TSTP Solution File: LAT328+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT328+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:27:52 EDT 2023
% Result : Theorem 139.87s 28.80s
% Output : Refutation 141.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1334
% Syntax : Number of formulae : 3326 ( 539 unt; 317 typ; 0 def)
% Number of atoms : 16779 (2564 equ; 0 cnn)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 57634 (3832 ~;1641 |;6476 &;40340 @)
% ( 240 <=>;5105 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 557 ( 557 >; 0 *; 0 +; 0 <<)
% Number of symbols : 320 ( 317 usr; 74 con; 0-9 aty)
% Number of variables : 7307 ( 0 ^;6980 !; 327 ?;7307 :)
% 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(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(r1_filter_2_type,type,
r1_filter_2: $i > $i > $i > $o ).
thf(k22_filter_2_type,type,
k22_filter_2: $i > $i > $i > $i ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(v1_funct_1_type,type,
v1_funct_1: $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(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $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(k3_funct_2_type,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(r6_binop_1_type,type,
r6_binop_1: $i > $i > $i > $o ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(m1_realset1_type,type,
m1_realset1: $i > $i > $i > $o ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(r4_binop_1_type,type,
r4_binop_1: $i > $i > $i > $o ).
thf(r5_binop_1_type,type,
r5_binop_1: $i > $i > $i > $o ).
thf(k1_funct_2_type,type,
k1_funct_2: $i > $i > $i ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(k2_funct_1_type,type,
k2_funct_1: $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(m2_realset1_type,type,
m2_realset1: $i > $i > $i > $o ).
thf(k5_partfun1_type,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(r2_binop_1_type,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k3_relat_1_type,type,
k3_relat_1: $i > $i ).
thf(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
thf(r3_binop_1_type,type,
r3_binop_1: $i > $i > $i > $o ).
thf(k1_funct_4_type,type,
k1_funct_4: $i > $i > $i ).
thf(v2_binop_1_type,type,
v2_binop_1: $i > $i > $o ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(v3_filter_0_type,type,
v3_filter_0: $i > $o ).
thf(v4_lattices_type,type,
v4_lattices: $i > $o ).
thf(v5_lattices_type,type,
v5_lattices: $i > $o ).
thf(v6_lattices_type,type,
v6_lattices: $i > $o ).
thf(v7_lattices_type,type,
v7_lattices: $i > $o ).
thf(v8_lattices_type,type,
v8_lattices: $i > $o ).
thf(v9_lattices_type,type,
v9_lattices: $i > $o ).
thf(v11_lattices_type,type,
v11_lattices: $i > $o ).
thf(v12_lattices_type,type,
v12_lattices: $i > $o ).
thf(k1_lattice2_type,type,
k1_lattice2: $i > $i ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(l2_lattices_type,type,
l2_lattices: $i > $o ).
thf(u2_lattices_type,type,
u2_lattices: $i > $i ).
thf(l1_lattices_type,type,
l1_lattices: $i > $o ).
thf(u1_lattices_type,type,
u1_lattices: $i > $i ).
thf(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(a_2_3_domain_1_type,type,
a_2_3_domain_1: $i > $i > $i ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(v6_group_1_type,type,
v6_group_1: $i > $o ).
thf(v14_lattices_type,type,
v14_lattices: $i > $o ).
thf(r1_realset1_type,type,
r1_realset1: $i > $i > $i > $o ).
thf(v13_lattices_type,type,
v13_lattices: $i > $o ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(m1_filter_0_type,type,
m1_filter_0: $i > $i > $o ).
thf(k8_filter_0_type,type,
k8_filter_0: $i > $i > $i ).
thf(l2_struct_0_type,type,
l2_struct_0: $i > $o ).
thf(v2_struct_0_type,type,
v2_struct_0: $i > $o ).
thf(m2_lattice4_type,type,
m2_lattice4: $i > $i > $o ).
thf(r1_lattice2_type,type,
r1_lattice2: $i > $i > $i > $o ).
thf(k7_domain_1_type,type,
k7_domain_1: $i > $i > $i > $i ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(k5_finsub_1_type,type,
k5_finsub_1: $i > $i ).
thf(v1_lattice2_type,type,
v1_lattice2: $i > $o ).
thf(k13_nat_lat_type,type,
k13_nat_lat: $i ).
thf(k3_binop_1_type,type,
k3_binop_1: $i > $i > $i ).
thf(k2_subset_1_type,type,
k2_subset_1: $i > $i ).
thf(m2_nat_lat_type,type,
m2_nat_lat: $i > $i > $o ).
thf(a_2_2_domain_1_type,type,
a_2_2_domain_1: $i > $i > $i ).
thf(a_2_0_domain_1_type,type,
a_2_0_domain_1: $i > $i > $i ).
thf(r8_relat_2_type,type,
r8_relat_2: $i > $i > $o ).
thf(k1_subset_1_type,type,
k1_subset_1: $i > $i ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $i > $i > $i ).
thf(r3_relat_2_type,type,
r3_relat_2: $i > $i > $o ).
thf(v15_lattices_type,type,
v15_lattices: $i > $o ).
thf(v16_lattices_type,type,
v16_lattices: $i > $o ).
thf(r7_binop_1_type,type,
r7_binop_1: $i > $i > $i > $o ).
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(r1_relat_2_type,type,
r1_relat_2: $i > $i > $o ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(a_1_0_domain_1_type,type,
a_1_0_domain_1: $i > $i ).
thf(m3_realset1_type,type,
m3_realset1: $i > $i > $i > $o ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(m2_filter_2_type,type,
m2_filter_2: $i > $i > $o ).
thf(k21_filter_2_type,type,
k21_filter_2: $i > $i > $i > $i ).
thf(k20_filter_2_type,type,
k20_filter_2: $i > $i > $i > $i ).
thf(k2_lattices_type,type,
k2_lattices: $i > $i > $i > $i ).
thf(r2_filter_2_type,type,
r2_filter_2: $i > $i > $o ).
thf(v1_filter_0_type,type,
v1_filter_0: $i > $i > $o ).
thf(k15_filter_2_type,type,
k15_filter_2: $i > $i > $i ).
thf(k5_filter_0_type,type,
k5_filter_0: $i > $i > $i > $i ).
thf(m1_lattice4_type,type,
m1_lattice4: $i > $i > $i > $o ).
thf(v2_lattice4_type,type,
v2_lattice4: $i > $i > $i > $o ).
thf(r2_lattice4_type,type,
r2_lattice4: $i > $i > $i > $o ).
thf(v17_lattices_type,type,
v17_lattices: $i > $o ).
thf(k17_filter_2_type,type,
k17_filter_2: $i > $i ).
thf(v1_filter_2_type,type,
v1_filter_2: $i > $i > $o ).
thf(r4_lattice4_type,type,
r4_lattice4: $i > $i > $i > $o ).
thf(k4_lattices_type,type,
k4_lattices: $i > $i > $i > $i ).
thf(m1_filter_2_type,type,
m1_filter_2: $i > $i > $o ).
thf(k4_filter_2_type,type,
k4_filter_2: $i > $i > $i > $i ).
thf(g2_struct_0_type,type,
g2_struct_0: $i > $i > $i ).
thf(k2_lattice2_type,type,
k2_lattice2: $i > $i > $i > $i > $i ).
thf(k8_funcop_1_type,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(k5_lattices_type,type,
k5_lattices: $i > $i ).
thf(k6_lattices_type,type,
k6_lattices: $i > $i ).
