ).
thf(499,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/sandbox/benchmark/theBenchmark.p',dt_k3_lattice2) ).
thf(3599,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)],[499]) ).
thf(643,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/sandbox/benchmark/theBenchmark.p',t19_filter_1) ).
thf(4251,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)],[643]) ).
thf(154,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 ) )
=> ( ( r3_binop_1 @ A @ B @ C )
<=> ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_binop_1) ).
thf(1786,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 ) )
=> ( ( ( r3_binop_1 @ A @ B @ C )
=> ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) ) )
& ( ( ( r1_binop_1 @ A @ B @ C )
& ( r2_binop_1 @ A @ B @ C ) )
=> ( r3_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(617,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ A )
=> ( A
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(4112,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ A )
=> ( A
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( r1_relat_2 @ B @ A )
=> ( ( ( k4_relset_1 @ A @ A @ B )
= A )
& ( ( k3_relat_1 @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_orders_1) ).
thf(3340,plain,
! [A: $i,B: $i] :
( ( m2_relset_1 @ B @ A @ A )
=> ( ( r1_relat_2 @ B @ A )
=> ( ( ( k4_relset_1 @ A @ A @ B )
= A )
& ( ( k3_relat_1 @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(48,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v4_lattice3 @ A )
<=> ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_lattice3) ).
thf(1332,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v4_lattice3 @ A )
=> ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) )
& ( ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) )
=> ( v4_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(470,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(3436,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(948,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/sandbox/benchmark/theBenchmark.p',t41_subset_1) ).
thf(5703,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)],[948]) ).
thf(494,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(3579,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(182,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 @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ ( k8_funct_2 @ A @ B @ C @ D ) @ ( k2_funct_2 @ A @ B @ C @ E ) )
=> ( r2_hidden @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_7) ).
thf(1897,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 @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ ( k8_funct_2 @ A @ B @ C @ D ) @ ( k2_funct_2 @ A @ B @ C @ E ) )
=> ( r2_hidden @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1120,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/sandbox/benchmark/theBenchmark.p',t6_filter_0) ).
thf(6334,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)],[1120]) ).
thf(3568,plain,
v1_funct_1 @ sk267,
inference(cnf,[status(esa)],[3567]) ).
thf(529,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v1_setwiseo @ B @ A )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_setwiseo) ).
thf(3719,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v1_setwiseo @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( r3_binop_1 @ A @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( r3_binop_1 @ A @ C @ B ) )
=> ( v1_setwiseo @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1038,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/sandbox/benchmark/theBenchmark.p',t49_lattices) ).
thf(6048,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)],[1038]) ).
thf(700,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/sandbox/benchmark/theBenchmark.p',t59_lattice2) ).
thf(4537,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)],[700]) ).
thf(1010,axiom,
? [A: $i] :
( ( l2_quantal1 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_quantal1) ).
thf(5965,plain,
? [A: $i] :
( ( l2_quantal1 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_3_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_lattice3) ).
thf(4485,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_3_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( a_3_3_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(910,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ( ( k6_lattices @ A )
= ( k15_lattice3 @ A @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_lattice3) ).
thf(5546,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ( ( k6_lattices @ A )
= ( k15_lattice3 @ A @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(3118,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(620,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/sandbox/benchmark/theBenchmark.p',t70_lattice2) ).
thf(4127,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)],[620]) ).
thf(585,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/sandbox/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(3964,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)],[585]) ).
thf(879,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/sandbox/benchmark/theBenchmark.p',d10_lattice4) ).
thf(5363,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)],[879]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',t62_lattice2) ).
thf(2293,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)],[248]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m1_filter_2 @ ( k16_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_filter_2) ).
thf(6357,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m1_filter_2 @ ( k16_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(531,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
=> ( D
= ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funcop_1) ).
thf(3726,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k8_funct_2 @ B @ A @ D @ G )
= ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
=> ( D
= ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( r3_orders_2 @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
thf(1371,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( r3_orders_2 @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(981,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ B @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) )
<=> ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relset_1) ).
thf(5859,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ! [E: $i] :
( ( m2_relset_1 @ E @ B @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ C )
=> ( ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) )
=> ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) ) )
& ( ? [H: $i] :
( ( m1_subset_1 @ H @ B )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
& ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) )
=> ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(521,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/sandbox/benchmark/theBenchmark.p',t21_tops_1) ).
thf(3695,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)],[521]) ).
thf(612,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(4099,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)],[612]) ).
thf(448,axiom,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_1) ).
thf(3330,plain,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(1635,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)],[117]) ).
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 @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).
thf(4672,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)],[724]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_1_ens_1 @ B ) )
<=> ? [C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ C @ B )
& ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
& ( A
= ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ D )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_ens_1) ).
thf(3091,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_1_ens_1 @ B ) )
=> ? [C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ C @ B )
& ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
& ( A
= ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ D )
& ( m2_relset_1 @ E @ C @ D ) ) )
& ( ? [C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ C @ B )
& ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
& ( A
= ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ D )
& ( m2_relset_1 @ E @ C @ D ) )
=> ( r2_hidden @ A @ ( a_1_1_ens_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(293,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funcop_1) ).
thf(2474,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',t8_realset1) ).
thf(1638,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)],[118]) ).
thf(776,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/sandbox/benchmark/theBenchmark.p',t45_lattices) ).
thf(4887,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)],[776]) ).
thf(934,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k6_lattice3 @ ( u1_struct_0 @ A ) @ ( k2_lattice3 @ A ) )
= ( k2_lattice3 @ ( k1_lattice2 @ A ) ) )
& ( ( k7_lattice3 @ ( k3_lattice3 @ A ) )
= ( k3_lattice3 @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_lattice3) ).
thf(5634,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k6_lattice3 @ ( u1_struct_0 @ A ) @ ( k2_lattice3 @ A ) )
= ( k2_lattice3 @ ( k1_lattice2 @ A ) ) )
& ( ( k7_lattice3 @ ( k3_lattice3 @ A ) )
= ( k3_lattice3 @ ( k1_lattice2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1103,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/sandbox/benchmark/theBenchmark.p',dt_k10_filter_1) ).
thf(6281,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)],[1103]) ).
thf(488,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v1_setwiseo @ C @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ D @ ( k2_setwiseo @ B @ F ) ) @ E )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ D @ E ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_setwiseo) ).
thf(3551,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v1_setwiseo @ C @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ D @ ( k2_setwiseo @ B @ F ) ) @ E )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ D @ E ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(760,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/sandbox/benchmark/theBenchmark.p',d11_filter_0) ).
thf(4828,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)],[760]) ).
thf(1117,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_2 @ B @ A )
<=> ( m1_filter_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
thf(6321,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( m1_filter_2 @ B @ A )
=> ( m1_filter_0 @ B @ A ) )
& ( ( m1_filter_0 @ B @ A )
=> ( m1_filter_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(526,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/sandbox/benchmark/theBenchmark.p',t24_finsub_1) ).
thf(3710,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)],[526]) ).
thf(1175,plain,
v1_relat_1 @ sk3,
inference(cnf,[status(esa)],[1171]) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',d7_realset2) ).
thf(2510,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)],[302]) ).
thf(1042,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/sandbox/benchmark/theBenchmark.p',commutativity_k1_filter_1) ).
thf(6061,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)],[1042]) ).
thf(1064,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m2_filter_2 @ ( k18_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_filter_2) ).
thf(6144,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m2_filter_2 @ ( k18_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(733,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] : ( r3_lattices @ A @ ( k3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) @ ( k16_lattice3 @ A @ ( a_3_4_lattice3 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lattice3) ).
thf(4716,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] : ( r3_lattices @ A @ ( k3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) @ ( k16_lattice3 @ A @ ( a_3_4_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(730,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k18_group_2 @ A @ B ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_group_2) ).
thf(4704,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k18_group_2 @ A @ B ) @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(1041,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/sandbox/benchmark/theBenchmark.p',t11_lattice4) ).
thf(6059,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)],[1041]) ).
thf(308,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v3_binop_1 @ C @ A ) )
=> ( ( D = k1_xboole_0 )
| ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( r2_hidden @ G @ D )
=> ( ( k8_funct_2 @ B @ A @ E @ G )
= F ) ) )
=> ( ( k7_setwiseo @ B @ A @ C @ D @ E )
= F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_setwiseo) ).
thf(2538,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v3_binop_1 @ C @ A ) )
=> ( ( D = k1_xboole_0 )
| ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( r2_hidden @ G @ D )
=> ( ( k8_funct_2 @ B @ A @ E @ G )
= F ) ) )
=> ( ( k7_setwiseo @ B @ A @ C @ D @ E )
= F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(1853,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)],[173]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( ( k4_relset_1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_partfun1) ).
thf(1408,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( ( k4_relset_1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 )
& ( ( k2_relat_1 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(433,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/sandbox/benchmark/theBenchmark.p',t45_lattice2) ).
thf(3238,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)],[433]) ).
thf(328,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v6_monoid_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_monoid_0) ).
thf(2624,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v6_monoid_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
=> ( D = E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
=> ( D = E ) ) ) ) )
=> ( v6_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(855,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/sandbox/benchmark/theBenchmark.p',t85_filter_0) ).
thf(5244,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)],[855]) ).
thf(276,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v3_binop_1 @ C @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ F @ D )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ F ) @ ( k7_setwiseo @ B @ A @ C @ D @ E ) )
= ( k7_setwiseo @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_setwiseo) ).
thf(2415,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ A )
& ( m2_relset_1 @ E @ B @ A ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v3_binop_1 @ C @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ F @ D )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ F ) @ ( k7_setwiseo @ B @ A @ C @ D @ E ) )
= ( k7_setwiseo @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(827,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/sandbox/benchmark/theBenchmark.p',t35_lattice4) ).
thf(5103,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)],[827]) ).
thf(466,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/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(3419,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)],[466]) ).
thf(1057,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] :
( ( m2_filter_2 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_2) ).
thf(6112,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] :
( ( m2_filter_2 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(784,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_quantal1 @ B @ A )
& ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_quantal1) ).
thf(4914,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_quantal1 @ B @ A )
& ( v1_xboole_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_6_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ E @ D )
& ( r2_hidden @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_6_lattice3) ).
thf(5827,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_6_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ E @ D )
& ( r2_hidden @ E @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ E @ D )
& ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_6_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(337,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r1_binop_1 @ A @ C @ E )
& ( r1_binop_1 @ B @ D @ F ) )
<=> ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_filter_1) ).
thf(2669,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r1_binop_1 @ A @ C @ E )
& ( r1_binop_1 @ B @ D @ F ) )
=> ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
& ( ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
=> ( ( r1_binop_1 @ A @ C @ E )
& ( r1_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(158,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( r1_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_binop_1) ).
thf(1801,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( r1_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
= D ) )
=> ( r1_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(905,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/sandbox/benchmark/theBenchmark.p',t43_lattices) ).
thf(5531,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)],[905]) ).
thf(1106,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/sandbox/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(6289,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)],[1106]) ).
thf(380,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(2855,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(2856,plain,
l1_struct_0 @ sk183,
inference(cnf,[status(esa)],[2855]) ).
thf(368,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 @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ D @ A )
& ( v1_binop_1 @ D @ A )
& ( v2_binop_1 @ D @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ C @ A )
& ( m2_relset_1 @ G @ C @ A ) )
=> ( ( k7_setwiseo @ C @ A @ D @ ( k8_setwiseo @ B @ C @ F @ E ) @ G )
= ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ C @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_setwiseo) ).
thf(2802,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 @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( v3_binop_1 @ D @ A )
& ( v1_binop_1 @ D @ A )
& ( v2_binop_1 @ D @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ! [G: $i] :
( ( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ C @ A )
& ( m2_relset_1 @ G @ C @ A ) )
=> ( ( k7_setwiseo @ C @ A @ D @ ( k8_setwiseo @ B @ C @ F @ E ) @ G )
= ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ C @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1068,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/sandbox/benchmark/theBenchmark.p',t18_lattice4) ).
thf(6154,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)],[1068]) ).
thf(267,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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(2378,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)],[267]) ).
thf(496,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v1_binop_1 @ D @ B ) )
<=> ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_1) ).
thf(3586,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( v1_binop_1 @ C @ A )
& ( v1_binop_1 @ D @ B ) )
=> ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( v1_binop_1 @ C @ A )
& ( v1_binop_1 @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(1084,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( r2_hidden @ ( k5_lattices @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_filter_2) ).
thf(6196,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( r2_hidden @ ( k5_lattices @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(742,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( m1_subset_1 @ ( k6_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(4773,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)],[742]) ).
thf(932,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_filter_2 @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).
thf(5616,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_filter_2 @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(1439,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)],[74]) ).
thf(687,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/sandbox/benchmark/theBenchmark.p',t50_lattices) ).
thf(4477,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)],[687]) ).
thf(615,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/sandbox/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(4107,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)],[615]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A )
& ( m2_filter_2 @ C @ A ) )
=> ( m2_filter_2 @ ( k21_filter_2 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k21_filter_2) ).
thf(6004,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A )
& ( m2_filter_2 @ C @ A ) )
=> ( m2_filter_2 @ ( k21_filter_2 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(921,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/sandbox/benchmark/theBenchmark.p',t54_filter_0) ).
thf(5584,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)],[921]) ).
thf(939,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/sandbox/benchmark/theBenchmark.p',t27_filter_0) ).
thf(5657,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)],[939]) ).
thf(998,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ( m2_filter_2 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k5_lattices @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_2) ).
thf(5920,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ( m2_filter_2 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k5_lattices @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(954,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/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(5730,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)],[954]) ).
thf(757,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
=> ( v11_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lattice2) ).
thf(4818,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
=> ( v11_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(362,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v1_setwiseo @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ E @ F ) @ D )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_setwiseo) ).
thf(2780,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A )
& ( v1_setwiseo @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ E @ F ) @ D )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(890,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/sandbox/benchmark/theBenchmark.p',t5_lattice4) ).
thf(5439,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)],[890]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(1862,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)],[176]) ).
thf(986,axiom,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(5885,plain,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(811,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_filter_2) ).
thf(5035,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(849,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/sandbox/benchmark/theBenchmark.p',t74_filter_0) ).
thf(5202,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)],[849]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) )
<=> ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_1) ).
thf(1162,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) )
=> ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(863,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/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(5286,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)],[863]) ).
thf(650,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/sandbox/benchmark/theBenchmark.p',d12_filter_0) ).
thf(4277,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)],[650]) ).
thf(355,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 ) ) )
=> ( ( k2_lattice2 @ A @ B @ C @ D )
= ( k7_setwiseo @ A @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice2) ).
thf(2757,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 ) ) )
=> ( ( k2_lattice2 @ A @ B @ C @ D )
= ( k7_setwiseo @ A @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(589,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k12_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_filter_2) ).
thf(3977,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k12_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(503,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( 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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( E
= ( k1_realset1 @ C @ B ) )
& ( F
= ( k1_realset1 @ D @ B ) )
& ( r6_binop_1 @ A @ C @ D ) )
=> ( r6_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_filter_2) ).