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_1_domain_1_type,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k3_lattice2_type,type,
k3_lattice2: $i > $i > $i > $i > $i ).
thf(k1_lattices_type,type,
k1_lattices: $i > $i > $i > $i ).
thf(r1_lattices_type,type,
r1_lattices: $i > $i > $i > $o ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $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(r3_lattices_type,type,
r3_lattices: $i > $i > $i > $o ).
thf(k10_filter_2_type,type,
k10_filter_2: $i > $i > $i ).
thf(k3_filter_0_type,type,
k3_filter_0: $i > $i > $i ).
thf(k4_filter_0_type,type,
k4_filter_0: $i > $i > $i > $i ).
thf(k13_filter_2_type,type,
k13_filter_2: $i > $i > $i ).
thf(k3_filter_2_type,type,
k3_filter_2: $i > $i > $i ).
thf(k7_filter_2_type,type,
k7_filter_2: $i > $i > $i ).
thf(k19_filter_2_type,type,
k19_filter_2: $i > $i > $i ).
thf(p1_s2_domain_1_type,type,
p1_s2_domain_1: $i > $i > $o ).
thf(k5_lattice4_type,type,
k5_lattice4: $i > $i ).
thf(k7_lattices_type,type,
k7_lattices: $i > $i > $i ).
thf(k1_lattice4_type,type,
k1_lattice4: $i > $i > $i ).
thf(k3_lattices_type,type,
k3_lattices: $i > $i > $i > $i ).
thf(k7_filter_0_type,type,
k7_filter_0: $i > $i > $i > $i ).
thf(a_0_0_domain_1_type,type,
a_0_0_domain_1: $i ).
thf(f1_s7_domain_1_type,type,
f1_s7_domain_1: $i ).
thf(k8_setwiseo_type,type,
k8_setwiseo: $i > $i > $i > $i > $i ).
thf(k16_filter_2_type,type,
k16_filter_2: $i > $i > $i ).
thf(k5_setwiseo_type,type,
k5_setwiseo: $i > $i > $i > $i ).
thf(k2_setwiseo_type,type,
k2_setwiseo: $i > $i > $i ).
thf(u2_struct_0_type,type,
u2_struct_0: $i > $i ).
thf(k10_filter_0_type,type,
k10_filter_0: $i > $i > $i ).
thf(k9_filter_0_type,type,
k9_filter_0: $i > $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(r2_lattices_type,type,
r2_lattices: $i > $i > $i > $o ).
thf(k10_domain_1_type,type,
k10_domain_1: $i > $i > $i > $i > $i > $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(v1_lattice4_type,type,
v1_lattice4: $i > $i > $i > $o ).
thf(m3_lattice4_type,type,
m3_lattice4: $i > $i > $o ).
thf(m1_struct_0_type,type,
m1_struct_0: $i > $i > $i > $o ).
thf(k7_setwiseo_type,type,
k7_setwiseo: $i > $i > $i > $i > $i > $i ).
thf(k24_filter_2_type,type,
k24_filter_2: $i > $i > $i ).
thf(k12_domain_1_type,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $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(a_3_6_domain_1_type,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(f1_s4_funct_2_type,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_type,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_type,type,
f3_s4_funct_2: $i > $i ).
thf(k1_finsub_1_type,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(k2_filter_0_type,type,
k2_filter_0: $i > $i > $i ).
thf(a_3_5_domain_1_type,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(k18_filter_2_type,type,
k18_filter_2: $i > $i > $i ).
thf(v3_lattice4_type,type,
v3_lattice4: $i > $i > $i > $o ).
thf(r1_lattice4_type,type,
r1_lattice4: $i > $i > $i > $o ).
thf(k1_filter_0_type,type,
k1_filter_0: $i > $i ).
thf(a_3_4_domain_1_type,type,
a_3_4_domain_1: $i > $i > $i > $i ).
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(f1_s14_funct_2_type,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_type,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_type,type,
p1_s14_funct_2: $i > $i > $o ).
thf(a_3_0_filter_0_type,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(f1_s12_funct_2_type,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_type,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_type,type,
f2_s12_funct_2: $i ).
thf(f1_s13_funct_2_type,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_type,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_type,type,
f2_s13_funct_2: $i ).
thf(a_3_1_domain_1_type,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k11_domain_1_type,type,
k11_domain_1: $i > $i > $i > $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(k7_funcop_1_type,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k7_grcat_1_type,type,
k7_grcat_1: $i > $i ).
thf(k8_domain_1_type,type,
k8_domain_1: $i > $i > $i > $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(f1_s3_funct_2_type,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_type,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_type,type,
p1_s3_funct_2: $i > $i > $o ).
thf(a_3_7_domain_1_type,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(a_4_1_domain_1_type,type,
a_4_1_domain_1: $i > $i > $i > $i > $i ).
thf(r1_filter_0_type,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(v1_setwiseo_type,type,
v1_setwiseo: $i > $i > $o ).
thf(a_2_0_filter_0_type,type,
a_2_0_filter_0: $i > $i > $i ).
thf(a_3_1_filter_0_type,type,
a_3_1_filter_0: $i > $i > $i > $i ).
thf(k2_struct_0_type,type,
k2_struct_0: $i > $i > $i > $i ).
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(k2_filter_2_type,type,
k2_filter_2: $i > $i > $i ).
thf(a_3_2_filter_2_type,type,
a_3_2_filter_2: $i > $i > $i > $i ).
thf(a_0_2_domain_1_type,type,
a_0_2_domain_1: $i ).
thf(f3_s9_domain_1_type,type,
f3_s9_domain_1: $i ).
thf(p1_s7_domain_1_type,type,
p1_s7_domain_1: $i > $o ).
thf(r1_filter_1_type,type,
r1_filter_1: $i > $i > $o ).
thf(f3_s11_funct_2_type,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_type,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_type,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_type,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_type,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_type,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_type,type,
f7_s11_funct_2: $i > $i ).
thf(k9_filter_2_type,type,
k9_filter_2: $i > $i > $i ).
thf(k1_struct_0_type,type,
k1_struct_0: $i > $i > $i ).
thf(k8_subset_1_type,type,
k8_subset_1: $i > $i ).
thf(a_0_1_domain_1_type,type,
a_0_1_domain_1: $i ).
thf(f2_s8_domain_1_type,type,
f2_s8_domain_1: $i ).
thf(k1_setwiseo_type,type,
k1_setwiseo: $i > $i ).
thf(a_2_0_filter_2_type,type,
a_2_0_filter_2: $i > $i > $i ).
thf(f1_s8_domain_1_type,type,
f1_s8_domain_1: $i ).
thf(f3_s8_domain_1_type,type,
f3_s8_domain_1: $i > $i ).
thf(p1_s8_domain_1_type,type,
p1_s8_domain_1: $i > $o ).
thf(k1_filter_2_type,type,
k1_filter_2: $i > $i ).
thf(f1_s9_domain_1_type,type,
f1_s9_domain_1: $i ).
thf(f2_s9_domain_1_type,type,
f2_s9_domain_1: $i ).
thf(f4_s9_domain_1_type,type,
f4_s9_domain_1: $i > $i > $i ).
thf(p1_s9_domain_1_type,type,
p1_s9_domain_1: $i > $i > $o ).
thf(f1_s4_subset_1_type,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_type,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_type,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_type,type,
f3_s4_subset_1: $i ).
thf(a_3_0_filter_2_type,type,
a_3_0_filter_2: $i > $i > $i > $i ).
thf(k23_filter_2_type,type,
k23_filter_2: $i > $i > $i ).
thf(a_3_1_filter_2_type,type,
a_3_1_filter_2: $i > $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i > $i > $o ).
thf(sk4_type,type,
sk4: $i > $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i > $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i > $i > $i ).
thf(sk9_type,type,
sk9: $i > $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(sk11_type,type,
sk11: $i > $i > $i ).
thf(sk12_type,type,
sk12: $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(sk14_type,type,
sk14: $i ).
thf(sk19_type,type,
sk19: $i > $i ).
thf(sk25_type,type,
sk25: $i > $i > $i ).
thf(sk71_type,type,
sk71: $i ).
thf(sk80_type,type,
sk80: $i > $i ).
thf(sk94_type,type,
sk94: $i ).
thf(sk95_type,type,
sk95: $i ).
thf(sk110_type,type,
sk110: $i > $i > $i ).
thf(sk111_type,type,
sk111: $i > $i > $i ).
thf(sk118_type,type,
sk118: $i ).
thf(sk138_type,type,
sk138: $i ).
thf(sk152_type,type,
sk152: $i ).
thf(sk157_type,type,
sk157: $i ).
thf(sk187_type,type,
sk187: $i ).
thf(sk188_type,type,
sk188: $i ).
thf(sk196_type,type,
sk196: $i ).
thf(sk197_type,type,
sk197: $i ).
thf(sk207_type,type,
sk207: $i ).
thf(sk216_type,type,
sk216: $i ).
thf(sk218_type,type,
sk218: $i ).
thf(sk251_type,type,
sk251: $i > $i ).
thf(sk279_type,type,
sk279: $i ).
thf(sk296_type,type,
sk296: $i ).
thf(sk300_type,type,
sk300: $i ).
thf(sk315_type,type,
sk315: $i ).
thf(sk317_type,type,
sk317: $i ).
thf(sk332_type,type,
sk332: $o ).
thf(sk333_type,type,
sk333: $i ).
thf(sk340_type,type,
sk340: $o ).
thf(sk341_type,type,
sk341: $i ).
thf(sk344_type,type,
sk344: $i ).
thf(sk347_type,type,
sk347: $i ).
thf(sk348_type,type,
sk348: $o ).
thf(sk349_type,type,
sk349: $i ).
thf(sk352_type,type,
sk352: $i > $i ).
thf(sk360_type,type,
sk360: $i ).
thf(sk361_type,type,
sk361: $i ).
thf(sk364_type,type,
sk364: $i ).
thf(sk375_type,type,
sk375: $o ).
thf(sk376_type,type,
sk376: $i ).
thf(sk389_type,type,
sk389: $i > $i ).
thf(sk407_type,type,
sk407: $i ).
thf(sk421_type,type,
sk421: $i ).
thf(sk446_type,type,
sk446: $o ).
thf(sk448_type,type,
sk448: $i ).
thf(sk456_type,type,
sk456: $i ).
thf(sk469_type,type,
sk469: $i ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(2163,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)],[207]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(1665,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)],[117]) ).
thf(843,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] :
( ( m2_filter_2 @ D @ A )
=> ~ ( ( r2_filter_2 @ A @ D )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_2) ).
thf(5365,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] :
( ( m2_filter_2 @ D @ A )
=> ~ ( ( r2_filter_2 @ A @ D )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(894,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ B @ ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattices) ).
thf(5561,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)],[894]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
= ( k1_tarski @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_funct_2) ).
thf(4262,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
= ( k1_tarski @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(1100,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_relat_1 @ B )
!= k1_xboole_0 )
| ( v1_funct_2 @ B @ k1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[1100]) ).
thf(1105,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( v1_funct_2 @ B @ k1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[1102]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).
thf(3434,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) ) )
=> ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(559,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4081,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(4082,plain,
v1_xboole_0 @ sk296,
inference(cnf,[status(esa)],[4081]) ).
thf(42,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(1194,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1196,plain,
~ ( v1_xboole_0 @ sk14 ),
inference(cnf,[status(esa)],[1194]) ).
thf(8269,plain,
( ( v1_xboole_0 @ sk296 )
!= ( v1_xboole_0 @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[4082,1196]) ).
thf(8283,plain,
sk296 != sk14,
inference(simp,[status(thm)],[8269]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',t23_binop_1) ).
thf(1075,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)],[15]) ).
thf(1079,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $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_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 )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( m1_subset_1 @ E @ A )
| ~ ( 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 ) ) ) ),
inference(cnf,[status(esa)],[1075]) ).
thf(1083,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( 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 ) ) )
| ~ ( 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_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 )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( m1_subset_1 @ E @ A )
| ~ ( m1_subset_1 @ F @ A ) ),
inference(lifteq,[status(thm)],[1079]) ).
thf(528,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_lattices @ A @ B @ ( k3_lattice2 @ C @ A @ D @ E ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_lattice2) ).
thf(3927,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)],[528]) ).
thf(756,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/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(5028,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)],[756]) ).
thf(1004,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_lattice2 @ A )
<=> ( ( v3_filter_0 @ A )
& ( v13_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice2) ).
thf(6014,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)],[1004]) ).
thf(168,axiom,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(1950,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(928,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/sandbox2/benchmark/theBenchmark.p',redefinition_k24_filter_2) ).
thf(5686,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)],[928]) ).
thf(311,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/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(2822,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)],[311]) ).
thf(584,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(4201,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)],[584]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(1058,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1059,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ),
inference(cnf,[status(esa)],[1058]) ).
thf(150,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(1883,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)],[150]) ).
thf(1886,plain,
v1_funct_1 @ sk71,
inference(cnf,[status(esa)],[1883]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( B = k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_partfun1) ).
thf(1046,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
& ( B = k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v1_partfun1 @ C @ A @ B )
| ( B != k1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1046]) ).
thf(1048,plain,
! [C: $i,B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A = k1_xboole_0 )
| ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v1_partfun1 @ C @ A @ B ) ),
inference(lifteq,[status(thm)],[1047]) ).
thf(1049,plain,
! [B: $i,A: $i] :
( ( A = k1_xboole_0 )
| ~ ( v1_funct_1 @ B )
| ~ ( m2_relset_1 @ B @ A @ k1_xboole_0 )
| ~ ( v1_partfun1 @ B @ A @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[1048]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k22_filter_2 @ A @ B @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k22_filter_2 @ A @ B @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1018,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k22_filter_2 @ A @ B @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1021,plain,
v10_lattices @ sk1,
inference(cnf,[status(esa)],[1018]) ).
thf(6267,plain,
! [B: $i,A: $i] :
( ~ ( v1_funct_1 @ B )
| ~ ( m2_relset_1 @ B @ A @ k1_xboole_0 )
| ~ ( v1_partfun1 @ B @ A @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1049,1021]) ).
thf(6268,plain,
! [A: $i] :
( ~ ( v1_funct_1 @ A )
| ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6267:[bind(A,$thf( sk1 ))]]) ).
thf(6496,plain,
! [A: $i] :
( ~ ( v1_funct_1 @ A )
| ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[6268]) ).
thf(6581,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk71 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1886,6496]) ).
thf(6582,plain,
( ~ ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6581:[bind(A,$thf( sk71 ))]]) ).
thf(7070,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1059,6582]) ).
thf(7102,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( B != sk71 )
| ( A != sk1 )
| ( ( k2_relat_1 @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7070]) ).
thf(7125,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ sk71 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7102]) ).
thf(1887,plain,
v1_relat_1 @ sk71,
inference(cnf,[status(esa)],[1883]) ).
thf(8959,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7125,1887]) ).
thf(8960,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[8959]) ).
thf(564,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
<=> ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattices) ).
thf(4094,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)],[564]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( E
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
=> ( ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
& ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relat_1) ).
thf(1024,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( v1_relat_1 @ E )
=> ( ( E
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
=> ( ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
& ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(985,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/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
thf(5918,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)],[985]) ).
thf(769,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_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ C ) ) )
& ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k19_filter_2 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_2) ).