thf(3614,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( 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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( E
= ( k1_realset1 @ C @ B ) )
& ( F
= ( k1_realset1 @ D @ B ) )
& ( r6_binop_1 @ A @ C @ D ) )
=> ( r6_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1149,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v17_lattices @ B )
| ( v3_realset2 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
| ( v1_filter_0 @ ( sk2 @ C @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[1144]) ).
thf(1116,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice2) ).
thf(6319,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(40,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v3_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_funcop_1) ).
thf(1293,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v3_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ C ) @ D )
=> ( ( r1_tarski @ C @ ( k4_relset_1 @ A @ B @ D ) )
& ( r1_tarski @ C @ ( k5_relset_1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_1) ).
thf(2553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ C ) @ D )
=> ( ( r1_tarski @ C @ ( k4_relset_1 @ A @ B @ D ) )
& ( r1_tarski @ C @ ( k5_relset_1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(255,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r6_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_binop_1) ).
thf(2329,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r6_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(976,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/sandbox/benchmark/theBenchmark.p',t42_subset_1) ).
thf(5838,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)],[976]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(1952,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)],[196]) ).
thf(1136,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(6376,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)],[1136]) ).
thf(169,axiom,
! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k1_setwiseo @ A ) @ ( k9_setwiseo @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_setwiseo) ).
thf(1841,plain,
! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k1_setwiseo @ A ) @ ( k9_setwiseo @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',t75_lattice2) ).
thf(2401,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)],[272]) ).
thf(851,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/sandbox/benchmark/theBenchmark.p',t16_subset_1) ).
thf(5216,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)],[851]) ).
thf(6288,plain,
~ ( v3_struct_0 @ k13_nat_lat ),
inference(cnf,[status(esa)],[6285]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',t16_funct_2) ).
thf(1176,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)],[10]) ).
thf(391,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/sandbox/benchmark/theBenchmark.p',t30_partfun1) ).
thf(2931,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)],[391]) ).
thf(151,axiom,
! [A: $i] : ( v1_setwiseo @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_setwiseo) ).
thf(1775,plain,
! [A: $i] : ( v1_setwiseo @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(446,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r1_lattice2 @ A @ C @ D )
& ( r1_lattice2 @ B @ E @ F ) )
<=> ( r1_lattice2 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_1) ).
thf(3310,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r1_lattice2 @ A @ C @ D )
& ( r1_lattice2 @ B @ E @ F ) )
=> ( r1_lattice2 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r1_lattice2 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r1_lattice2 @ A @ C @ D )
& ( r1_lattice2 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(1052,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k15_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(6100,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k15_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(652,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k14_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).
thf(4304,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k14_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).
thf(2207,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)],[243]) ).
thf(632,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/sandbox/benchmark/theBenchmark.p',t56_lattice2) ).
thf(4209,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)],[632]) ).
thf(217,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k4_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relset_1) ).
thf(2069,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ~ ( r2_hidden @ E @ ( k4_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(2418,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)],[277]) ).
thf(790,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/sandbox/benchmark/theBenchmark.p',t12_filter_0) ).
thf(4933,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)],[790]) ).
thf(1094,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/sandbox/benchmark/theBenchmark.p',t38_filter_1) ).
thf(6255,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)],[1094]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',t27_relat_1) ).
thf(1926,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)],[190]) ).
thf(958,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/sandbox/benchmark/theBenchmark.p',t20_filter_0) ).
thf(5742,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)],[958]) ).
thf(638,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_4_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_lattice3) ).
thf(4232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_4_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ C @ E ) )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_4_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
=> ( ( B
= ( k4_relset_1 @ B @ A @ C ) )
& ( r1_tarski @ B @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relset_1) ).
thf(2350,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
=> ( ( B
= ( k4_relset_1 @ B @ A @ C ) )
& ( r1_tarski @ B @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(891,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).
thf(5442,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)],[891]) ).
thf(6436,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ B )
| ~ ( v17_lattices @ B )
| ( v3_realset2 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
| ( v1_filter_0 @ ( sk2 @ C @ B @ A ) @ B )
| ( ( v10_lattices @ sk1 )
!= ( v10_lattices @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1142,1149]) ).
thf(6437,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( l3_lattices @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( v1_filter_0 @ ( sk2 @ B @ sk1 @ A ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[6436:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(6442,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( l3_lattices @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( v1_filter_0 @ ( sk2 @ B @ sk1 @ A ) @ sk1 ) ),
inference(simp,[status(thm)],[6437]) ).
thf(6448,plain,
! [B: $i,A: $i] :
( $false
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ $true
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( v1_filter_0 @ ( sk2 @ B @ sk1 @ A ) @ sk1 ) ),
inference(rewrite,[status(thm)],[6442,1141,1143]) ).
thf(6449,plain,
! [B: $i,A: $i] :
( ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( v1_filter_0 @ ( sk2 @ B @ sk1 @ A ) @ sk1 ) ),
inference(simp,[status(thm)],[6448]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_6_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( r3_lattices @ B @ ( k4_lattices @ B @ C @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_lattice3) ).
thf(4373,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_6_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( r3_lattices @ B @ ( k4_lattices @ B @ C @ E ) @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ( r3_lattices @ B @ ( k4_lattices @ B @ C @ E ) @ D ) )
=> ( r2_hidden @ A @ ( a_3_6_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',t4_cat_1) ).
thf(1643,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)],[119]) ).
thf(856,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_relset_1) ).
thf(5248,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
=> ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(548,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/sandbox/benchmark/theBenchmark.p',t49_filter_0) ).
thf(3806,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)],[548]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',d5_lopclset) ).
thf(3159,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)],[415]) ).
thf(215,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( r3_binop_1 @ A @ C @ B )
<=> ( r2_binop_1 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_binop_1) ).
thf(2064,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 @ A )
=> ( ( v1_binop_1 @ B @ A )
=> ( ( ( r3_binop_1 @ A @ C @ B )
=> ( r2_binop_1 @ A @ C @ B ) )
& ( ( r2_binop_1 @ A @ C @ B )
=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(583,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 )
<=> ( r3_orders_2 @ ( k3_lattice3 @ A ) @ ( k4_lattice3 @ A @ B ) @ ( k4_lattice3 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
thf(3953,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 )
=> ( r3_orders_2 @ ( k3_lattice3 @ A ) @ ( k4_lattice3 @ A @ B ) @ ( k4_lattice3 @ A @ C ) ) )
& ( ( r3_orders_2 @ ( k3_lattice3 @ A ) @ ( k4_lattice3 @ A @ B ) @ ( k4_lattice3 @ A @ C ) )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(1014,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/sandbox/benchmark/theBenchmark.p',t54_lattice2) ).
thf(5976,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)],[1014]) ).
thf(366,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/sandbox/benchmark/theBenchmark.p',t26_relset_1) ).
thf(2797,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)],[366]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_partfun1) ).
thf(1496,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)],[83]) ).
thf(868,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/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(5299,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)],[868]) ).
thf(629,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(4196,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_lattice3 @ A )
=> ~ ( v3_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k16_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(6180,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k16_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(419,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(3178,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(453,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relset_1) ).
thf(3348,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r4_lattice3 @ B @ C @ A )
<=> ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattice3) ).
thf(2156,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r4_lattice3 @ B @ C @ A )
=> ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) )
& ( ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) )
=> ( r4_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ D @ C )
& ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( D
!= ( k4_tarski @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_grcat_1) ).
thf(5089,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ D @ C )
& ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( D
!= ( k4_tarski @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(572,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 ) ) )
=> ( ! [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 @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_2) ).
thf(3908,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 ) ) )
=> ( ! [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 @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(129,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 ) )
=> ! [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 )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_2) ).
thf(1694,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 ) )
=> ! [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 )
=> ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
= ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(796,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r4_wellord1 @ A @ B )
=> ( r4_wellord1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_wellord1) ).
thf(4965,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r4_wellord1 @ A @ B )
=> ( r4_wellord1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(301,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( v6_lattice3 @ A )
<=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k16_lattice3 @ A @ ( a_3_5_lattice3 @ A @ B @ C ) ) @ ( k3_lattices @ A @ C @ ( k16_lattice3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lattice3) ).
thf(2506,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v6_lattice3 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k16_lattice3 @ A @ ( a_3_5_lattice3 @ A @ B @ C ) ) @ ( k3_lattices @ A @ C @ ( k16_lattice3 @ A @ B ) ) ) ) )
& ( ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k16_lattice3 @ A @ ( a_3_5_lattice3 @ A @ B @ C ) ) @ ( k3_lattices @ A @ C @ ( k16_lattice3 @ A @ B ) ) ) )
=> ( v6_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(933,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v1_lattice3 @ 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_orders_2 @ A @ B @ D )
& ( r1_orders_2 @ A @ C @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_orders_2 @ A @ B @ E )
& ( r1_orders_2 @ A @ C @ E ) )
=> ( r1_orders_2 @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_lattice3) ).
thf(5619,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v1_lattice3 @ 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_orders_2 @ A @ B @ D )
& ( r1_orders_2 @ A @ C @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_orders_2 @ A @ B @ E )
& ( r1_orders_2 @ A @ C @ E ) )
=> ( r1_orders_2 @ A @ D @ E ) ) ) ) ) ) )
& ( ! [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_orders_2 @ A @ B @ D )
& ( r1_orders_2 @ A @ C @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_orders_2 @ A @ B @ E )
& ( r1_orders_2 @ A @ C @ E ) )
=> ( r1_orders_2 @ A @ D @ E ) ) ) ) ) )
=> ( v1_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mssubfam) ).
thf(4084,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(1413,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)],[69]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(1626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(4207,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)],[631]) ).
thf(160,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k7_grcat_1 @ A )
= ( k6_partfun1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_grcat_1) ).
thf(1809,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k7_grcat_1 @ A )
= ( k6_partfun1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(468,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/sandbox/benchmark/theBenchmark.p',t60_setwiseo) ).
thf(3427,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)],[468]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_4) ).
thf(1166,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,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 ) )
=> ( ( ( ( k4_relset_1 @ A @ B @ C )
= ( k4_relset_1 @ A @ B @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_partfun1) ).
thf(1208,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 ) )
=> ( ( ( ( k4_relset_1 @ A @ B @ C )
= ( k4_relset_1 @ A @ B @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(697,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(4529,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(575,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/sandbox/benchmark/theBenchmark.p',t41_lattices) ).
thf(3921,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)],[575]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(3455,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)],[473]) ).
thf(971,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(5807,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
=> ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(1060,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 ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( m2_filter_2 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_filter_2) ).
thf(6132,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 ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( m2_filter_2 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(783,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(4907,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) )
=> ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(399,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/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(3031,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)],[399]) ).
thf(126,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 @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ C )
& ( m2_relset_1 @ E @ A @ C ) )
=> ~ ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( k8_funct_2 @ A @ B @ D @ F )
= ( k8_funct_2 @ A @ B @ D @ G ) )
=> ( ( k8_funct_2 @ A @ C @ E @ F )
= ( k8_funct_2 @ A @ C @ E @ G ) ) ) ) )
& ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ F )
!= E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_borsuk_1) ).
thf(1662,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 @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ C )
& ( m2_relset_1 @ E @ A @ C ) )
=> ~ ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( k8_funct_2 @ A @ B @ D @ F )
= ( k8_funct_2 @ A @ B @ D @ G ) )
=> ( ( k8_funct_2 @ A @ C @ E @ F )
= ( k8_funct_2 @ A @ C @ E @ G ) ) ) ) )
& ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ B @ C )
& ( m2_relset_1 @ F @ B @ C ) )
=> ( ( k7_funct_2 @ A @ B @ C @ D @ F )
!= E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(669,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/sandbox/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(4394,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)],[669]) ).
thf(1101,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/sandbox/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(6276,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)],[1101]) ).
thf(769,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/sandbox/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(4868,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)],[769]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( ( k10_setwiseo @ A @ A @ B @ ( k11_setwiseo @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_setwiseo) ).
thf(1467,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( ( k10_setwiseo @ A @ A @ B @ ( k11_setwiseo @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(645,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(4260,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1080,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice2) ).
thf(6185,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(807,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/sandbox/benchmark/theBenchmark.p',t51_filter_1) ).
thf(5025,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)],[807]) ).
thf(443,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 ) ) )
=> ( ( k3_lattice2 @ A @ B @ C @ D )
= ( k7_setwiseo @ A @ ( u1_struct_0 @ B ) @ ( u1_lattices @ B ) @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice2) ).
thf(3293,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 ) ) )
=> ( ( k3_lattice2 @ A @ B @ C @ D )
= ( k7_setwiseo @ A @ ( u1_struct_0 @ B ) @ ( u1_lattices @ B ) @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(292,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( k15_lattice3 @ A @ B )
= ( k16_lattice3 @ A @ ( a_2_2_lattice3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice3) ).
thf(2471,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( k15_lattice3 @ A @ B )
= ( k16_lattice3 @ A @ ( a_2_2_lattice3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(711,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/sandbox/benchmark/theBenchmark.p',t82_lattice2) ).
thf(4598,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)],[711]) ).
thf(34,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(1277,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_5_quantal1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ E ) )
& ( r2_hidden @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_quantal1) ).
thf(2124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_5_quantal1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ E ) )
& ( r2_hidden @ E @ D ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ E ) )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ A @ ( a_3_5_quantal1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(657,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( B
= ( k16_lattice3 @ A @ C ) )
<=> ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice3) ).
thf(4319,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( B
= ( k16_lattice3 @ A @ C ) )
=> ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) ) )
& ( ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) )
=> ( B
= ( k16_lattice3 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(401,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( v3_lattice3 @ A )
<=> ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_lattice3 @ A @ B @ D )
=> ( r1_orders_2 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_lattice3) ).
thf(3048,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ( ( v3_lattice3 @ A )
=> ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_lattice3 @ A @ B @ D )
=> ( r1_orders_2 @ A @ C @ D ) ) ) ) )
& ( ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_lattice3 @ A @ B @ D )
=> ( r1_orders_2 @ A @ C @ D ) ) ) )
=> ( v3_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(943,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/sandbox/benchmark/theBenchmark.p',t77_lattice2) ).
thf(5678,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)],[943]) ).
thf(1026,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_0) ).
thf(6008,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)],[1026]) ).
thf(1058,axiom,
! [A: $i] :
( ( u1_struct_0 @ ( k2_pcomps_1 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_pcomps_1) ).
thf(6115,plain,
! [A: $i] :
( ( u1_struct_0 @ ( k2_pcomps_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(755,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/sandbox/benchmark/theBenchmark.p',t26_lattice4) ).
thf(4812,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)],[755]) ).
thf(658,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(4336,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_3_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_lattice3) ).
thf(4045,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_3_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(737,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/sandbox/benchmark/theBenchmark.p',t34_lopclset) ).
thf(4749,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)],[737]) ).
thf(1091,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/sandbox/benchmark/theBenchmark.p',t80_filter_0) ).
thf(6249,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)],[1091]) ).
thf(598,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_2 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_2) ).