thf(5088,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_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ C ) ) )
& ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k19_filter_2 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(2744,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(324,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v3_filter_0 @ A )
& ( v1_lattice2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice2) ).
thf(2887,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v3_filter_0 @ A )
& ( v1_lattice2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(2889,plain,
v10_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
<=> ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_partfun1) ).
thf(1187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_partfun1 @ C @ A @ B )
=> ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) )
& ( ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) )
=> ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v1_partfun1 @ C @ A @ B )
| ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) ) ),
inference(cnf,[status(esa)],[1187]) ).
thf(1190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_partfun1 @ A @ B @ C )
= ( k1_tarski @ C ) )
| ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v1_partfun1 @ C @ A @ B ) ),
inference(lifteq,[status(thm)],[1188]) ).
thf(228,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice2) ).
thf(2285,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(2295,plain,
v6_lattices @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(231,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(2306,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(644,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_0) ).
thf(4464,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)],[644]) ).
thf(238,axiom,
( ~ ( v3_struct_0 @ k13_nat_lat )
& ( v3_lattices @ k13_nat_lat )
& ( v4_lattices @ k13_nat_lat )
& ( v5_lattices @ k13_nat_lat )
& ( v6_lattices @ k13_nat_lat )
& ( v7_lattices @ k13_nat_lat )
& ( v8_lattices @ k13_nat_lat )
& ( v9_lattices @ k13_nat_lat )
& ( v10_lattices @ k13_nat_lat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_nat_lat) ).
thf(2335,plain,
( ~ ( v3_struct_0 @ k13_nat_lat )
& ( v3_lattices @ k13_nat_lat )
& ( v4_lattices @ k13_nat_lat )
& ( v5_lattices @ k13_nat_lat )
& ( v6_lattices @ k13_nat_lat )
& ( v7_lattices @ k13_nat_lat )
& ( v8_lattices @ k13_nat_lat )
& ( v9_lattices @ k13_nat_lat )
& ( v10_lattices @ k13_nat_lat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(2341,plain,
v4_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[2335]) ).
thf(2336,plain,
v6_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[2335]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice4) ).
thf(5593,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)],[903]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',t11_binop_1) ).
thf(1454,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)],[85]) ).
thf(729,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(4898,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(4899,plain,
( ! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(miniscope,[status(thm)],[4898]) ).
thf(4903,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k1_tarski @ A ) )
| ( C != A )
| ( r2_hidden @ C @ B ) ),
inference(cnf,[status(esa)],[4899]) ).
thf(4908,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k1_tarski @ A ) )
| ( C != A )
| ( r2_hidden @ C @ B ) ),
inference(lifteq,[status(thm)],[4903]) ).
thf(4909,plain,
! [A: $i] : ( r2_hidden @ A @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[4908]) ).
thf(198,axiom,
? [A: $i] :
( ( l2_struct_0 @ A )
& ( v2_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_struct_0) ).
thf(2109,plain,
? [A: $i] :
( ( l2_struct_0 @ A )
& ( v2_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k6_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(4824,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)],[708]) ).
thf(784,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( a_3_0_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_0) ).
thf(5136,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)],[784]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',d2_binop_1) ).
thf(1633,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)],[111]) ).
thf(303,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_lattices) ).
thf(2770,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(2778,plain,
v9_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(690,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) )
& ( r1_tarski @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice4) ).
thf(4729,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)],[690]) ).
thf(549,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(4022,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)],[549]) ).
thf(323,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_lattices) ).
thf(2872,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(2876,plain,
v7_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(350,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(3009,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(3011,plain,
v1_relat_1 @ sk207,
inference(cnf,[status(esa)],[3009]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(1044,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
inference(cnf,[status(esa)],[1044]) ).
thf(7890,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) )
| ( ( v1_relat_1 @ sk207 )
!= ( v1_relat_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3011,1045]) ).
thf(7891,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk207 @ A ) @ ( k9_relat_1 @ sk207 @ ( k1_relat_1 @ sk207 ) ) ),
inference(pattern_uni,[status(thm)],[7890:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).
thf(26,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(1123,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1124,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1123]) ).
thf(1125,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ~ ( v1_relat_1 @ A ) ),
inference(lifteq,[status(thm)],[1124]) ).
thf(13752,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk207 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3011,1125]) ).
thf(13753,plain,
( ( k9_relat_1 @ sk207 @ ( k1_relat_1 @ sk207 ) )
= ( k2_relat_1 @ sk207 ) ),
inference(pattern_uni,[status(thm)],[13752:[bind(A,$thf( sk207 ))]]) ).
thf(20993,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk207 @ A ) @ ( k2_relat_1 @ sk207 ) ),
inference(rewrite,[status(thm)],[7891,13753]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(2921,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(608,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(4290,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)],[608]) ).
thf(436,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(3477,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(1031,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(514,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 @ ( k20_filter_2 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k3_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_2) ).
thf(3863,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 @ ( k20_filter_2 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k3_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(304,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_filter_0) ).
thf(2784,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(2787,plain,
v5_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_subset_1) ).
thf(2544,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_filter_0 @ C @ B )
& ( m1_filter_0 @ D @ B ) )
=> ( ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(5999,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)],[1002]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(1179,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)],[38]) ).
thf(1013,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 @ ( k20_filter_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_filter_2) ).
thf(6042,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 @ ( k20_filter_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(935,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_relset_1 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_filter_0) ).
thf(5733,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)],[935]) ).
thf(226,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A ) )
=> ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattice2) ).
thf(2280,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A ) )
=> ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(331,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(2928,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)],[331]) ).
thf(2929,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)],[2928]) ).
thf(2930,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[2929]) ).
thf(2932,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[2930]) ).
thf(2933,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[2932]) ).
thf(371,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(3121,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(3123,plain,
~ ( v1_xboole_0 @ sk218 ),
inference(cnf,[status(esa)],[3121]) ).
thf(7535,plain,
( ( v1_xboole_0 @ sk218 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2933,3123]) ).
thf(7549,plain,
sk218 != k1_xboole_0,
inference(simp,[status(thm)],[7535]) ).
thf(21,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(1108,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1109,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[1108]) ).
thf(1110,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[1109]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(1211,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(204,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(2155,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(2156,plain,
! [B: $i,A: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(cnf,[status(esa)],[2155]) ).
thf(369,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(3111,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(3112,plain,
v1_funct_1 @ sk216,
inference(cnf,[status(esa)],[3111]) ).
thf(1023,plain,
~ ( v3_struct_0 @ sk1 ),
inference(cnf,[status(esa)],[1018]) ).
thf(6357,plain,
! [B: $i,A: $i] :
( ~ ( v1_funct_1 @ B )
| ~ ( m2_relset_1 @ B @ A @ k1_xboole_0 )
| ~ ( v1_partfun1 @ B @ A @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1049,1023]) ).
thf(6358,plain,
! [A: $i] :
( ~ ( v1_funct_1 @ A )
| ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6357:[bind(A,$thf( sk1 ))]]) ).
thf(6539,plain,
! [A: $i] :
( ~ ( v1_funct_1 @ A )
| ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[6358]) ).
thf(7939,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk216 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3112,6539]) ).
thf(7940,plain,
( ~ ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7939:[bind(A,$thf( sk216 ))]]) ).
thf(14298,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,7940]) ).
thf(14381,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk216 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14298]) ).
thf(14414,plain,
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk216 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14381]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(1066,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1067,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ( A = k1_xboole_0 )
| ~ ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
| ( ( k9_relat_1 @ B @ A )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1066]) ).
thf(1068,plain,
! [B: $i,A: $i] :
( ( A = k1_xboole_0 )
| ( ( k9_relat_1 @ B @ A )
!= k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ A @ ( k1_relat_1 @ B ) ) ),
inference(lifteq,[status(thm)],[1067]) ).
thf(108,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(1618,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(631,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v17_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_lattices) ).
thf(4383,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v17_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(4391,plain,
v3_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(809,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/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_2) ).
thf(5237,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)],[809]) ).
thf(61,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(1305,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(1041,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)],[5]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(1200,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(860,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v12_lattices @ A )
=> ( v12_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_filter_0) ).
thf(5444,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)],[860]) ).
thf(687,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k5_lattices @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).
thf(4714,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( B
= ( k5_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(32,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
=> ( ( ( k1_funct_1 @ A @ C )
= D )
<=> ( ( k1_funct_1 @ B @ D )
= C ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
thf(1148,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
=> ( ( ( ( k1_funct_1 @ A @ C )
= D )
=> ( ( k1_funct_1 @ B @ D )
= C ) )
& ( ( ( k1_funct_1 @ B @ D )
= C )
=> ( ( k1_funct_1 @ A @ C )
= D ) ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( r2_hidden @ ( sk11 @ B @ A ) @ ( k1_relat_1 @ B ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1148]) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( r2_hidden @ ( sk11 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
inference(lifteq,[status(thm)],[1154]) ).
thf(232,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relat_1) ).
thf(2309,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1884,plain,
v1_xboole_0 @ sk71,
inference(cnf,[status(esa)],[1883]) ).
thf(722,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(4869,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(4870,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(miniscope,[status(thm)],[4869]) ).
thf(4871,plain,
~ ( v1_xboole_0 @ sk364 ),
inference(cnf,[status(esa)],[4870]) ).
thf(6175,plain,
( ( v1_xboole_0 @ sk364 )
!= ( v1_xboole_0 @ sk71 ) ),
inference(paramod_ordered,[status(thm)],[1884,4871]) ).
thf(6177,plain,
sk364 != sk71,
inference(simp,[status(thm)],[6175]) ).
thf(333,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(2938,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(2939,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(miniscope,[status(thm)],[2938]) ).
thf(2940,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(cnf,[status(esa)],[2939]) ).
thf(786,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/sandbox2/benchmark/theBenchmark.p',t14_filter_2) ).
thf(5141,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)],[786]) ).
thf(197,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_lattices) ).
thf(2098,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(2104,plain,
v10_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',d3_relat_2) ).
thf(2644,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)],[286]) ).
thf(655,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/sandbox2/benchmark/theBenchmark.p',d4_lattice2) ).
thf(4515,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)],[655]) ).
thf(3113,plain,
v1_xboole_0 @ sk216,
inference(cnf,[status(esa)],[3111]) ).
thf(8071,plain,
( ( v1_xboole_0 @ sk218 )
!= ( v1_xboole_0 @ sk216 ) ),
inference(paramod_ordered,[status(thm)],[3113,3123]) ).
thf(8082,plain,
sk218 != sk216,
inference(simp,[status(thm)],[8071]) ).
thf(823,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_0) ).
thf(5292,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)],[823]) ).
thf(327,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(2906,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(2907,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2906]) ).
thf(2908,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2907]) ).
thf(448,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k1_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice4) ).
thf(3549,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)],[448]) ).
thf(2776,plain,
v13_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relat_1) ).
thf(1808,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(282,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_lattices) ).
thf(2578,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(2590,plain,
v12_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(1401,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(621,axiom,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s4_funct_2 )
=> ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
= ( f3_s4_funct_2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_funct_2) ).
thf(4351,plain,
? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s4_funct_2 )
=> ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
= ( f3_s4_funct_2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(4353,plain,
m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2,
inference(cnf,[status(esa)],[4351]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(1117,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m2_relset_1 @ C @ A @ B )
| ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ),
inference(cnf,[status(esa)],[1117]) ).
thf(13106,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k2_relat_1 @ C ) @ B )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4353,1119]) ).
thf(13107,plain,
r1_tarski @ ( k2_relat_1 @ sk315 ) @ f2_s4_funct_2,
inference(pattern_uni,[status(thm)],[13106:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk315 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(1072,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)],[14]) ).
thf(1073,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(miniscope,[status(thm)],[1072]) ).
thf(1074,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ A @ B )
| ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[1073]) ).
thf(13121,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ ( k2_relat_1 @ sk315 ) @ f2_s4_funct_2 )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13107,1074]) ).
thf(13122,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ sk315 ) @ A ) @ f2_s4_funct_2 ),
inference(pattern_uni,[status(thm)],[13121:[bind(A,$thf( k2_relat_1 @ sk315 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(13159,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ sk315 ) @ A ) @ f2_s4_funct_2 ),
inference(simp,[status(thm)],[13122]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_partfun1) ).
thf(2947,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(2248,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)],[221]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(1939,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)],[165]) ).
thf(685,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(4697,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)],[685]) ).
thf(971,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/sandbox2/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
thf(5878,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)],[971]) ).
thf(366,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/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
thf(3098,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)],[366]) ).
thf(912,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v1_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 @ ( k4_lattices @ A @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_filter_2) ).
thf(5625,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( v1_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 @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( 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 @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) ) )
=> ( v1_filter_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(2014,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(523,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v13_lattices @ A )
& ( r3_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice4) ).
thf(3910,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)],[523]) ).
thf(740,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/sandbox2/benchmark/theBenchmark.p',t83_lattice2) ).
thf(4960,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)],[740]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(3108,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)],[368]) ).
thf(686,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(4706,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(4707,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[4706]) ).
thf(4711,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk352 @ A ) ),
inference(cnf,[status(esa)],[4707]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(4603,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)],[669]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( m2_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).
thf(3012,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)],[351]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(1205,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)],[45]) ).
thf(2099,plain,
~ ( v3_struct_0 @ sk94 ),
inference(cnf,[status(esa)],[2098]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(2282,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)],[227]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(2114,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)],[200]) ).
thf(852,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k17_filter_2 @ A ) @ ( k18_filter_2 @ A @ ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_2) ).
thf(5405,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k17_filter_2 @ A ) @ ( k18_filter_2 @ A @ ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_funct_2) ).
thf(1140,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v1_partfun1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v1_partfun1 @ C @ A @ B )
| ( v1_funct_2 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[1140]) ).
thf(3010,plain,
v1_funct_1 @ sk207,
inference(cnf,[status(esa)],[3009]) ).
thf(1022,plain,
l3_lattices @ sk1,
inference(cnf,[status(esa)],[1018]) ).
thf(6323,plain,
! [B: $i,A: $i] :
( ~ ( v1_funct_1 @ B )
| ~ ( m2_relset_1 @ B @ A @ k1_xboole_0 )
| ~ ( v1_partfun1 @ B @ A @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1049,1022]) ).
thf(6324,plain,
! [A: $i] :
( ~ ( v1_funct_1 @ A )
| ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6323:[bind(A,$thf( sk1 ))]]) ).
thf(6524,plain,
! [A: $i] :
( ~ ( v1_funct_1 @ A )
| ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[6324]) ).
thf(7849,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk207 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3010,6524]) ).
thf(7850,plain,
( ~ ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7849:[bind(A,$thf( sk207 ))]]) ).
thf(817,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/sandbox2/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
thf(5265,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)],[817]) ).
thf(589,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k5_lattice4 @ A ) )
& ( v1_funct_2 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice4) ).
thf(4215,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)],[589]) ).
thf(1009,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(6031,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(884,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_filter_0 @ A @ ( k1_filter_0 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_0) ).
thf(5529,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)],[884]) ).
thf(837,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_0) ).
thf(5348,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)],[837]) ).
thf(450,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(3554,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)],[450]) ).
thf(3555,plain,
! [A: $i] : ( v1_xboole_0 @ ( sk251 @ A ) ),
inference(cnf,[status(esa)],[3554]) ).