thf(4035,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_2 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(928,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/sandbox/benchmark/theBenchmark.p',t32_filter_0) ).
thf(5602,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)],[928]) ).
thf(556,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(3842,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1039,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/sandbox/benchmark/theBenchmark.p',t4_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_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)],[1039]) ).
thf(571,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/sandbox/benchmark/theBenchmark.p',t19_filter_0) ).
thf(3904,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)],[571]) ).
thf(699,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(4534,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(58,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(1368,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(379,axiom,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(2850,plain,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(5570,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)],[915]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(1748,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)],[142]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k2_ens_1 @ A )
= ( a_1_1_ens_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ens_1) ).
thf(1798,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k2_ens_1 @ A )
= ( a_1_1_ens_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(5229,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( A = E )
& ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) )
=> ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(266,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_struct_0 @ A )
<=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
thf(2375,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)],[266]) ).
thf(882,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice4 @ A @ B )
= ( k7_setwiseo @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ B @ ( k7_grcat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_lattice4) ).
thf(5388,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice4 @ A @ B )
= ( k7_setwiseo @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ B @ ( k7_grcat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(4272,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)],[648]) ).
thf(792,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
<=> ( v14_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).
thf(4939,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)],[792]) ).
thf(885,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/sandbox/benchmark/theBenchmark.p',t51_lattices) ).
thf(5399,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)],[885]) ).
thf(786,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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(4922,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)],[786]) ).
thf(120,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(1647,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r3_lattice3 @ B @ C @ A )
<=> ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_lattice3) ).
thf(2732,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r3_lattice3 @ B @ C @ A )
=> ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) )
& ( ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) )
=> ( r3_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',fc3_lopclset) ).
thf(1252,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)],[28]) ).
thf(1015,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/sandbox/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(5980,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)],[1015]) ).
thf(339,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_orders_1) ).
thf(2678,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(778,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/sandbox/benchmark/theBenchmark.p',t7_lattice4) ).
thf(4894,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)],[778]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k10_relset_1 @ A @ B @ C @ A )
= ( k5_relset_1 @ A @ B @ C ) )
& ( ( k11_relset_1 @ A @ B @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_relset_1) ).
thf(3058,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( k10_relset_1 @ A @ B @ C @ A )
= ( k5_relset_1 @ A @ B @ C ) )
& ( ( k11_relset_1 @ A @ B @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1065,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/sandbox/benchmark/theBenchmark.p',t48_filter_1) ).
thf(6146,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)],[1065]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(2689,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)],[343]) ).
thf(679,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/sandbox/benchmark/theBenchmark.p',t46_lattice4) ).
thf(4437,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)],[679]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',redefinition_k9_lopclset) ).
thf(1790,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)],[155]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',t62_setwiseo) ).
thf(1300,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)],[43]) ).
thf(403,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v5_monoid_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ? [F: $i] :
( ( m1_subset_1 @ F @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
= D )
& ( ( k2_binop_1 @ A @ A @ A @ B @ F @ C )
= D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_monoid_0) ).
thf(3063,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v5_monoid_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ? [F: $i] :
( ( m1_subset_1 @ F @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
= D )
& ( ( k2_binop_1 @ A @ A @ A @ B @ F @ C )
= D ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ A )
& ? [F: $i] :
( ( m1_subset_1 @ F @ A )
& ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
= D )
& ( ( k2_binop_1 @ A @ A @ A @ B @ F @ C )
= D ) ) ) ) )
=> ( v5_monoid_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(1034,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_0) ).
thf(6037,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)],[1034]) ).
thf(489,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/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(3554,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)],[489]) ).
thf(912,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/sandbox/benchmark/theBenchmark.p',t34_filter_0) ).
thf(5555,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)],[912]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( k4_relset_1 @ A @ A @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_2) ).
thf(1262,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( k4_relset_1 @ A @ A @ B )
= A )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(487,axiom,
! [A: $i] :
( ( v1_funct_1 @ ( k11_setwiseo @ A ) )
& ( v1_funct_2 @ ( k11_setwiseo @ A ) @ A @ ( k5_finsub_1 @ A ) )
& ( m2_relset_1 @ ( k11_setwiseo @ A ) @ A @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_setwiseo) ).
thf(3544,plain,
! [A: $i] :
( ( v1_funct_1 @ ( k11_setwiseo @ A ) )
& ( v1_funct_2 @ ( k11_setwiseo @ A ) @ A @ ( k5_finsub_1 @ A ) )
& ( m2_relset_1 @ ( k11_setwiseo @ A ) @ A @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(909,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_lattice4 @ A @ B )
= ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k7_grcat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_lattice4) ).
thf(5543,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_lattice4 @ A @ B )
= ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k7_grcat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k11_lattice3 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_lattice3) ).
thf(4781,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k11_lattice3 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(619,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(4117,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)],[619]) ).
thf(772,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 ) )
=> ( ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
<=> ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lattice3) ).
thf(4875,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 ) )
=> ( ( ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ D @ A )
& ! [E: $i,F: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( D
= ( k4_tarski @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(2354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ D @ A )
& ! [E: $i,F: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ F @ C )
& ( D
= ( k4_tarski @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(334,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(2656,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(405,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattice3 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ B )
=> ( r1_orders_2 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
thf(3080,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ B )
=> ( r1_orders_2 @ A @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ B )
=> ( r1_orders_2 @ A @ C @ D ) ) )
=> ( r1_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(509,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/sandbox/benchmark/theBenchmark.p',t69_lattice2) ).
thf(3642,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)],[509]) ).
thf(704,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/sandbox/benchmark/theBenchmark.p',t24_filter_0) ).
thf(4561,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)],[704]) ).
thf(671,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/sandbox/benchmark/theBenchmark.p',d5_filter_0) ).
thf(4398,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)],[671]) ).
thf(782,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/sandbox/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(4905,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)],[782]) ).
thf(551,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 ) )
=> ( ( m2_nat_lat @ B @ A )
<=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u2_lattices @ B )
= ( k1_realset1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_lattices @ B )
= ( k1_realset1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_nat_lat) ).
thf(3823,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 ) )
=> ( ( ( m2_nat_lat @ B @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u2_lattices @ B )
= ( k1_realset1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_lattices @ B )
= ( k1_realset1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ B ) ) ) ) )
& ( ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u2_lattices @ B )
= ( k1_realset1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_lattices @ B )
= ( k1_realset1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ B ) ) ) )
=> ( m2_nat_lat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(913,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/sandbox/benchmark/theBenchmark.p',t29_lattices) ).
thf(5560,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)],[913]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(2337,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)],[256]) ).
thf(809,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(5030,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(547,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v1_setwiseo @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ ( k3_binop_1 @ A @ B ) @ C )
= C )
& ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k3_binop_1 @ A @ B ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_setwiseo) ).
thf(3801,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v1_setwiseo @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( k2_binop_1 @ A @ A @ A @ B @ ( k3_binop_1 @ A @ B ) @ C )
= C )
& ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k3_binop_1 @ A @ B ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(871,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/sandbox/benchmark/theBenchmark.p',t18_filter_1) ).
thf(5309,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)],[871]) ).
thf(45,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( 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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( E
= ( k1_realset1 @ C @ B ) )
& ( F
= ( k1_realset1 @ D @ B ) ) )
=> ( ( ( r4_binop_1 @ A @ C @ D )
=> ( r4_binop_1 @ B @ E @ F ) )
& ( ( r5_binop_1 @ A @ C @ D )
=> ( r5_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_filter_2) ).
thf(1317,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( 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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( E
= ( k1_realset1 @ C @ B ) )
& ( F
= ( k1_realset1 @ D @ B ) ) )
=> ( ( ( r4_binop_1 @ A @ C @ D )
=> ( r4_binop_1 @ B @ E @ F ) )
& ( ( r5_binop_1 @ A @ C @ D )
=> ( r5_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(346,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funcop_1) ).
thf(2701,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
= ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(296,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funcop_1) ).
thf(2486,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( v3_binop_1 @ C @ A )
=> ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(639,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/sandbox/benchmark/theBenchmark.p',t8_lattice4) ).
thf(4241,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)],[639]) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(2545,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)],[309]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',t65_partfun1) ).
thf(2599,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)],[322]) ).
thf(558,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
& ( ( u2_lattices @ A )
= ( u1_lattices @ ( k1_lattice2 @ A ) ) )
& ( ( u1_lattices @ A )
= ( u2_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_lattice2) ).
thf(3847,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
& ( ( u2_lattices @ A )
= ( u1_lattices @ ( k1_lattice2 @ A ) ) )
& ( ( u1_lattices @ A )
= ( u2_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',t30_lopclset) ).
thf(1285,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)],[37]) ).
thf(892,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 @ ( k1_lattice2 @ A ) ) ) )
=> ( ( k8_filter_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_filter_2) ).
thf(5450,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 @ ( k1_lattice2 @ A ) ) ) )
=> ( ( k8_filter_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(828,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/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(5106,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)],[828]) ).
thf(291,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r1_tarski @ A @ B )
<=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_orders_1) ).
thf(2468,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r1_tarski @ A @ B )
=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) )
& ( ( r2_hidden @ A @ ( k1_orders_1 @ B ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(1220,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)],[20]) ).
thf(836,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/sandbox/benchmark/theBenchmark.p',t62_filter_1) ).
thf(5147,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)],[836]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r4_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_binop_1) ).
thf(1934,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r4_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) )
=> ( r4_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(942,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/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
thf(5675,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)],[942]) ).
thf(1096,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/sandbox/benchmark/theBenchmark.p',t21_lattice2) ).
thf(6262,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)],[1096]) ).
thf(900,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/sandbox/benchmark/theBenchmark.p',t18_setwiseo) ).
thf(5504,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)],[900]) ).
thf(2579,plain,
~ ( v3_struct_0 @ sk149 ),
inference(cnf,[status(esa)],[2578]) ).
thf(86,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 ) )
=> ( ( r2_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_binop_1) ).
thf(1504,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 ) )
=> ( ( ( r2_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k1_binop_1 @ C @ D @ B )
= D ) )
=> ( r2_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( C = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_funct_2) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( C = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_sysrel) ).
thf(2939,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(2848,plain,
v3_realset2 @ sk182,
inference(cnf,[status(esa)],[2847]) ).
thf(1054,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/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(6105,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)],[1054]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( m1_subset_1 @ ( k10_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(4414,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A ) )
=> ( m1_subset_1 @ ( k10_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1111,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( k6_filter_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_filter_2) ).
thf(6301,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( k6_filter_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ D @ E )
!= ( k1_funct_1 @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_funct_2) ).
thf(1543,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ~ ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
& ( ( k1_funct_1 @ D @ E )
!= ( k1_funct_1 @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(752,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/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(4802,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)],[752]) ).
thf(992,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v14_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_filter_0) ).
thf(5902,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)],[992]) ).
thf(603,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k15_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B )
& ( ( k16_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattice3) ).
thf(4057,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k15_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B )
& ( ( k16_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',d6_realset1) ).
thf(1849,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)],[172]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_1) ).
thf(3652,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(376,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/sandbox/benchmark/theBenchmark.p',t57_lattice2) ).
thf(2838,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)],[376]) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',dt_m1_lattice4) ).
thf(2558,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)],[313]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
<=> ( ( k5_relset_1 @ A @ B @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
thf(2113,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
=> ( ( k5_relset_1 @ A @ B @ C )
= B ) )
& ( ( ( k5_relset_1 @ A @ B @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(956,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(5736,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(280,axiom,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(2426,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( g1_orders_2 @ A @ B )
= ( g1_orders_2 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(1536,plain,
! [A: $i,B: $i] :
( ( m1_relset_1 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( g1_orders_2 @ A @ B )
= ( g1_orders_2 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(198,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(1981,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k16_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k16_filter_2) ).
thf(5998,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k16_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(456,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
thf(3356,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_funct_1 @ ( k7_grcat_1 @ A ) )
& ( v1_funct_2 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k7_grcat_1 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( m1_subset_1 @ ( k9_domain_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(5240,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( m1_subset_1 @ ( k9_domain_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(348,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r8_relat_2 @ A @ B )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
thf(2711,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r8_relat_2 @ A @ B )
=> ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ C @ E ) @ A ) ) )
& ( ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ C @ E ) @ A ) )
=> ( r8_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1083,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/sandbox/benchmark/theBenchmark.p',t17_lattice4) ).
thf(6193,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)],[1083]) ).
thf(893,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/sandbox/benchmark/theBenchmark.p',t39_lattice4) ).
thf(5453,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)],[893]) ).
thf(623,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/sandbox/benchmark/theBenchmark.p',redefinition_k1_filter_1) ).
thf(4143,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)],[623]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(1585,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)],[104]) ).
thf(1140,plain,
~ ( m2_filter_2 @ ( u1_struct_0 @ sk1 ) @ sk1 ),
inference(cnf,[status(esa)],[1139]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_lattice3 @ B ) ) )
=> ( ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ C )
<=> ( r4_lattice3 @ B @ ( k5_lattice3 @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice3) ).
thf(4838,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_lattice3 @ B ) ) )
=> ( ( ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ C )
=> ( r4_lattice3 @ B @ ( k5_lattice3 @ B @ C ) @ A ) )
& ( ( r4_lattice3 @ B @ ( k5_lattice3 @ B @ C ) @ A )
=> ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(1090,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/sandbox/benchmark/theBenchmark.p',idempotence_k1_filter_1) ).
thf(6245,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)],[1090]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k13_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_filter_2) ).
thf(6161,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k13_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(414,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k2_setwiseo @ B @ E ) @ D )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_setwiseo) ).
thf(3156,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k2_setwiseo @ B @ E ) @ D )
= ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(826,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ! [B: $i] :
( ( l3_lattices @ B )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k1_lattice2 @ A )
= ( k1_lattice2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_filter_2) ).
thf(5100,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ! [B: $i] :
( ( l3_lattices @ B )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k1_lattice2 @ A )
= ( k1_lattice2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(750,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/sandbox/benchmark/theBenchmark.p',t37_filter_1) ).
thf(4795,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)],[750]) ).
thf(383,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( ( v1_funct_1 @ ( u1_lattices @ A ) )
& ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(2875,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( ( v1_funct_1 @ ( u1_lattices @ A ) )
& ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(794,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_2 @ ( k3_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_filter_2) ).
thf(4945,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_2 @ ( k3_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(163,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(1817,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)],[163]) ).
thf(1062,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/sandbox/benchmark/theBenchmark.p',t53_lattice2) ).
thf(6137,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)],[1062]) ).
thf(259,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k4_setwiseo @ B @ E @ F @ G ) @ D )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ A @ D @ F ) ) @ ( k8_funct_2 @ B @ A @ D @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_setwiseo) ).
thf(2347,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( v3_binop_1 @ C @ A )
& ( v1_binop_1 @ C @ A )
& ( v2_binop_1 @ C @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k7_setwiseo @ B @ A @ C @ ( k4_setwiseo @ B @ E @ F @ G ) @ D )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ A @ D @ F ) ) @ ( k8_funct_2 @ B @ A @ D @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(578,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k5_lattices @ A )
= ( k5_lattices @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_filter_2) ).
thf(3928,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k5_lattices @ A )
= ( k5_lattices @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_orders_2 @ A @ B @ C )
<=> ( r1_orders_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
thf(1575,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r3_orders_2 @ A @ B @ C )
=> ( r1_orders_2 @ A @ B @ C ) )
& ( ( r1_orders_2 @ A @ B @ C )
=> ( r3_orders_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(546,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( ( v1_funct_1 @ ( u2_lattices @ A ) )
& ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(3797,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( ( v1_funct_1 @ ( u2_lattices @ A ) )
& ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(284,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_tarski @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(2435,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
~ ( ( ( r2_hidden @ C @ A )
| ( r2_hidden @ D @ A ) )
& ( B
= ( k4_tarski @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(716,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/sandbox/benchmark/theBenchmark.p',t46_filter_0) ).
thf(4639,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)],[716]) ).
thf(356,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 ) ) )
=> ( ( D != k1_xboole_0 )
=> ( ( k4_lattices @ A @ B @ ( k3_lattice2 @ C @ A @ D @ E ) )
= ( k3_lattice2 @ C @ A @ D @ ( k8_funcop_1 @ ( u1_struct_0 @ A ) @ C @ ( u1_lattices @ A ) @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_lattice2) ).
thf(2760,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 ) ) )
=> ( ( D != k1_xboole_0 )
=> ( ( k4_lattices @ A @ B @ ( k3_lattice2 @ C @ A @ D @ E ) )
= ( k3_lattice2 @ C @ A @ D @ ( k8_funcop_1 @ ( u1_struct_0 @ A ) @ C @ ( u1_lattices @ A ) @ B @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(71,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(1421,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)],[71]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( k4_relset_1 @ A @ B @ C )
= A )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_funct_2) ).
thf(3400,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( k4_relset_1 @ A @ B @ C )
= A )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(622,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/sandbox/benchmark/theBenchmark.p',t56_filter_0) ).
thf(4138,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)],[622]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',t85_funct_2) ).
thf(1649,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)],[121]) ).
thf(295,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ C @ D ) @ B ) @ ( k2_ens_1 @ A ) )
=> ( ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ C @ D )
& ( m2_relset_1 @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ens_1) ).
thf(2479,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ C @ D ) @ B ) @ ( k2_ens_1 @ A ) )
=> ( ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ C @ D )
& ( m2_relset_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ B )
| ~ ( v10_lattices @ B )
| ~ ( v17_lattices @ B )
| ( v3_realset2 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
| ( m1_filter_0 @ ( sk2 @ C @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[1144]) ).
thf(6410,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ B )
| ~ ( v17_lattices @ B )
| ( v3_realset2 @ B )
| ~ ( l3_lattices @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
| ( m1_filter_0 @ ( sk2 @ C @ B @ A ) @ B )
| ( ( v10_lattices @ sk1 )
!= ( v10_lattices @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1142,1148]) ).
thf(6411,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( l3_lattices @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( m1_filter_0 @ ( sk2 @ B @ sk1 @ A ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[6410:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(6416,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( l3_lattices @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( m1_filter_0 @ ( sk2 @ B @ sk1 @ A ) @ sk1 ) ),
inference(simp,[status(thm)],[6411]) ).
thf(6424,plain,
! [B: $i,A: $i] :
( $false
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ $true
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( m1_filter_0 @ ( sk2 @ B @ sk1 @ A ) @ sk1 ) ),
inference(rewrite,[status(thm)],[6416,1141,1143]) ).
thf(6425,plain,
! [B: $i,A: $i] :
( ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ sk1 ) )
| ~ ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ sk1 ) @ B ) )
| ( m1_filter_0 @ ( sk2 @ B @ sk1 @ A ) @ sk1 ) ),
inference(simp,[status(thm)],[6424]) ).
thf(960,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/sandbox/benchmark/theBenchmark.p',d8_filter_0) ).
thf(5749,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)],[960]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).
thf(2045,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)],[209]) ).
thf(195,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funcop_1) ).
thf(1949,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(4763,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)],[741]) ).
thf(5,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v5_lattice3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_lattice3) ).
thf(1157,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v5_lattice3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(675,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/sandbox/benchmark/theBenchmark.p',t17_relset_1) ).
thf(4419,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)],[675]) ).
thf(485,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(3533,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(5966,plain,
~ ( v3_struct_0 @ sk489 ),
inference(cnf,[status(esa)],[5965]) ).
thf(719,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice3) ).
thf(4646,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(994,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 ) ) )
=> ( ~ ( v1_xboole_0 @ ( k22_filter_2 @ A @ B @ C ) )
& ( m2_lattice4 @ ( k22_filter_2 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k22_filter_2) ).
thf(5907,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 ) ) )
=> ( ~ ( v1_xboole_0 @ ( k22_filter_2 @ A @ B @ C ) )
& ( m2_lattice4 @ ( k22_filter_2 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(613,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_tarski @ ( k1_ens_1 @ B ) @ ( k1_ens_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ens_1) ).
thf(4102,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_tarski @ ( k1_ens_1 @ B ) @ ( k1_ens_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',t60_lattice2) ).
thf(2187,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)],[239]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',t79_funct_2) ).
thf(1189,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)],[12]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',t8_funct_2) ).
thf(1866,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)],[177]) ).
thf(360,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 ) )
=> ( ( k4_filter_2 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_filter_2) ).
thf(2775,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 ) )
=> ( ( k4_filter_2 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(364,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
= ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funcop_1) ).
thf(2792,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
= ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(1807,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)],[159]) ).
thf(842,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/sandbox/benchmark/theBenchmark.p',dt_k5_filter_1) ).
thf(5184,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)],[842]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( ( k1_domain_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(2907,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ B ) )
=> ( ( k1_domain_1 @ A @ B @ C @ D )
= ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(285,axiom,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_1) ).
thf(2443,plain,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1047,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u1_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattice2) ).
thf(6077,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u1_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(229,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(2135,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)],[229]) ).
thf(609,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/sandbox/benchmark/theBenchmark.p',t24_lattice4) ).
thf(4089,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)],[609]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
=> ( ( r1_tarski @ B @ ( k4_relset_1 @ A @ B @ C ) )
& ( B
= ( k5_relset_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relset_1) ).
thf(3336,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
=> ( ( r1_tarski @ B @ ( k4_relset_1 @ A @ B @ C ) )
& ( B
= ( k5_relset_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(1745,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(538,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/sandbox/benchmark/theBenchmark.p',t26_lopclset) ).
thf(3748,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)],[538]) ).
thf(282,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/sandbox/benchmark/theBenchmark.p',dt_k5_setwiseo) ).
thf(2431,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)],[282]) ).
thf(774,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice4 @ A @ B )
= ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k7_grcat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_lattice4) ).
thf(4881,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice4 @ A @ B )
= ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k7_grcat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(4823,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)],[759]) ).
thf(543,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/sandbox/benchmark/theBenchmark.p',t15_setwiseo) ).
thf(3780,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)],[543]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_partfun1) ).
thf(2934,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)],[392]) ).
thf(859,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/sandbox/benchmark/theBenchmark.p',t52_lattice2) ).
thf(5258,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)],[859]) ).
thf(321,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v2_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_binop_1) ).
thf(2591,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v2_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) )
=> ( v2_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funcop_1) ).
thf(1590,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ( v2_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
= ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(816,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/sandbox/benchmark/theBenchmark.p',t6_lattice4) ).
thf(5055,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)],[816]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(2283,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)],[246]) ).
thf(753,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/sandbox/benchmark/theBenchmark.p',t62_filter_0) ).
thf(4806,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)],[753]) ).
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_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/sandbox/benchmark/theBenchmark.p',t5_filter_0) ).
thf(6341,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)],[1122]) ).
thf(3482,plain,
( ( v1_funct_1 @ k1_xboole_0 )
& ! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
inference(miniscope,[status(thm)],[3481]) ).
thf(3484,plain,
v1_funct_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[3482]) ).
thf(726,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4681,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(844,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/sandbox/benchmark/theBenchmark.p',t78_lattice2) ).
thf(5191,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)],[844]) ).
thf(969,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/sandbox/benchmark/theBenchmark.p',d6_lattice2) ).
thf(5800,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)],[969]) ).
thf(831,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/sandbox/benchmark/theBenchmark.p',t52_filter_0) ).
thf(5132,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)],[831]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).
thf(1481,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)],[79]) ).
thf(727,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/sandbox/benchmark/theBenchmark.p',fc2_filter_1) ).
thf(4683,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)],[727]) ).
thf(461,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( C
= ( k8_filter_0 @ A @ B ) )
<=> ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ? [E: $i] :
( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( D
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( E
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) )
& ( C
= ( g3_lattices @ B @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_filter_0) ).
thf(3369,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( C
= ( k8_filter_0 @ A @ B ) )
=> ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ? [E: $i] :
( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( D
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( E
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) )
& ( C
= ( g3_lattices @ B @ D @ E ) ) ) ) )
& ( ? [D: $i] :
( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ? [E: $i] :
( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( D
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( E
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) )
& ( C
= ( g3_lattices @ B @ D @ E ) ) ) )
=> ( C
= ( k8_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(2823,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(702,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/sandbox/benchmark/theBenchmark.p',t59_filter_0) ).
thf(4542,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)],[702]) ).
thf(748,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/sandbox/benchmark/theBenchmark.p',t14_setwiseo) ).
thf(4791,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)],[748]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funcop_1) ).
thf(1629,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ 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 @ B )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v1_funct_2 @ C @ A @ B )
<=> ( A
= ( k4_relset_1 @ A @ B @ C ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( ( v1_funct_2 @ C @ A @ B )
<=> ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
thf(3501,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( v1_funct_2 @ C @ A @ B )
=> ( A
= ( k4_relset_1 @ A @ B @ C ) ) )
& ( ( A
= ( k4_relset_1 @ A @ B @ C ) )
=> ( v1_funct_2 @ C @ A @ B ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( ( ( v1_funct_2 @ C @ A @ B )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(884,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relset_1) ).
thf(5394,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
& ( r2_hidden @ F @ B ) )
=> ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(822,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/sandbox/benchmark/theBenchmark.p',t20_filter_1) ).
thf(5087,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)],[822]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',t38_funct_2) ).
thf(1523,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)],[90]) ).
thf(561,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/sandbox/benchmark/theBenchmark.p',d9_filter_0) ).
thf(3859,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)],[561]) ).
thf(999,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/sandbox/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(5922,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)],[999]) ).
thf(406,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_orders_2 @ A @ B @ C )
<=> ( r1_orders_2 @ ( k7_lattice3 @ A ) @ ( k8_lattice3 @ A @ C ) @ ( k8_lattice3 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_lattice3) ).
thf(3085,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_orders_2 @ A @ B @ C )
=> ( r1_orders_2 @ ( k7_lattice3 @ A ) @ ( k8_lattice3 @ A @ C ) @ ( k8_lattice3 @ A @ B ) ) )
& ( ( r1_orders_2 @ ( k7_lattice3 @ A ) @ ( k8_lattice3 @ A @ C ) @ ( k8_lattice3 @ A @ B ) )
=> ( r1_orders_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(682,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/sandbox/benchmark/theBenchmark.p',t43_filter_1) ).
thf(4451,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)],[682]) ).
thf(927,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r4_wellord1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_wellord1) ).
thf(5600,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r4_wellord1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(396,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( v3_binop_1 @ C @ B )
& ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B ) )
=> ( ( ( D = k1_xboole_0 )
& ~ ( v1_setwiseo @ C @ B ) )
| ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( F
= ( k7_setwiseo @ A @ B @ C @ D @ E ) )
<=> ? [G: $i] :
( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( F
= ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ( ( r3_binop_1 @ B @ H @ C )
=> ( ( k1_funct_1 @ G @ k1_xboole_0 )
= H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
= ( k8_funct_2 @ A @ B @ E @ H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( r1_tarski @ H @ D )
=> ( ( H = k1_xboole_0 )
| ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( r2_hidden @ I @ D )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_setwiseo) ).
thf(2944,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( v3_binop_1 @ C @ B )
& ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B ) )
=> ( ( ( D = k1_xboole_0 )
& ~ ( v1_setwiseo @ C @ B ) )
| ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( ( F
= ( k7_setwiseo @ A @ B @ C @ D @ E ) )
=> ? [G: $i] :
( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( F
= ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ( ( r3_binop_1 @ B @ H @ C )
=> ( ( k1_funct_1 @ G @ k1_xboole_0 )
= H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
= ( k8_funct_2 @ A @ B @ E @ H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( r1_tarski @ H @ D )
=> ( ( H = k1_xboole_0 )
| ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( r2_hidden @ I @ D )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( v1_funct_1 @ G )
& ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
& ( F
= ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ B )
=> ( ( r3_binop_1 @ B @ H @ C )
=> ( ( k1_funct_1 @ G @ k1_xboole_0 )
= H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ A )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
= ( k8_funct_2 @ A @ B @ E @ H ) ) )
& ! [H: $i] :
( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
=> ( ( r1_tarski @ H @ D )
=> ( ( H = k1_xboole_0 )
| ! [I: $i] :
( ( m1_subset_1 @ I @ A )
=> ( ( r2_hidden @ I @ D )
=> ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) )
=> ( F
= ( k7_setwiseo @ A @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1009,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_lattice4) ).
thf(5963,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)],[1009]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ B @ D ) )
=> ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_partfun1) ).
thf(1689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ B @ D ) )
=> ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(270,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( 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 @ ( k8_setwiseo @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ C @ B ) @ D )
= ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattice4) ).
thf(2384,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( 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 @ ( k8_setwiseo @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ C @ B ) @ D )
= ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(720,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relset_1) ).
thf(4649,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
& ( r2_hidden @ F @ B ) )
=> ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(625,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 ) ) ) )
=> ( ( k3_filter_2 @ A @ B )
= ( k3_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
thf(4153,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 ) ) ) )
=> ( ( k3_filter_2 @ A @ B )
= ( k3_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(806,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_tarski @ ( k2_ens_1 @ B ) @ ( k2_ens_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ens_1) ).
thf(5023,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_tarski @ ( k2_ens_1 @ B ) @ ( k2_ens_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(340,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/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(2680,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)],[340]) ).
thf(112,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice3) ).
thf(1607,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r3_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) )
=> ( r3_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',t56_setwiseo) ).
thf(2421,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)],[278]) ).
thf(557,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
<=> ( v13_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_lattice2) ).
thf(3844,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)],[557]) ).
thf(469,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/sandbox/benchmark/theBenchmark.p',d19_lattices) ).
thf(3430,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)],[469]) ).
thf(1059,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/sandbox/benchmark/theBenchmark.p',d4_filter_0) ).
thf(6118,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)],[1059]) ).
thf(152,axiom,
! [A: $i] :
( ( r1_relat_2 @ ( k6_partfun1 @ A ) @ A )
& ( r3_relat_2 @ ( k6_partfun1 @ A ) @ A )
& ( r8_relat_2 @ ( k6_partfun1 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_eqrel_1) ).
thf(1777,plain,
! [A: $i] :
( ( r1_relat_2 @ ( k6_partfun1 @ A ) @ A )
& ( r3_relat_2 @ ( k6_partfun1 @ A ) @ A )
& ( r8_relat_2 @ ( k6_partfun1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(651,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/sandbox/benchmark/theBenchmark.p',t49_lattice4) ).
thf(4299,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)],[651]) ).
thf(1037,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/sandbox/benchmark/theBenchmark.p',t26_filter_0) ).
thf(6045,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)],[1037]) ).