thf(11709,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk251 @ A ) )
!= ( v1_xboole_0 @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[3555,1196]) ).
thf(11724,plain,
! [A: $i] :
( ( sk251 @ A )
!= sk14 ),
inference(simp,[status(thm)],[11709]) ).
thf(846,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v11_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ ( k2_lattices @ A @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_lattices) ).
thf(5383,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v11_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ ( k2_lattices @ A @ B @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ ( k2_lattices @ A @ B @ D ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(694,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v1_filter_2 @ B @ A )
<=> ( v2_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_2) ).
thf(4747,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( v1_filter_2 @ B @ A )
=> ( v2_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) )
& ( ( v2_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) )
=> ( v1_filter_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(4355,plain,
v1_funct_1 @ sk315,
inference(cnf,[status(esa)],[4351]) ).
thf(8298,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk315 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4355,6539]) ).
thf(8299,plain,
( ~ ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[8298:[bind(A,$thf( sk315 ))]]) ).
thf(14354,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,8299]) ).
thf(14376,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk315 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14354]) ).
thf(14409,plain,
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk315 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14376]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',d4_binop_1) ).
thf(1173,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)],[37]) ).
thf(658,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/sandbox2/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(4532,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)],[658]) ).
thf(6187,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) )
| ( ( v1_relat_1 @ sk71 )
!= ( v1_relat_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1887,1045]) ).
thf(6188,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk71 @ A ) @ ( k9_relat_1 @ sk71 @ ( k1_relat_1 @ sk71 ) ) ),
inference(pattern_uni,[status(thm)],[6187:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).
thf(13750,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk71 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1887,1125]) ).
thf(13751,plain,
( ( k9_relat_1 @ sk71 @ ( k1_relat_1 @ sk71 ) )
= ( k2_relat_1 @ sk71 ) ),
inference(pattern_uni,[status(thm)],[13750:[bind(A,$thf( sk71 ))]]) ).
thf(18878,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk71 @ A ) @ ( k2_relat_1 @ sk71 ) ),
inference(rewrite,[status(thm)],[6188,13751]) ).
thf(18894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ ( k9_relat_1 @ sk71 @ A ) @ ( k2_relat_1 @ sk71 ) )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18878,1074]) ).
thf(18895,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk71 @ B ) @ A ) @ ( k2_relat_1 @ sk71 ) ),
inference(pattern_uni,[status(thm)],[18894:[bind(A,$thf( F )),bind(B,$thf( k9_relat_1 @ sk71 @ F )),bind(C,$thf( k2_relat_1 @ sk71 )),bind(D,$thf( D ))]]) ).
thf(18951,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk71 @ B ) @ A ) @ ( k2_relat_1 @ sk71 ) ),
inference(simp,[status(thm)],[18895]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(3217,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(820,axiom,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
= f5_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
= f6_s11_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s11_funct_2 )
=> ~ ( ( B != f3_s11_funct_2 )
& ( B != f4_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
!= ( f7_s11_funct_2 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s11_funct_2) ).
thf(5274,plain,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
= f5_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
= f6_s11_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s11_funct_2 )
=> ~ ( ( B != f3_s11_funct_2 )
& ( B != f4_s11_funct_2 )
& ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
!= ( f7_s11_funct_2 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(5280,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( m2_relset_1 @ sk407 @ f1_s11_funct_2 @ f2_s11_funct_2 ) ),
inference(cnf,[status(esa)],[5274]) ).
thf(5286,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( m2_relset_1 @ sk407 @ f1_s11_funct_2 @ f2_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5280]) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m2_relset_1 @ C @ A @ B )
| ( r1_tarski @ ( k1_relat_1 @ C ) @ A ) ),
inference(cnf,[status(esa)],[1117]) ).
thf(13186,plain,
! [C: $i,B: $i,A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
| ( ( m2_relset_1 @ sk407 @ f1_s11_funct_2 @ f2_s11_funct_2 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5286,1118]) ).
thf(13187,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k1_relat_1 @ sk407 ) @ f1_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[13186:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk407 ))]]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(5361,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)],[841]) ).
thf(19,axiom,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(1095,plain,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1097,plain,
( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1095]) ).
thf(1099,plain,
( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1097]) ).
thf(172,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(1976,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1977,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(cnf,[status(esa)],[1976]) ).
thf(1096,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1095]) ).
thf(1098,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1096]) ).
thf(247,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(2402,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(2404,plain,
v1_funct_1 @ sk138,
inference(cnf,[status(esa)],[2402]) ).
thf(6704,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk138 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2404,6524]) ).
thf(6705,plain,
( ~ ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6704:[bind(A,$thf( sk138 ))]]) ).
thf(7081,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1059,6705]) ).
thf(7105,plain,
! [B: $i,A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( B != sk138 )
| ( A != sk1 )
| ( ( k2_relat_1 @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7081]) ).
thf(7109,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ sk138 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7105]) ).
thf(2405,plain,
v1_relat_1 @ sk138,
inference(cnf,[status(esa)],[2402]) ).
thf(7450,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7109,2405]) ).
thf(7451,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7450]) ).
thf(10319,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= ( k2_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1098,7451]) ).
thf(10322,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[10319]) ).
thf(12035,plain,
! [A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,10322]) ).
thf(12039,plain,
! [A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[12035]) ).
thf(12044,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[12039]) ).
thf(12221,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= ( k1_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1099,12044]) ).
thf(12237,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[12221]) ).
thf(12244,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[12237]) ).
thf(901,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_filter_2 @ ( u1_struct_0 @ A ) @ ( k20_filter_2 @ A @ B @ C ) @ ( k20_filter_2 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_2) ).
thf(5589,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_filter_2 @ ( u1_struct_0 @ A ) @ ( k20_filter_2 @ A @ B @ C ) @ ( k20_filter_2 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(147,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1867,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(4279,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
thf(2459,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)],[257]) ).
thf(70,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(1354,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice4) ).
thf(3794,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)],[502]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).
thf(1608,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(633,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(4403,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)],[633]) ).
thf(491,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/sandbox2/benchmark/theBenchmark.p',t66_lattice2) ).
thf(3745,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)],[491]) ).
thf(57,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(1258,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1260,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1258]) ).
thf(1266,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( v1_relat_1 @ ( sk19 @ A ) ) ),
inference(lifteq,[status(thm)],[1260]) ).
thf(1020,plain,
m1_subset_1 @ sk2 @ ( u1_struct_0 @ sk1 ),
inference(cnf,[status(esa)],[1018]) ).
thf(26200,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( m1_subset_1 @ sk2 @ k1_xboole_0 )
| ( A
!= ( u1_struct_0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1266,1020]) ).
thf(26201,plain,
( ( v1_relat_1 @ ( sk19 @ ( u1_struct_0 @ sk1 ) ) )
| ( m1_subset_1 @ sk2 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26200:[bind(A,$thf( u1_struct_0 @ sk1 ))]]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',t3_filter_2) ).
thf(1133,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)],[29]) ).
thf(1134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( 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_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( 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 ) ),
inference(cnf,[status(esa)],[1133]) ).
thf(1136,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
!= ( k1_realset1 @ C @ B ) )
| ( F
!= ( k1_realset1 @ D @ B ) )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( 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_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( 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 ) ),
inference(lifteq,[status(thm)],[1134]) ).
thf(1137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( 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_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( 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 )
| ~ ( v1_funct_1 @ ( k1_realset1 @ D @ B ) )
| ~ ( v1_funct_2 @ ( k1_realset1 @ D @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ ( k1_realset1 @ D @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( r4_binop_1 @ A @ C @ D )
| ( r4_binop_1 @ B @ ( k1_realset1 @ C @ B ) @ ( k1_realset1 @ D @ B ) ) ),
inference(simp,[status(thm)],[1136]) ).