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 ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
<=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattice3) ).
thf(5040,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_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) )
& ( ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
=> ( r3_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(454,axiom,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_relat_1) ).
thf(3351,plain,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(592,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/sandbox/benchmark/theBenchmark.p',t84_lattice2) ).
thf(3993,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)],[592]) ).
thf(957,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/sandbox/benchmark/theBenchmark.p',t37_lattice4) ).
thf(5739,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)],[957]) ).
thf(835,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/sandbox/benchmark/theBenchmark.p',t81_filter_0) ).
thf(5144,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)],[835]) ).
thf(207,axiom,
! [A: $i] :
( ( v1_funct_1 @ ( k9_setwiseo @ A ) )
& ( v1_funct_2 @ ( k9_setwiseo @ A ) @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) )
& ( m2_relset_1 @ ( k9_setwiseo @ A ) @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_setwiseo) ).
thf(2036,plain,
! [A: $i] :
( ( v1_funct_1 @ ( k9_setwiseo @ A ) )
& ( v1_funct_2 @ ( k9_setwiseo @ A ) @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) )
& ( m2_relset_1 @ ( k9_setwiseo @ A ) @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(510,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r7_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_binop_1) ).
thf(3645,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r7_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) )
=> ( r7_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(299,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 ) )
& ! [G: $i,H: $i] :
( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
<=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(2494,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 ) )
& ! [G: $i,H: $i] :
( ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) )
& ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ D )
=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ A ) ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(846,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 @ ( k1_lattice2 @ A ) ) ) ) )
=> ~ ( v1_xboole_0 @ ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_filter_2) ).
thf(5196,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 @ ( k1_lattice2 @ A ) ) ) ) )
=> ~ ( v1_xboole_0 @ ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mssubfam) ).
thf(5194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(788,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/sandbox/benchmark/theBenchmark.p',t18_filter_0) ).
thf(4927,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)],[788]) ).
thf(1085,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_nat_lat @ B @ A ) )
=> ( ( k24_filter_2 @ A @ B )
= ( k1_lattice2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k24_filter_2) ).
thf(6198,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_nat_lat @ B @ A ) )
=> ( ( k24_filter_2 @ A @ B )
= ( k1_lattice2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(982,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_filter_2 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).
thf(5864,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_filter_2 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( r1_filter_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(663,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r7_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_2) ).
thf(4356,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r7_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r7_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m2_filter_2 @ ( k14_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_filter_2) ).
thf(6361,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m2_filter_2 @ ( k14_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(907,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
<=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(5537,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r1_tarski @ A @ B )
=> ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
& ( ! [C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(304,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/sandbox/benchmark/theBenchmark.p',t37_lopclset) ).
thf(2522,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)],[304]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_3_5_lattice3 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_lattice3) ).
thf(5371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_5_lattice3 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k3_lattices @ B @ D @ E ) )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( a_3_5_lattice3 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(664,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/sandbox/benchmark/theBenchmark.p',t73_filter_0) ).
thf(4367,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)],[664]) ).
thf(417,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r6_binop_1 @ A @ C @ B )
<=> ( r5_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_binop_1) ).
thf(3164,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r6_binop_1 @ A @ C @ B )
=> ( r5_binop_1 @ A @ C @ B ) )
& ( ( r5_binop_1 @ A @ C @ B )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1118,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
<=> ( m1_filter_2 @ B @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).
thf(6326,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( m2_filter_2 @ B @ A )
=> ( m1_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
& ( ( m1_filter_2 @ B @ ( k1_lattice2 @ A ) )
=> ( m2_filter_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(803,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/sandbox/benchmark/theBenchmark.p',t18_lopclset) ).
thf(5009,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)],[803]) ).
thf(303,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k8_funct_2 @ A @ B @ F @ G )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
=> ( F
= ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funcop_1) ).
thf(2517,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ A @ B )
& ( m2_relset_1 @ F @ A @ B ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( k8_funct_2 @ A @ B @ F @ G )
= ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
=> ( F
= ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k7_filter_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_2) ).
thf(5728,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k7_filter_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( ( k6_setwiseo @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setwiseo) ).
thf(1725,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( ( k6_setwiseo @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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 @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funcop_1) ).
thf(1280,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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 @ B @ B )
& ( m2_relset_1 @ E @ B @ B ) )
=> ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
= ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(1578,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)],[103]) ).
thf(1086,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/sandbox/benchmark/theBenchmark.p',t39_filter_1) ).
thf(6201,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)],[1086]) ).
thf(731,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/sandbox/benchmark/theBenchmark.p',t43_lattice2) ).
thf(4706,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)],[731]) ).
thf(723,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r3_binop_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) @ ( u1_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_lattice2) ).
thf(4670,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r3_binop_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) @ ( u1_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1012,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_filter_2 @ A @ B )
= ( k2_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
thf(5971,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_filter_2 @ A @ B )
= ( k2_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ! [C: $i] :
( ( m2_filter_1 @ 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/sandbox/benchmark/theBenchmark.p',dt_m2_filter_1) ).
thf(3232,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ! [C: $i] :
( ( m2_filter_1 @ 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)],[431]) ).
thf(754,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ B ) )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_relat_1) ).
thf(4809,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k4_tarski @ C @ C ) @ B ) )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(563,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/sandbox/benchmark/theBenchmark.p',t83_filter_0) ).
thf(3865,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)],[563]) ).
thf(861,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/sandbox/benchmark/theBenchmark.p',d6_filter_0) ).
thf(5268,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)],[861]) ).
thf(500,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k5_finsub_1 @ A ) )
& ( m2_relset_1 @ B @ A @ ( k5_finsub_1 @ A ) ) )
=> ( ( B
= ( k11_setwiseo @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ B @ C )
= ( k2_setwiseo @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_setwiseo) ).
thf(3601,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ ( k5_finsub_1 @ A ) )
& ( m2_relset_1 @ B @ A @ ( k5_finsub_1 @ A ) ) )
=> ( ( ( B
= ( k11_setwiseo @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ B @ C )
= ( k2_setwiseo @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ B @ C )
= ( k2_setwiseo @ A @ C ) ) )
=> ( B
= ( k11_setwiseo @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(1593,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)],[107]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_1_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattice3 @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice3) ).
thf(2604,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattice3 @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattice3 @ B @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_1_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(765,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/sandbox/benchmark/theBenchmark.p',t51_filter_0) ).
thf(4843,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)],[765]) ).
thf(482,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( 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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( E
= ( k1_realset1 @ C @ B ) )
& ( F
= ( k1_realset1 @ D @ B ) )
& ( r1_lattice2 @ A @ C @ D ) )
=> ( r1_lattice2 @ B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_filter_2) ).
thf(3521,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( 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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( E
= ( k1_realset1 @ C @ B ) )
& ( F
= ( k1_realset1 @ D @ B ) )
& ( r1_lattice2 @ A @ C @ D ) )
=> ( r1_lattice2 @ B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',t25_funct_2) ).
thf(1303,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)],[44]) ).
thf(764,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_domain_1) ).
thf(4841,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(903,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/sandbox/benchmark/theBenchmark.p',t40_lattice4) ).
thf(5522,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)],[903]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun1) ).
thf(1757,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)],[145]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m2_lattice4 @ ( k11_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_filter_2) ).
thf(6150,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m2_lattice4 @ ( k11_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(683,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/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).
thf(4455,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)],[683]) ).
thf(1001,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/sandbox/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(5926,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)],[1001]) ).
thf(591,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/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).
thf(3982,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)],[591]) ).
thf(624,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r2_relat_2 @ A @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_2) ).
thf(4146,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r2_relat_2 @ A @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) )
=> ( r2_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(569,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/sandbox/benchmark/theBenchmark.p',t88_filter_0) ).
thf(3897,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)],[569]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_sysrel) ).
thf(1363,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1019,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/sandbox/benchmark/theBenchmark.p',dt_k1_filter_1) ).
thf(5990,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)],[1019]) ).
thf(686,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/sandbox/benchmark/theBenchmark.p',t45_lattice4) ).
thf(4474,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)],[686]) ).
thf(353,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(2746,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(1172,plain,
v1_xboole_0 @ sk3,
inference(cnf,[status(esa)],[1171]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',t59_funct_2) ).
thf(1288,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)],[38]) ).
thf(423,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r1_tarski @ ( k2_ens_1 @ A ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_ens_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ens_1) ).
thf(3196,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r1_tarski @ ( k2_ens_1 @ A ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_ens_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(541,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/sandbox/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(3765,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)],[541]) ).
thf(365,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_1) ).
thf(2795,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r1_tarski @ B @ D ) )
=> ( ( C = k1_xboole_0 )
| ( r1_tarski @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mssubfam) ).
thf(2619,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r1_tarski @ B @ D ) )
=> ( ( C = k1_xboole_0 )
| ( r1_tarski @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1035,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ A ) )
=> ( m2_lattice4 @ ( k9_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_2) ).
thf(6040,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ A ) )
=> ( m2_lattice4 @ ( k9_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(1098,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/sandbox/benchmark/theBenchmark.p',t82_filter_0) ).
thf(6269,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)],[1098]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r1_relat_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_orders_1) ).
thf(2800,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r1_relat_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(584,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 ) ) )
=> ( ! [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 ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_2) ).
thf(3956,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 ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(738,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(4755,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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 ) )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
= ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funcop_1) ).
thf(1657,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [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 ) )
=> ( ( v1_binop_1 @ C @ B )
=> ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
= ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1108,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(6294,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)],[1108]) ).
thf(950,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/sandbox/benchmark/theBenchmark.p',t45_filter_0) ).
thf(5709,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)],[950]) ).
thf(440,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( v5_orders_2 @ ( k2_struct_0 @ A @ B @ C ) @ A )
& ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
<=> ( ( r3_orders_2 @ A @ B @ C )
| ( r3_orders_2 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_orders_2) ).
thf(3277,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( v5_orders_2 @ ( k2_struct_0 @ A @ B @ C ) @ A )
& ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r3_orders_2 @ A @ B @ C )
| ( r3_orders_2 @ A @ C @ B ) ) )
& ( ( ( r3_orders_2 @ A @ B @ C )
| ( r3_orders_2 @ A @ C @ B ) )
=> ( ( v5_orders_2 @ ( k2_struct_0 @ A @ B @ C ) @ A )
& ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(805,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relset_1) ).
thf(5019,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
=> ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(4024,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)],[597]) ).
thf(528,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] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( k4_lattices @ C @ E @ ( k2_lattice2 @ A @ C @ B @ D ) )
= ( k2_lattice2 @ A @ C @ B @ ( k8_funcop_1 @ ( u1_struct_0 @ C ) @ A @ ( u1_lattices @ C ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_lattice2) ).
thf(3716,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] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ( k4_lattices @ C @ E @ ( k2_lattice2 @ A @ C @ B @ D ) )
= ( k2_lattice2 @ A @ C @ B @ ( k8_funcop_1 @ ( u1_struct_0 @ C ) @ A @ ( u1_lattices @ C ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(97,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r5_binop_1 @ A @ C @ B )
<=> ( r4_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_binop_1) ).
thf(1561,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r5_binop_1 @ A @ C @ B )
=> ( r4_binop_1 @ A @ C @ B ) )
& ( ( r4_binop_1 @ A @ C @ B )
=> ( r5_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(347,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/sandbox/benchmark/theBenchmark.p',t61_lattice2) ).
thf(2704,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)],[347]) ).
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 ) )
=> ( ( m2_filter_2 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v13_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_2) ).
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 ) )
=> ( ( m2_filter_2 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v13_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k10_relset_1 @ B @ A @ C @ ( k11_relset_1 @ B @ A @ C @ A ) )
= ( k5_relset_1 @ B @ A @ C ) )
& ( ( k11_relset_1 @ B @ A @ C @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k4_relset_1 @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_relset_1) ).
thf(2404,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( ( k10_relset_1 @ B @ A @ C @ ( k11_relset_1 @ B @ A @ C @ A ) )
= ( k5_relset_1 @ B @ A @ C ) )
& ( ( k11_relset_1 @ B @ A @ C @ ( k10_relset_1 @ B @ A @ C @ B ) )
= ( k4_relset_1 @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(5586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(841,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_lopclset) ).
thf(5176,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) )
=> ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(848,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/sandbox/benchmark/theBenchmark.p',dt_k10_filter_0) ).
thf(5200,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)],[848]) ).
thf(515,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/sandbox/benchmark/theBenchmark.p',t58_partfun1) ).
thf(3673,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)],[515]) ).
thf(1100,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/sandbox/benchmark/theBenchmark.p',t23_filter_0) ).
thf(6273,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)],[1100]) ).
thf(363,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [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_filter_1 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
& ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_1) ).
thf(2783,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [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_filter_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
& ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
& ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) )
=> ( m2_filter_1 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(875,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(5324,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1126,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/sandbox/benchmark/theBenchmark.p',t42_filter_1) ).
thf(6351,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)],[1126]) ).
thf(899,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 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_mssubfam) ).
thf(5500,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 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( B
= ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ D ) )
=> ( ( k8_setfam_1 @ A @ B )
= ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(167,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 @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r7_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_binop_1) ).
thf(1829,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 @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r7_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
= ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
=> ( r7_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(838,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( m2_card_fil @ B @ A )
<=> ( ~ ( r2_hidden @ A @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
& ( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_card_fil) ).
thf(5151,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( ( m2_card_fil @ B @ A )
=> ( ~ ( r2_hidden @ A @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
& ( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) )
& ( ( ~ ( r2_hidden @ A @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
& ( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_card_fil @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(457,axiom,
! [A: $i] : ( v4_lattice3 @ ( k1_lattice3 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_lattice3) ).
thf(3360,plain,
! [A: $i] : ( v4_lattice3 @ ( k1_lattice3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(1135,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_lattice3 @ ( k3_lattice3 @ A ) )
& ( v2_lattice3 @ ( k3_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_lattice3) ).
thf(6373,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_lattice3 @ ( k3_lattice3 @ A ) )
& ( v2_lattice3 @ ( k3_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(476,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(3489,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(761,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/sandbox/benchmark/theBenchmark.p',t36_filter_1) ).
thf(4831,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)],[761]) ).
thf(963,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/sandbox/benchmark/theBenchmark.p',t68_filter_0) ).
thf(5774,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)],[963]) ).
thf(1056,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/sandbox/benchmark/theBenchmark.p',t49_filter_1) ).