thf(980,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/sandbox2/benchmark/theBenchmark.p',t34_lattice2) ).
thf(5906,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)],[980]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(1310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(3004,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)],[348]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(2035,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)],[186]) ).
thf(714,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/sandbox2/benchmark/theBenchmark.p',t4_filter_2) ).
thf(4839,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)],[714]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_tarski @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(3367,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_tarski @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(550,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( D = k1_xboole_0 )
| ( r3_lattices @ A @ B @ ( k3_lattice2 @ C @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_lattice2) ).
thf(4026,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)],[550]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(1735,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).
thf(1163,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v2_funct_1 @ C )
| ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ),
inference(cnf,[status(esa)],[1163]) ).
thf(234,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/sandbox2/benchmark/theBenchmark.p',t9_domain_1) ).
thf(2316,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)],[234]) ).
thf(430,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ F @ C )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ D @ F ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( C = k1_xboole_0 )
| ( r3_lattices @ A @ ( k3_lattice2 @ B @ A @ C @ D ) @ ( k3_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_lattice2) ).
thf(3446,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)],[430]) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',t12_binop_1) ).
thf(2448,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)],[254]) ).
thf(252,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_nat_lat @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_lattices @ B )
& ( v4_lattices @ B )
& ( v5_lattices @ B )
& ( v6_lattices @ B )
& ( v7_lattices @ B )
& ( v8_lattices @ B )
& ( v9_lattices @ B )
& ( v10_lattices @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_nat_lat) ).
thf(2434,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_nat_lat @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_lattices @ B )
& ( v4_lattices @ B )
& ( v5_lattices @ B )
& ( v6_lattices @ B )
& ( v7_lattices @ B )
& ( v8_lattices @ B )
& ( v9_lattices @ B )
& ( v10_lattices @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ~ ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(2712,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)],[293]) ).
thf(262,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(2508,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(2510,plain,
v1_xboole_0 @ sk152,
inference(cnf,[status(esa)],[2508]) ).
thf(500,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(3788,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(3789,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[3788]) ).
thf(3790,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[3789]) ).
thf(6847,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk152 ) ),
inference(paramod_ordered,[status(thm)],[2510,3790]) ).
thf(6851,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk152 ),
inference(simp,[status(thm)],[6847]) ).
thf(12681,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4353,1118]) ).
thf(12682,plain,
r1_tarski @ ( k1_relat_1 @ sk315 ) @ f1_s4_funct_2,
inference(pattern_uni,[status(thm)],[12681:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk315 ))]]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(1085,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)],[16]) ).
thf(1086,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] : ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(miniscope,[status(thm)],[1085]) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ A @ B )
| ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(cnf,[status(esa)],[1086]) ).
thf(12695,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) )
| ( ( r1_tarski @ ( k1_relat_1 @ sk315 ) @ f1_s4_funct_2 )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12682,1087]) ).
thf(12696,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ f1_s4_funct_2 ) @ ( k4_xboole_0 @ A @ ( k1_relat_1 @ sk315 ) ) ),
inference(pattern_uni,[status(thm)],[12695:[bind(A,$thf( k1_relat_1 @ sk315 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(12742,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ f1_s4_funct_2 ) @ ( k4_xboole_0 @ A @ ( k1_relat_1 @ sk315 ) ) ),
inference(simp,[status(thm)],[12696]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(1640,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(2580,plain,
v10_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(2901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(407,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
<=> ( v13_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_lattice2) ).
thf(3313,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)],[407]) ).
thf(797,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattices) ).
thf(5178,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)],[797]) ).
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_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_0) ).
thf(5636,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)],[913]) ).
thf(7534,plain,
( ( v1_xboole_0 @ sk364 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2933,4871]) ).
thf(7550,plain,
sk364 != k1_xboole_0,
inference(simp,[status(thm)],[7534]) ).
thf(26300,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A != sk364 ) ),
inference(paramod_ordered,[status(thm)],[1266,7550]) ).
thf(26301,plain,
v1_relat_1 @ ( sk19 @ sk364 ),
inference(pattern_uni,[status(thm)],[26300:[bind(A,$thf( sk364 ))]]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(2042,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)],[188]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(1222,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)],[49]) ).
thf(482,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/sandbox2/benchmark/theBenchmark.p',t68_lattice2) ).
thf(3717,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)],[482]) ).
thf(1015,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(6046,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)],[1015]) ).
thf(399,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( v7_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lattices) ).
thf(3276,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( ( v7_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ D ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ D ) ) ) ) )
=> ( v7_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(281,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(2575,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)],[281]) ).
thf(127,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 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_2) ).
thf(1746,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 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(1835,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)],[140]) ).
thf(341,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(2972,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)],[341]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(3502,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)],[441]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(4371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(3505,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)],[442]) ).
thf(3506,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[3505]) ).
thf(3508,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( r1_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[3506]) ).
thf(3512,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( r1_tarski @ A @ B ) ),
inference(lifteq,[status(thm)],[3508]) ).
thf(3513,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(simp,[status(thm)],[3512]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(3688,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)],[479]) ).
thf(4386,plain,
v7_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(735,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattices) ).
thf(4941,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(2965,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)],[339]) ).
thf(2966,plain,
( ( v1_funct_1 @ k1_xboole_0 )
& ! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
inference(miniscope,[status(thm)],[2965]) ).
thf(2968,plain,
v1_funct_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[2966]) ).
thf(7567,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ k1_xboole_0 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2968,6524]) ).
thf(7568,plain,
( ~ ( m2_relset_1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7567:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(14291,plain,
( ~ $true
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7568,2156]) ).
thf(14292,plain,
( ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[14291]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_2) ).
thf(3335,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)],[412]) ).
thf(7841,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk207 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3010,6539]) ).
thf(7842,plain,
( ~ ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7841:[bind(A,$thf( sk207 ))]]) ).
thf(11119,plain,
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,7842]) ).
thf(11171,plain,
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk315 != sk207 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11119]) ).
thf(25610,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v9_lattices @ k1_xboole_0 )
| ( A != sk187 ) ),
inference(paramod_ordered,[status(thm)],[1266,2778]) ).
thf(25611,plain,
( ( v1_relat_1 @ ( sk19 @ sk187 ) )
| ( v9_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25610:[bind(A,$thf( sk187 ))]]) ).
thf(417,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( r2_hidden @ B @ A ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(3350,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)],[417]) ).
thf(938,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(5740,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',t120_funct_2) ).
thf(2723,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)],[294]) ).
thf(27,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_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ B @ C ) )
& ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_realset1) ).
thf(1126,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_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ ( k1_realset1 @ B @ C ) )
& ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
& ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1127,plain,
! [C: $i,B: $i,A: $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 )
| ~ ( m1_realset1 @ C @ A @ B )
| ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ),
inference(cnf,[status(esa)],[1126]) ).
thf(873,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_nat_lat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_nat_lat) ).
thf(5486,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)],[873]) ).
thf(344,axiom,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v3_lattices @ k6_nat_lat )
& ( v4_lattices @ k6_nat_lat )
& ( v5_lattices @ k6_nat_lat )
& ( v6_lattices @ k6_nat_lat )
& ( v7_lattices @ k6_nat_lat )
& ( v8_lattices @ k6_nat_lat )
& ( v9_lattices @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_nat_lat) ).
thf(2980,plain,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v3_lattices @ k6_nat_lat )
& ( v4_lattices @ k6_nat_lat )
& ( v5_lattices @ k6_nat_lat )
& ( v6_lattices @ k6_nat_lat )
& ( v7_lattices @ k6_nat_lat )
& ( v8_lattices @ k6_nat_lat )
& ( v9_lattices @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(2985,plain,
v8_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[2980]) ).