thf(6109,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)],[1056]) ).
thf(184,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r4_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_binop_1) ).
thf(1902,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r4_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) ) ) ) )
=> ( r4_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1088,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/sandbox/benchmark/theBenchmark.p',t19_lattices) ).
thf(6222,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)],[1088]) ).
thf(978,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/sandbox/benchmark/theBenchmark.p',dt_k7_lopclset) ).
thf(5845,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)],[978]) ).
thf(235,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r6_binop_1 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
& ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_binop_1) ).
thf(2159,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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( r6_binop_1 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
& ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
& ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) )
=> ( r6_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(458,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/sandbox/benchmark/theBenchmark.p',dt_k2_lattice2) ).
thf(3362,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)],[458]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',t5_lattice2) ).
thf(1268,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)],[33]) ).
thf(523,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/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(3701,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)],[523]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',t28_relat_1) ).
thf(1532,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)],[91]) ).
thf(751,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/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(4799,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)],[751]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_2_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r4_lattice3 @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
thf(3570,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v4_lattice3 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r4_lattice3 @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r4_lattice3 @ B @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_2_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) )
<=> ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_1) ).
thf(1384,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [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] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) )
=> ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(542,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( r6_binop_1 @ A @ C @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_binop_1) ).
thf(3772,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v1_binop_1 @ C @ A )
=> ( ( ( r6_binop_1 @ A @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r4_lattice3 @ B @ C @ A )
<=> ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice3) ).
thf(5061,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r4_lattice3 @ B @ C @ A )
=> ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) ) )
& ( ( r2_lattice3 @ ( k3_lattice3 @ B ) @ A @ ( k4_lattice3 @ B @ C ) )
=> ( r4_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',d7_lopclset) ).
thf(1357,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)],[54]) ).
thf(436,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( v1_binop_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_binop_1) ).
thf(3259,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 ) )
=> ( ( ( v1_binop_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
= ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) )
=> ( v1_binop_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funcop_1) ).
thf(1500,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m1_relset_1 @ D @ B @ A )
& ( m1_subset_1 @ E @ A ) )
=> ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
& ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
& ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(434,axiom,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ~ ( ? [D: $i] :
( ( v5_orders_2 @ D @ A )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
& ~ ( r1_orders_2 @ A @ B @ C )
& ~ ( r1_orders_2 @ A @ C @ B ) )
& ~ ( ( ( r1_orders_2 @ A @ B @ C )
| ( r1_orders_2 @ A @ C @ B ) )
& ! [D: $i] :
( ( ( v5_orders_2 @ D @ A )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_orders_2) ).
thf(3245,plain,
! [A: $i] :
( ( ( v2_orders_2 @ A )
& ( l1_orders_2 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ~ ( ? [D: $i] :
( ( v5_orders_2 @ D @ A )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
& ~ ( r1_orders_2 @ A @ B @ C )
& ~ ( r1_orders_2 @ A @ C @ B ) )
& ~ ( ( ( r1_orders_2 @ A @ B @ C )
| ( r1_orders_2 @ A @ C @ B ) )
& ! [D: $i] :
( ( ( v5_orders_2 @ D @ A )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(962,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ C ) )
<=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_setwiseo) ).
thf(5768,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(637,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/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(4229,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)],[637]) ).
thf(972,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/sandbox/benchmark/theBenchmark.p',t29_filter_0) ).
thf(5821,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)],[972]) ).
thf(791,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( a_3_1_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_domain_1) ).
thf(4936,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( a_3_1_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(580,axiom,
? [A: $i] : ( l1_funcsdom @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_funcsdom) ).
thf(3939,plain,
? [A: $i] : ( l1_funcsdom @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(988,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( m1_subset_1 @ ( k5_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(5891,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)],[988]) ).
thf(109,axiom,
! [A: $i] : ( v5_lattice3 @ ( k1_lattice3 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattice3) ).
thf(1597,plain,
! [A: $i] : ( v5_lattice3 @ ( k1_lattice3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(535,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/sandbox/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(3740,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)],[535]) ).
thf(384,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/sandbox/benchmark/theBenchmark.p',dt_k5_lattice4) ).
thf(2879,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)],[384]) ).
thf(1070,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/sandbox/benchmark/theBenchmark.p',t77_filter_0) ).
thf(6158,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)],[1070]) ).
thf(559,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_2 @ ( k4_filter_2 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_filter_2) ).
thf(3854,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_2 @ ( k4_filter_2 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(219,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_zfmisc_1 @ A ) @ A )
& ( m2_relset_1 @ B @ ( k1_zfmisc_1 @ A ) @ A ) )
=> ~ ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ A ) @ A @ B @ ( k6_domain_1 @ A @ C ) )
= C ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ A ) @ A @ B @ ( k10_relset_1 @ ( k1_zfmisc_1 @ A ) @ A @ B @ C ) )
= ( k1_funct_1 @ B @ ( k3_tarski @ C ) ) ) )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_lattices @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( l3_lattices @ C ) )
=> ~ ( ( ( u1_struct_0 @ C )
= A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
=> ( ( k15_lattice3 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_lattice3) ).
thf(2074,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_zfmisc_1 @ A ) @ A )
& ( m2_relset_1 @ B @ ( k1_zfmisc_1 @ A ) @ A ) )
=> ~ ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ A ) @ A @ B @ ( k6_domain_1 @ A @ C ) )
= C ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ A ) @ A @ B @ ( k10_relset_1 @ ( k1_zfmisc_1 @ A ) @ A @ B @ C ) )
= ( k1_funct_1 @ B @ ( k3_tarski @ C ) ) ) )
& ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v3_lattices @ C )
& ( v10_lattices @ C )
& ( v4_lattice3 @ C )
& ( l3_lattices @ C ) )
=> ~ ( ( ( u1_struct_0 @ C )
= A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
=> ( ( k15_lattice3 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',t63_partfun1) ).
thf(2018,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)],[203]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(2059,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1045,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_0) ).
thf(6072,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)],[1045]) ).
thf(1063,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/sandbox/benchmark/theBenchmark.p',t3_filter_0) ).
thf(6141,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)],[1063]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k5_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(1812,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ ( k5_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(444,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( r3_binop_1 @ A @ C @ E )
& ( r3_binop_1 @ B @ D @ F ) )
<=> ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_1) ).
thf(3296,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [F: $i] :
( ( ( v1_funct_1 @ F )
& ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( ( r3_binop_1 @ A @ C @ E )
& ( r3_binop_1 @ B @ D @ F ) )
=> ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
& ( ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
=> ( ( r3_binop_1 @ A @ C @ E )
& ( r3_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1007,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/sandbox/benchmark/theBenchmark.p',t47_filter_1) ).
thf(5943,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)],[1007]) ).
thf(3437,plain,
l1_lattices @ sk253,
inference(cnf,[status(esa)],[3436]) ).
thf(582,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/sandbox/benchmark/theBenchmark.p',t90_filter_0) ).
thf(3950,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)],[582]) ).
thf(924,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_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 ) )
=> ( ( k3_lattices @ A @ ( k2_lattice4 @ A @ B ) @ C )
= ( k2_lattice4 @ A @ ( k8_setwiseo @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k7_funcop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( k7_grcat_1 @ A ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lattice4) ).
thf(5591,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_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 ) )
=> ( ( k3_lattices @ A @ ( k2_lattice4 @ A @ B ) @ C )
= ( k2_lattice4 @ A @ ( k8_setwiseo @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k7_funcop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( k7_grcat_1 @ A ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(996,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/sandbox/benchmark/theBenchmark.p',t24_lattice2) ).
thf(5913,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)],[996]) ).
thf(1075,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/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
thf(6173,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)],[1075]) ).
thf(649,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r4_lattice3 @ A @ B @ C ) )
=> ( ( k15_lattice3 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice3) ).
thf(4274,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r4_lattice3 @ A @ B @ C ) )
=> ( ( k15_lattice3 @ A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',t36_lopclset) ).
thf(2321,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)],[253]) ).
thf(717,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/sandbox/benchmark/theBenchmark.p',t34_lattice4) ).
thf(4642,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)],[717]) ).
thf(81,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funcop_1) ).
thf(1490,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [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 @ A )
=> ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
= ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(858,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/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).
thf(5255,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)],[858]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(1917,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)],[188]) ).
thf(799,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/sandbox/benchmark/theBenchmark.p',t57_filter_0) ).
thf(4977,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)],[799]) ).
thf(677,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( m2_filter_2 @ 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 @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_filter_2) ).
thf(4423,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( m2_filter_2 @ 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 @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_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 @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_filter_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',t2_binop_1) ).
thf(2106,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)],[224]) ).
thf(866,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/sandbox/benchmark/theBenchmark.p',t60_filter_1) ).
thf(5293,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)],[866]) ).
thf(1050,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_relat_1 @ ( k9_filter_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(6094,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)],[1050]) ).
thf(917,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/sandbox/benchmark/theBenchmark.p',t47_lattices) ).
thf(5574,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)],[917]) ).
thf(186,axiom,
! [A: $i] : ( v2_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_setwiseo) ).
thf(1912,plain,
! [A: $i] : ( v2_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1417,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)],[70]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k3_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_setwiseo) ).
thf(4734,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k3_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1044,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/sandbox/benchmark/theBenchmark.p',d8_lattice4) ).
thf(6067,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)],[1044]) ).
thf(28005,plain,
$false,
inference(cvc4,[status(thm)],[5509,5422,2778,3666,3167,3698,3581,5654,3969,6042,5028,6014,5582,5659,3021,4094,5918,6355,1823,4571,3345,2341,2072,4262,4062,2412,5320,6283,6285,2463,1899,4015,6074,2280,1554,5898,6022,2309,2210,5069,3153,2014,1728,5982,1142,1793,6017,5614,4592,1173,1855,1200,5141,1406,4226,4500,4339,5718,4311,2644,2659,3417,5242,3285,5265,3498,4215,2380,5425,6278,1655,3745,2686,4575,5288,4110,2316,2448,5316,5701,4440,3693,6336,6370,2146,2360,2575,3332,3367,4884,4870,2740,6359,1342,3121,3481,4247,2580,1196,3088,4916,5301,4198,2531,1254,4775,4249,3836,3236,3634,5252,6251,1914,2763,5486,4496,5935,1391,5825,5938,3809,2173,1366,4760,2067,2825,4156,3880,6291,1518,4610,1709,2735,3689,5064,3612,3485,4778,6315,2562,3353,5279,3820,5553,3204,4539,5765,3221,5306,4896,1430,3275,6034,1660,1298,3495,5910,4654,1860,2682,1826,2897,6006,2571,3713,6010,1379,2169,6396,5127,6310,6365,5052,1931,5746,4460,3180,5338,6253,2857,4788,2373,3919,1347,1572,1741,4317,3734,3014,2024,4632,4793,1875,1232,4967,4595,5974,2451,6135,6054,5650,1283,2456,2007,5682,6081,4411,6259,4988,2616,4396,1465,3966,2324,1714,2027,4903,4443,4578,3075,5597,4018,2090,4857,4258,2893,1632,4820,2650,3527,6189,3525,2122,3438,6187,4815,6176,5804,1978,5541,5032,3569,5985,3923,5135,3300,4115,4686,5457,4783,1843,4718,4055,5379,1215,2190,3036,2809,2103,6156,3559,4211,5572,5059,3537,1928,5648,1886,2424,6347,1394,5296,3676,2137,5321,4307,4924,5169,1345,2286,4038,2154,6103,1521,3492,2205,3184,2586,4082,4483,1564,1604,2011,3450,2910,6015,1153,5968,5291,2047,4370,2641,1736,3679,4853,3229,6020,6183,4589,3567,1691,6296,4480,4531,5017,6064,5167,1470,2093,6307,2307,1768,2382,2061,4999,2673,3735,2409,1723,1223,5734,1519,1355,1217,2937,4493,6107,2528,1238,5924,6079,2428,2805,3972,5794,4434,4878,5579,1570,1174,5349,5455,1751,5719,1487,3742,4091,2032,5893,6178,2132,4836,5594,3207,4021,2445,5391,1920,5690,2872,5534,5038,5566,1291,2769,2653,3980,3618,4053,2433,2477,2565,3198,3314,2820,4947,3499,3556,1296,3877,5988,3894,5779,1819,1836,5113,6096,4942,6168,3926,6267,2344,2492,4104,3931,1910,3731,3218,1425,3704,3518,2726,4930,5497,1360,1350,5189,2300,3784,5904,1234,1541,3831,1143,5609,1762,2100,1772,5098,1259,1534,5006,4974,3862,5577,5798,2692,1498,1587,5847,4012,3916,3941,6218,4898,1493,1160,1942,1182,4167,6304,4545,5588,5662,2551,1567,4676,6299,5941,1329,3407,5705,5651,5992,5791,6363,4421,4315,2053,2196,6164,5213,2613,3723,2666,6271,4736,3654,2845,5639,5900,2581,5776,5823,3409,1720,2370,6349,1324,2504,4846,5850,1150,1478,4384,5149,6033,3787,2836,4508,1266,6331,2387,1192,4244,2766,1599,1246,3109,6152,4689,4069,4416,3364,2140,4086,3162,3201,4223,1759,6171,3755,2634,3834,1241,2883,3856,2748,5434,2368,6378,3639,5840,5872,1202,4352,1814,4644,3624,5402,2043,4889,2057,1712,3592,1846,5887,1895,5513,5198,1616,3422,6368,2941,2602,1374,5043,3660,2001,3707,5327,1510,1764,5996,4131,5524,2176,4708,4470,1146,1754,4872,2904,2556,4354,4613,5138,4657,5960,6243,6001,1595,3888,3839,5928,4503,5882,5095,3111,4269,3686,5698,3187,3636,1884,5067,2489,5612,3900,4381,4341,5933,1784,5488,3255,2525,3609,4159,2849,1652,3758,3283,3266,1388,3272,4605,5876,1403,6344,1701,3590,1520,3868,2817,4758,2695,1226,4505,3599,4251,1786,4112,3340,1332,3436,5703,3579,1897,6334,3568,3719,6048,4537,5965,1139,4485,5546,3118,4127,3964,5363,2293,6357,3726,1371,5859,3695,4099,3330,1635,4672,3091,2474,1638,4887,5634,6281,3551,4828,6321,3710,1175,2510,6061,6144,4716,4704,6059,2538,1853,1408,3238,2624,5244,2415,5103,3419,6112,4914,5827,2669,1144,1801,5531,6289,2856,2802,6154,2378,3586,6196,4773,5616,1439,4477,4107,6004,5584,5657,5920,5730,4818,2780,5439,1862,5885,5035,5202,1162,5286,4277,2757,3977,3614,1149,6319,1293,2553,2329,5838,1952,6376,2578,1171,1841,2401,5216,6288,1176,2931,1775,3310,6100,4304,2207,6029,4209,2069,2418,4933,6255,1926,5742,4232,2350,5442,6449,4373,1643,5248,3806,3159,2064,3953,5976,2797,1496,5299,4196,6180,3178,3348,2156,5089,3908,1694,4965,2506,5619,4084,1413,1626,4207,1809,3427,1166,1208,4529,3921,3455,5807,6132,4907,3031,1662,4394,6276,4868,1467,4260,6185,5025,3293,2471,4598,1277,2124,4319,3048,5678,6008,6115,4812,4336,4045,4749,5716,6249,4035,5602,3842,6051,3904,4534,1368,2850,5570,1748,1798,5229,2375,5388,4272,4939,5399,4922,1647,2732,1252,5980,2678,4894,3058,6146,2689,4437,1790,1300,3063,6037,3554,5555,1262,3544,5543,3412,4781,4117,4875,2354,2656,3080,3642,4561,4398,4905,3823,5560,2337,5030,3801,5309,1317,2701,2486,4241,2545,2599,3847,1285,5450,5106,2468,1220,5147,1934,5675,6262,5504,2579,1504,1717,2939,2848,6105,4414,6301,1543,4802,5902,4057,1849,3652,2838,2558,2113,5736,1141,2426,1536,1981,5998,3356,5240,2711,6193,5453,4143,1585,1140,4838,6245,6161,3156,5100,4795,2875,4945,1817,6137,2347,1517,3928,1575,3797,2435,4639,2760,1421,3400,4138,1649,2479,6425,5749,2045,1949,4763,1157,4419,3533,5966,4646,5907,4102,2187,1189,1866,2775,2792,1807,5184,2907,2443,6077,2855,2135,4089,3336,1745,3748,2431,4881,4823,3780,2934,5258,2591,1590,5055,2283,4806,6341,3484,4681,5191,5800,5132,1481,4683,3369,2823,4542,4791,1629,3501,5394,5087,1523,3859,5922,3085,4451,5600,2944,5963,1689,2384,4649,4153,5023,2680,1607,2421,3844,3430,6118,1777,4299,6045,5040,3351,3993,5739,5144,2036,3645,2494,5196,5194,4927,6198,5864,4356,6361,5537,2522,5371,4367,3164,6326,5009,2517,5728,1725,1280,1578,6201,4706,4670,5971,3232,4809,3865,5268,3601,1593,2604,4843,3521,1303,4841,5522,1148,1757,6150,4455,5926,3982,4146,3897,1363,5990,4474,2746,1172,1288,3196,3765,2795,2619,6040,6269,2800,3956,4755,1657,6294,5709,3277,5019,4024,3716,1561,2704,6380,2404,5586,5176,5200,3673,6273,2783,5324,6351,5500,1829,5151,3360,6373,3489,4831,5774,6109,1902,6222,5845,2159,3362,1268,3701,1532,4799,2847,3570,1384,3772,5061,1357,3259,1500,3245,5768,4229,5821,4936,3939,5891,1597,3740,2879,6158,3854,2074,2018,2059,6072,6141,1812,3296,5943,3437,3950,5591,5913,6173,4274,2321,4642,1490,5255,1917,4977,4423,2106,5293,6094,5574,1912,1417,4734,6067]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : LAT304+3 : TPTP v8.1.2. Released v3.4.0.
% 0.14/0.17 % Command : run_Leo-III %s %d
% 0.17/0.39 % Computer : n004.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Thu May 18 13:54:26 EDT 2023
% 0.17/0.39 % CPUTime :
% 1.00/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.70/1.74 % [INFO] Parsing done (853ms).
% 3.70/1.75 % [INFO] Running in sequential loop mode.
% 4.08/1.96 % [INFO] eprover registered as external prover.
% 4.08/1.96 % [INFO] cvc4 registered as external prover.
% 4.08/1.96 % [INFO] Scanning for conjecture ...
% 6.70/2.56 % [INFO] Found a conjecture and 13610 axioms. Running axiom selection ...
% 9.69/3.92 % [INFO] Axiom selection finished. Selected 1136 axioms (removed 12474 axioms).
% 11.58/4.61 % [INFO] Problem is first-order (TPTP FOF).
% 11.91/4.66 % [INFO] Type checking passed.
% 11.91/4.66 % [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 ...
% 137.22/31.58 % External prover 'cvc4' found a proof!
% 137.22/31.58 % [INFO] Killing All external provers ...
% 137.22/31.58 % Time passed: 31025ms (effective reasoning time: 29827ms)
% 137.22/31.58 % 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)>
% 137.22/31.58 % Axioms used in derivation (1136): t119_funct_2, d5_monoid_0, t17_lattice4, dt_k4_filter_2, t1_filter_2, t34_sysrel, d16_lattice3, t70_setwiseo, dt_k7_filter_0, d13_filter_0, t48_funcop_1, t62_partfun1, t7_filter_0, t23_funct_2, t45_lattice4, t51_filter_1, t30_lopclset, t37_orders_2, t2_filter_0, t39_relset_1, dt_k9_filter_2, dt_k5_filter_1, t50_lattice4, fraenkel_a_1_0_domain_1, redefinition_m2_relset_1, dt_k7_grcat_1, t2_quantal1, t20_filter_1, t11_filter_2, t24_filter_0, t55_funcop_1, fraenkel_a_3_2_domain_1, fraenkel_a_3_6_lattice3, t19_xboole_1, t31_filter_0, commutativity_k3_setwiseo, t35_subset_1, dt_k2_lattice2, t135_zfmisc_1, t25_relset_1, d20_binop_1, t30_relat_1, t53_setwiseo, t45_setwiseo, t20_lattice4, t39_lattices, t76_lattice2, t26_lopclset, t17_xboole_1, t37_lattice2, t4_funct_4, dt_k1_filter_1, t78_filter_0, t42_subset_1, t30_setwiseo, t36_lopclset, t43_lattice2, dt_m1_lattice4, t15_setwiseo, fc1_zfmisc_1, d5_lopclset, t62_filter_0, t66_partfun1, t60_funcop_1, dt_k3_borsuk_1, dt_k1_filter_2, t80_filter_0, t56_filter_1, t53_subset_1, t8_pcomps_1, d6_filter_0, t54_filter_1, t1_funct_4, t10_filter_2, t36_lattice4, t19_filter_2, t15_filter_1, symmetry_r1_filter_1, t29_filter_0, redefinition_k5_subset_1, fraenkel_a_1_1_ens_1, t48_filter_1, t24_lattice4, d14_binop_1, dt_k9_domain_1, dt_k5_relset_1, d5_relat_1, t49_setwiseo, fraenkel_a_1_0_filter_1, t109_xboole_1, idempotence_k3_xboole_0, t5_ens_1, t67_funcop_1, redefinition_k16_filter_2, t25_lattice2, t63_funcop_1, d10_binop_1, t35_filter_1, t47_relset_1, d6_lattice2, t7_subset_1, t30_lattice2, d11_binop_1, t2_realset1, dt_k8_funcop_1, t81_filter_0, dt_k7_setwiseo, t3_xboole_1, t180_orders_1, d4_lattice4, dt_k4_relset_1, dt_k6_filter_1, idempotence_k5_setwiseo, t34_xboole_1, t111_zfmisc_1, d1_lattice2, t56_partfun1, t32_lattice4, t53_funcop_1, t43_lattices, t6_ens_1, fc1_xboole_0, t53_filter_1, t42_filter_0, cc6_lattices, t57_lattice2, t51_lattice3, t33_lattice2, t16_funct_2, t113_zfmisc_1, t67_lattice2, t27_setwiseo, t48_domain_1, t8_subset_1, t80_lattice2, t9_filter_2, existence_l1_lattices, dt_k11_domain_1, fc4_relat_1, t19_lattices, t4_ordinal1, t29_lattice3, t1_group_6, t59_partfun1, t1_subset, dt_k1_lattice4, t10_partfun1, existence_l1_funcsdom, t28_lattice3, t47_lattice2, t29_subset_1, t4_lattice4, t33_setwiseo, fc4_subset_1, t12_filter_2, t74_funct_2, t54_partfun1, t18_xboole_1, t42_setwiseo, d5_relat_2, dt_k15_filter_2, t14_binop_1, t30_filter_1, d5_xboole_0, dt_k7_relset_1, t38_filter_1, t57_domain_1, dt_k9_lopclset, existence_l3_lattices, dt_k6_nat_lat, t79_funcop_1, t53_lattices, dt_k5_lattices, t7_funct_2, t25_filter_1, t23_lopclset, t87_filter_0, t16_setwiseo, t6_lattice3, fc3_relat_1, t45_filter_1, t43_lattice3, t21_lattice2, d10_lattice3, dt_k16_filter_2, t28_binop_1, dt_k13_domain_1, fc1_lattice2, t69_filter_0, t31_setwiseo, t72_lattice2, t16_lattice4, existence_m3_lattice4, dt_k1_lattice2, t117_zfmisc_1, d10_filter_0, t53_lattice3, d9_monoid_0, t35_lattice4, t110_zfmisc_1, t23_filter_0, redefinition_k12_filter_2, t46_lattice4, dt_m2_nat_lat, d7_binop_1, t2_boole, dt_m1_filter_1, t18_filter_0, dt_k3_lattice4, t65_partfun1, t29_lopclset, t56_lattice3, fraenkel_a_2_0_lattice4, dt_k4_subset_1, t27_xboole_1, t122_zfmisc_1, t83_filter_0, dt_k1_struct_0, existence_m1_filter_1, t26_lattice4, t85_filter_0, t22_lattice3, t103_zfmisc_1, dt_k19_filter_2, rc2_partfun1, fc1_filter_0, t48_filter_0, d9_lattice4, t7_orders_1, t41_lattice2, t6_mssubfam, t64_funcop_1, dt_m2_filter_1, t95_zfmisc_1, t12_lattice3, t63_partfun1, t63_setwiseo, t78_funcop_1, t15_relset_1, d2_lattice3, t14_filter_0, fraenkel_a_2_0_filter_0, t99_zfmisc_1, t50_wellord1, cc4_lattices, redefinition_k11_filter_0, fc2_filter_2, rc3_funct_1, fraenkel_a_3_3_domain_1, t34_lattice3, dt_k5_filter_0, dt_k3_filter_0, t37_xboole_1, t21_filter_2, cc1_lattice3, dt_m2_relset_1, cc1_relat_1, d22_lattice3, dt_k7_funct_2, d4_monoid_0, dt_k5_filter_2, reflexivity_r1_filter_1, commutativity_k3_xboole_0, dt_k10_filter_1, t47_filter_1, t25_setwiseo, d1_struct_0, t56_relat_1, t83_lattice2, t10_lattice3, t39_setwiseo, idempotence_k5_subset_1, t59_lattice2, fraenkel_a_3_4_lattice3, t2_funct_1, t36_subset_1, t29_partfun1, t33_lattice4, t31_relset_1, t12_binop_1, t32_filter_0, t95_orders_1, dt_k8_lopclset, t26_filter_0, t130_funct_2, t80_funcop_1, t56_setwiseo, dt_k4_lattice3, involutiveness_k3_subset_1, rc1_funct_1, t53_filter_0, t83_funcop_1, t17_binop_1, t25_funct_2, t31_relat_1, t15_binop_1, existence_l2_quantal1, redefinition_k13_filter_2, redefinition_k6_filter_0, dt_k1_filter_0, dt_k6_filter_2, t115_zfmisc_1, t52_funcop_1, existence_m2_card_fil, t66_lattice2, t46_lattice2, t58_setwiseo, dt_m2_lattice4, d11_filter_0, t26_filter_2, t31_lattices, dt_k2_binop_1, t137_zfmisc_1, fraenkel_a_2_2_domain_1, t2_binop_1, t37_lattice3, dt_m2_realset1, d6_binop_1, dt_m1_filter_2, t41_setwiseo, t27_relat_1, t20_filter_2, d1_xboole_0, t5_mssubfam, d6_monoid_0, t108_xboole_1, t34_partfun1, dt_k3_setwiseo, t72_filter_0, t3_mssubfam, t138_zfmisc_1, t37_filter_0, t36_filter_1, redefinition_k1_filter_1, t3_filter_2, t108_zfmisc_1, fraenkel_a_3_7_domain_1, d18_lattice3, d16_lattice4, t70_filter_0, t20_lattice3, t56_filter_0, t2_mssubfam, t29_setwiseo, t46_filter_0, t40_lattice2, dt_k5_lattice3, fraenkel_a_3_0_filter_0, rc3_lattices, t52_filter_0, t57_filter_0, dt_l1_lattices, dt_k4_setwiseo, t19_lopclset, t28_lattice2, t31_partfun1, dt_k7_lattices, d15_lattice4, rc2_subset_1, fraenkel_a_3_2_lattice3, t10_relat_1, t24_finsub_1, t37_setwiseo, t27_relset_1, t52_domain_1, t40_setwiseo, t32_lattice3, dt_k12_filter_2, t79_funct_3, t52_relset_1, dt_k4_lattice4, t118_zfmisc_1, t8_funct_2, t3_tops_2, fraenkel_a_3_4_quantal1, t118_funct_2, t29_lattice4, t76_nat_lat, t14_relset_1, dt_m2_card_fil, t33_lattice3, fraenkel_a_2_6_lattice3, t39_lattice4, t16_relset_1, t38_lattice4, dt_k11_filter_2, t53_relset_1, t28_lopclset, t6_boole, t26_lattice3, t4_orders_1, t67_setwiseo, existence_l2_lattices, t50_xboole_1, t59_setfam_1, t2_filter_1, d1_relat_1, t59_filter_0, t26_relset_1, d14_lattice4, t27_lattice3, t64_partfun1, t47_lattice4, t4_tex_2, t26_binop_1, t44_lattice4, t31_lattice3, dt_k10_setwiseo, t5_subset, t30_lattice3, t44_filter_1, t36_lattice3, t1_xboole_1, t17_filter_2, redefinition_k12_filter_0, redefinition_r3_orders_2, t77_funct_2, t59_domain_1, dt_k4_card_fil, d5_filter_2, t32_lattices, idempotence_k1_filter_1, rc3_funcsdom, t34_filter_0, d4_filter_2, t32_relset_1, t5_lattice4, t59_setwiseo, t32_partfun1, t73_relat_1, t36_orders_2, t19_filter_0, t49_filter_0, t34_relat_1, d17_lattice4, t2_lattice3, t8_lattice4, redefinition_k10_filter_1, dt_m2_filter_2, t52_funct_1, t21_filter_1, t22_setwiseo, t123_zfmisc_1, t17_filter_1, t45_funct_2, t79_zfmisc_1, fraenkel_a_3_3_lattice3, dt_k8_funct_2, t94_zfmisc_1, redefinition_k4_filter_2, t22_filter_1, t23_binop_1, existence_m1_relset_1, t61_setwiseo, commutativity_k5_subset_1, fraenkel_a_2_3_lattice3, t50_lattices, dt_l3_lattices, t48_lattice2, t45_lattice3, d16_nat_lat, t16_filter_2, fc1_orders_1, t40_funct_2, t28_relset_1, t51_funcop_1, t27_lattice4, t9_relat_1, t84_lattice2, t75_lattice2, d12_lattice4, t50_setwiseo, t18_setwiseo, fc1_lattice3, t50_lattice3, t24_filter_1, dt_l2_lattices, t97_zfmisc_1, t28_partfun1, fc2_funct_1, d4_lattice3, t102_zfmisc_1, d2_ens_1, t40_filter_0, d3_filter_2, dt_k10_lattice3, t24_binop_1, t2_tarski, t23_setwiseo, dt_k4_filter_0, t33_xboole_1, t47_lattices, t25_borsuk_1, d1_filter_1, d7_filter_2, d20_lattices, t4_filter_0, t2_zfmisc_1, rc4_quantal1, t89_filter_0, t61_funcop_1, t1_filter_1, d6_realset1, t39_filter_1, t38_filter_0, t74_funcop_1, t71_lattice2, d21_lattice3, t35_lattice3, cc5_lattices, t4_subset, t34_lopclset, fraenkel_a_1_1_lopclset, t22_lattice2, t44_lattices, t71_setwiseo, t18_lopclset, t15_lattice4, d8_filter_0, t32_xboole_1, dt_k8_filter_0, t42_filter_1, t52_subset_1, t60_filter_0, dt_k9_filter_1, t5_ordinal1, t4_boole, t38_orders_2, t22_lopclset, t4_cat_1, rc3_orders_2, t34_lattice4, dt_k11_relset_1, t33_sysrel, t3_quantal1, t70_lattice2, dt_k8_domain_1, dt_k17_filter_2, d4_tarski, t56_lattice2, t5_filter_2, t25_lattice3, d12_binop_1, t44_lattice3, d7_realset2, redefinition_k6_setwiseo, d3_lattice3, dt_k1_domain_1, t17_funct_2, t85_lattice2, redefinition_k14_filter_2, fc1_realset1, t24_orders_2, t25_filter_2, fraenkel_a_3_5_quantal1, dt_k14_funct_3, t45_lattices, t49_lattice4, existence_m2_realset1, t52_filter_1, t35_setwiseo, fraenkel_a_2_0_lopclset, d7_lopclset, dt_k11_lattice3, d2_lattice4, t38_lattice2, t75_filter_0, t5_orders_1, t139_zfmisc_1, t32_lopclset, t16_lattice2, t11_card_fil, existence_l1_orders_2, cc1_funct_1, d2_filter_1, redefinition_k1_filter_2, t4_eqrel_1, d10_lattice4, d17_lattice3, d3_relat_2, d1_setwiseo, reflexivity_r3_orders_2, t3_ordinal1, t9_domain_1, d6_filter_2, t7_boole, dt_k14_filter_2, t104_zfmisc_1, dt_k5_lattice4, t11_binop_1, d10_relat_1, rc3_struct_0, t55_filter_0, t98_orders_1, t50_filter_1, t1_t_0topsp, d2_subset_1, redefinition_k9_filter_2, fc1_subset_1, t33_zfmisc_1, commutativity_k2_struct_0, t7_filter_2, redefinition_k6_partfun1, t23_filter_2, t48_xboole_1, dt_k6_domain_1, t21_lattice3, t66_funcop_1, rc2_funct_1, t37_filter_1, t81_funcop_1, t3_lattice3, dt_k9_filter_0, t90_filter_0, t26_filter_1, redefinition_k1_domain_1, fc3_lopclset, t34_filter_1, t31_lattice4, t16_subset_1, dt_k2_partfun1, t6_filter_2, dt_k8_filter_1, t7_ordinal1, t38_relset_1, dt_k10_filter_2, t9_funct_2, dt_k14_lattice3, rc1_subset_1, t49_relset_1, redefinition_k15_filter_2, t17_ens_1, dt_k6_funcop_1, t4_subset_1, t48_lattice4, t68_filter_0, t30_relset_1, rc1_funct_2, t91_orders_1, t113_funct_2, t5_filter_0, t116_zfmisc_1, existence_m1_filter_0, t30_filter_0, t27_lopclset, t40_lattice4, t13_filter_2, t40_lattices, t4_isocat_2, t4_filter_2, d21_lattices, t41_lattices, t49_filter_1, dt_k3_lattice2, t76_funcop_1, t58_filter_1, redefinition_m1_filter_2, t4_ens_1, dt_k2_struct_0, t49_lattices, t27_binop_1, t48_lattices, t20_xboole_1, dt_k2_lattice4, t9_filter_0, t124_zfmisc_1, t47_lattice3, fraenkel_a_3_1_domain_1, t7_lattice4, t46_filter_1, t40_lattice3, t61_filter_1, t17_lattice2, t1_toler_1, t8_mssubfam, t50_lattice2, t79_funct_2, d9_filter_1, t56_funcop_1, d2_zfmisc_1, t3_relat_1, t22_filter_0, t10_ens_1, cc2_funct_1, dt_k16_lattice3, dt_k15_lattice3, fraenkel_a_2_1_lattice4, t26_lattice2, dt_k24_filter_2, dt_k8_setfam_1, d3_lattice2, t4_relset_1, t10_filter_0, t31_subset_1, t3_subset, cc1_relset_1, fc1_filter_2, t22_relset_1, t25_binop_1, d2_binop_1, d6_lattice4, t30_lattice4, s1_domain_1, t31_sysrel, t12_filter_0, t41_lattice4, t51_setwiseo, t44_setwiseo, dt_k7_filter_2, dt_u1_lattices, t136_funct_2, t18_filter_1, fraenkel_a_2_1_domain_1, existence_m1_subset_1, t22_lattice4, existence_m1_filter_2, t35_xboole_1, t71_tops_3, t1_monoid_0, t44_setfam_1, d2_filter_0, redefinition_k9_lopclset, t5_lattice2, t44_filter_0, dt_k9_setwiseo, d9_binop_1, t19_lattice2, t92_zfmisc_1, t106_zfmisc_1, dt_k11_setwiseo, t125_zfmisc_1, t42_lattice3, t30_subset_1, d17_binop_1, dt_k2_filter_0, dt_k2_funct_2, t38_lattice3, t73_filter_0, t47_xboole_1, fraenkel_a_3_5_lattice3, t27_filter_2, d2_card_fil, t15_subset_1, dt_k20_filter_2, t17_relset_1, cc3_lattices, d5_subset_1, t54_setwiseo, t107_zfmisc_1, t9_realset1, t64_setwiseo, t114_zfmisc_1, dt_k23_filter_2, t100_zfmisc_1, t15_filter_2, rc2_relat_1, t36_lattice2, existence_m2_relset_1, d4_binop_1, t64_filter_0, t49_funcop_1, t7_ens_1, t55_setwiseo, d8_ens_1, t3_funct_7, t48_lattice3, t58_partfun1, t60_setwiseo, d1_zfmisc_1, t16_xboole_1, t75_nat_lat, t9_lattice4, t1_ens_1, t82_lattice2, t14_filter_2, d1_filter_0, t27_filter_0, t26_xboole_1, redefinition_k7_filter_0, t1_filter_0, commutativity_k4_subset_1, t62_lattice2, t39_filter_0, dt_k7_lopclset, t11_lattice4, t74_lattice2, t11_filter_0, rc2_realset2, t49_lattice3, dt_k5_subset_1, existence_m2_lattice4, t23_lattice4, d4_lattice2, t116_funct_2, d2_relat_2, fraenkel_a_3_6_domain_1, t62_setwiseo, t51_filter_0, t14_lattice4, redefinition_k2_binop_1, t74_filter_0, t65_lattice2, d5_filter_0, dt_k7_funcop_1, t60_nat_lat, t60_filter_1, t61_lattice2, commutativity_k1_filter_1, t6_funct_2, redefinition_k24_filter_2, dt_l1_orders_2, t69_funcop_1, t44_lattice2, t41_subset_1, d3_lattice4, t11_lattice3, fraenkel_a_2_4_lattice3, t37_lattice4, existence_m2_filter_1, t51_subset_1, existence_m1_lattice4, t111_xboole_1, fraenkel_a_2_2_lattice3, d4_filter_0, reflexivity_r1_filter_2, d8_monoid_0, d7_monoid_0, t21_lopclset, t48_wellord1, t84_funct_3, t8_realset1, d3_tarski, t31_filter_1, fraenkel_a_3_1_filter_0, t25_lattice4, t57_setwiseo, t14_setwiseo, t45_lattice2, free_g1_orders_2, dt_m3_lattice4, t6_relset_1, t28_xboole_1, d1_relset_1, redefinition_k11_filter_2, d7_relat_2, fc1_struct_0, t62_filter_1, d8_filter_1, t52_lattice2, t18_binop_1, t78_lattice2, d15_lattices, d12_lattice3, t72_setwiseo, dt_k22_filter_2, t119_zfmisc_1, rc1_relat_1, d7_filter_1, t24_filter_2, t19_setwiseo, t40_subset_1, t83_zfmisc_1, rc1_lattice4, t77_lattice2, fraenkel_a_2_5_lattice3, t2_monoid_0, fraenkel_a_3_4_domain_1, t24_lattice2, t19_lattice4, reflexivity_r1_tarski, t6_orders_1, dt_k10_relset_1, symmetry_r1_filter_2, t52_wellord1, t18_funct_2, t7_lattice3, t52_lattices, t2_xboole_1, t35_lattice2, t32_setwiseo, t57_partfun1, t25_lopclset, t9_mcart_1, d11_grcat_1, dt_k6_relat_1, t35_orders_2, t18_filter_2, t10_subset_1, dt_k7_filter_1, t56_setfam_1, t96_orders_1, t24_lattice3, t41_filter_0, existence_m2_nat_lat, t1_realset1, t38_lopclset, t36_setwiseo, dt_g3_lattices, fc6_relat_1, d15_binop_1, rc6_lattices, d1_funct_2, dt_k6_setwiseo, t67_filter_0, free_g3_lattices, t77_filter_0, t35_funct_1, t54_lattice2, t29_relset_1, t21_lattice4, dt_k5_setwiseo, commutativity_k5_setwiseo, t36_xboole_1, d7_lattice4, t69_lattice2, redefinition_k2_filter_2, d4_xboole_0, dt_k10_filter_0, t43_setwiseo, t65_setwiseo, t68_setwiseo, t47_filter_0, t39_lattice2, dt_k3_filter_2, t3_ens_1, fc2_filter_1, t58_filter_0, dt_k12_domain_1, t46_relset_1, t18_lattice4, d5_binop_1, t51_relset_1, t20_filter_0, t40_filter_1, t49_xboole_1, t88_filter_0, d1_relat_2, t51_lattice2, t54_filter_0, redefinition_k2_lattice3, redefinition_k8_funct_2, t15_filter_0, dt_k2_filter_2, t59_filter_1, dt_k8_setwiseo, d16_binop_1, t19_borsuk_1, t54_subset_1, dt_k1_lattice3, t70_funcop_1, t50_relset_1, t35_partfun1, d8_binop_1, t29_lattices, t16_filter_1, abstractness_v3_lattices, t26_finsub_1, t82_filter_0, fc1_relat_1, d3_setwiseo, t4_mssubfam, t8_boole, rc1_xboole_0, t26_setwiseo, t55_lattice2, t54_funcop_1, t120_funct_2, t59_funct_2, t2_subset, t75_funcop_1, t52_setwiseo, dt_k6_filter_0, t23_finsub_1, d8_lattice3, t109_zfmisc_1, t28_filter_1, dt_k6_lattices, t134_zfmisc_1, dt_m1_filter_0, fc8_relat_1, t4_lattice3, rc5_struct_0, t19_filter_1, redefinition_k21_filter_2, d9_filter_0, t38_funct_2, t33_partfun1, d3_relat_1, t85_funct_2, d4_setwiseo, dt_k21_filter_2, d6_lattice3, fraenkel_a_2_7_lattice3, t82_funcop_1, d1_lattice3, t13_filter_1, dt_k3_binop_1, t37_lopclset, d18_binop_1, t23_lattice3, d1_lattice4, t35_lopclset, t51_lattices, t27_filter_1, fc2_realset1, d13_lattice4, t11_grcat_1, redefinition_k10_filter_2, t58_domain_1, t115_funct_2, t32_finsub_1, t48_subset_1, t28_relat_1, cc2_lattice3, d1_funct_1, d1_filter_2, t57_filter_1, t32_filter_1, fc2_ens_1, t81_lattice2, t34_lattices, d12_filter_0, t42_lattice4, t50_subset_1, t65_filter_0, d10_xboole_0, d2_lattice2, t2_grcat_1, d11_lattice3, t41_lattice3, t28_setwiseo, redefinition_k5_relset_1, t34_lattice2, d19_lattices, t3_boole, t6_ordinal1, t20_lopclset, dt_k18_filter_2, t58_setfam_1, t14_filter_1, fraenkel_a_2_0_lattice3, d8_relat_2, t43_filter_1, dt_k8_filter_2, t77_funcop_1, dt_k18_group_2, t53_lattice2, existence_l1_struct_0, t45_filter_0, t49_subset_1, t7_tarski, rc1_partfun1, t71_filter_0, redefinition_r1_filter_2, fraenkel_a_3_0_ens_1, t27_partfun1, t28_lattice4, t79_lattice2, dt_k2_setwiseo, t23_filter_1, fc1_lattice4, t48_relset_1, t69_setwiseo, dt_u2_lattices, fc1_sysrel, t13_binop_1, t60_lattice2, t50_filter_0, t55_filter_1, d5_setwiseo, t34_setwiseo, t58_lattice2, d3_filter_0, t72_funcop_1, rc2_xboole_0, t67_funct_2, t41_filter_1, t26_partfun1, dt_k13_nat_lat, dt_k10_domain_1, t49_lattice2, t16_binop_1, t66_filter_0, d9_lattice3, t43_lattice4, t6_filter_0, redefinition_k3_filter_2, d13_binop_1, idempotence_k4_subset_1, d2_setwiseo, t22_filter_2, t81_relat_1, d1_binop_1, t63_filter_0, t9_lattice3, t63_lattice2, fraenkel_a_3_5_domain_1, fraenkel_a_2_1_lattice3, t38_partfun1, d3_monoid_0, t93_orders_1, t18_lattice2, t112_zfmisc_1, t73_lattice2, existence_m2_filter_2, fc3_lattices, d3_binop_1, t38_setwiseo, t6_lattice4, t15_ens_1, t30_partfun1, t38_xboole_1, d2_relat_1, t3_filter_0, t68_lattice2, t46_lattice3, t23_relset_1, t52_lattice3, t64_lattice2, dt_k3_subset_1, t5_lattice3, cc1_binop_1, t6_relat_1, dt_k13_filter_2, t29_filter_1, fc2_lopclset, t13_filter_0, d3_xboole_0, t10_lattice4, antisymmetry_r2_hidden, dt_k1_setwiseo, d19_binop_1, d5_lattice4, t21_tops_1, d8_lattice4, dt_k8_lattice3
% 137.22/31.58 % No. of inferences in proof: 2329
% 137.22/31.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 31025 ms resp. 29827 ms w/o parsing
% 138.69/32.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 138.69/32.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------