thf(990,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( v1_filter_0 @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_0) ).
thf(5935,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)],[990]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k7_domain_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k7_domain_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(13178,plain,
! [C: $i,B: $i,A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k2_relat_1 @ C ) @ B )
| ( ( m2_relset_1 @ sk407 @ f1_s11_funct_2 @ f2_s11_funct_2 )
!= ( m2_relset_1 @ C @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5286,1119]) ).
thf(13179,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k2_relat_1 @ sk407 ) @ f2_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[13178:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk407 ))]]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(1391,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1868,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1867]) ).
thf(761,axiom,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(5058,plain,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(5059,plain,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[5058]) ).
thf(16680,plain,
! [A: $i] :
( ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1868,5059]) ).
thf(16681,plain,
r1_tarski @ ( k5_finsub_1 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[16680:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(246,axiom,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(2400,plain,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(2401,plain,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2400]) ).
thf(16720,plain,
r1_tarski @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ),
inference(rewrite,[status(thm)],[16681,2401]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( m1_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).
thf(1935,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( m1_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
=> ( m1_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(533,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/sandbox2/benchmark/theBenchmark.p',t12_filter_2) ).
thf(3947,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)],[533]) ).
thf(2886,plain,
v16_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(979,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(5902,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(5903,plain,
v3_lattices @ sk456,
inference(cnf,[status(esa)],[5902]) ).
thf(71,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( C
= ( k1_funct_1 @ A @ B ) )
<=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) )
& ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( C
= ( k1_funct_1 @ A @ B ) )
<=> ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(1359,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( C
= ( k1_funct_1 @ A @ B ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) )
& ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( C
= ( k1_funct_1 @ A @ B ) ) ) ) )
& ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( C
= ( k1_funct_1 @ A @ B ) )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( C
= ( k1_funct_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
<=> ~ ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(1601,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
=> ~ ( r2_hidden @ A @ B ) )
& ( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(3466,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)],[435]) ).
thf(505,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( C
= ( k3_filter_0 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_filter_0) ).
thf(3809,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)],[505]) ).
thf(671,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_lattices @ A @ ( k2_lattice4 @ A @ B ) )
= ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k5_lattice4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice4) ).
thf(4607,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)],[671]) ).
thf(29075,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ ( sk19 @ sk364 ) )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26301,1125]) ).
thf(29076,plain,
( ( k9_relat_1 @ ( sk19 @ sk364 ) @ ( k1_relat_1 @ ( sk19 @ sk364 ) ) )
= ( k2_relat_1 @ ( sk19 @ sk364 ) ) ),
inference(pattern_uni,[status(thm)],[29075:[bind(A,$thf( sk19 @ sk364 ))]]) ).
thf(741,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s3_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s3_funct_2 )
& ( p1_s3_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_funct_2 )
=> ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_2) ).
thf(4963,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s3_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s3_funct_2 )
& ( p1_s3_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s3_funct_2 )
=> ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( ( k1_funct_1 @ D @ F )
= ( k1_funct_1 @ E @ F ) ) ) )
=> ( ( k1_funct_4 @ E @ ( k2_partfun1 @ A @ B @ D @ C ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice2) ).
thf(2825,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( ( k1_funct_1 @ D @ F )
= ( k1_funct_1 @ E @ F ) ) ) )
=> ( ( k1_funct_4 @ E @ ( k2_partfun1 @ A @ B @ D @ C ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(203,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ! [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 @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( C
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( D
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) )
=> ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v1_binop_1 @ D @ B )
& ( v2_binop_1 @ D @ B )
& ( r1_lattice2 @ B @ C @ D )
& ( r1_lattice2 @ B @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_2) ).
thf(2136,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ! [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 @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
=> ( ( ( C
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( D
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) )
=> ( ( v1_binop_1 @ C @ B )
& ( v2_binop_1 @ C @ B )
& ( v1_binop_1 @ D @ B )
& ( v2_binop_1 @ D @ B )
& ( r1_lattice2 @ B @ C @ D )
& ( r1_lattice2 @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(672,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_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 ) )
=> ( r1_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
thf(4610,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_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 ) )
=> ( r1_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(270,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/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(2531,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)],[270]) ).
thf(645,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice2) ).
thf(4467,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)],[645]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(1228,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(1482,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)],[91]) ).
thf(653,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lattice4) ).
thf(4511,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)],[653]) ).
thf(11710,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk251 @ A ) )
!= ( v1_xboole_0 @ sk364 ) ),
inference(paramod_ordered,[status(thm)],[3555,4871]) ).
thf(11720,plain,
! [A: $i] :
( ( sk251 @ A )
!= sk364 ),
inference(simp,[status(thm)],[11710]) ).
thf(835,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(5342,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(891,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/sandbox2/benchmark/theBenchmark.p',dt_k11_filter_2) ).
thf(5553,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)],[891]) ).
thf(396,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/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(3263,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)],[396]) ).
thf(899,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( v11_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattice4) ).
thf(5585,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)],[899]) ).
thf(187,axiom,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(2039,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(3114,plain,
v1_relat_1 @ sk216,
inference(cnf,[status(esa)],[3111]) ).
thf(8105,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) )
| ( ( v1_relat_1 @ sk216 )
!= ( v1_relat_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3114,1045]) ).
thf(8106,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk216 @ A ) @ ( k9_relat_1 @ sk216 @ ( k1_relat_1 @ sk216 ) ) ),
inference(pattern_uni,[status(thm)],[8105:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).
thf(13770,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk216 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3114,1125]) ).
thf(13771,plain,
( ( k9_relat_1 @ sk216 @ ( k1_relat_1 @ sk216 ) )
= ( k2_relat_1 @ sk216 ) ),
inference(pattern_uni,[status(thm)],[13770:[bind(A,$thf( sk216 ))]]) ).
thf(21086,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk216 @ A ) @ ( k2_relat_1 @ sk216 ) ),
inference(rewrite,[status(thm)],[8106,13771]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( k3_relat_1 @ C )
= ( k2_tarski @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relat_1) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
=> ( ( k3_relat_1 @ C )
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(2217,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)],[215]) ).
thf(67,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 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_2) ).
thf(1323,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 ) )
=> ( ( k3_funct_2 @ A @ B @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(60,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(1279,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_partfun1) ).
thf(3248,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k6_domain_1 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(4238,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k6_domain_1 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(1050,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)],[8]) ).
thf(1051,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(miniscope,[status(thm)],[1050]) ).
thf(1052,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ A @ B )
| ~ ( m2_relset_1 @ D @ A @ B )
| ~ ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
| ( E
= ( k1_funct_1 @ D @ ( sk5 @ E @ D @ C @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[1051]) ).
thf(1055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_funct_1 @ D @ ( sk5 @ E @ D @ C @ B @ A ) )
= E )
| ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ A @ B )
| ~ ( m2_relset_1 @ D @ A @ B )
| ~ ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) ) ),
inference(lifteq,[status(thm)],[1052]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(1409,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
<=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(3195,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) )
& ( ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) )
=> ( r1_tarski @ A @ ( k2_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(620,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ ( k2_lattice4 @ A @ B ) @ ( k2_lattice4 @ A @ C ) )
= ( k2_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice4) ).
thf(4348,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)],[620]) ).
thf(11113,plain,
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,7940]) ).
thf(11203,plain,
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk315 != sk216 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11113]) ).
thf(116,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(1660,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(973,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/sandbox2/benchmark/theBenchmark.p',dt_k23_filter_2) ).
thf(5883,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)],[973]) ).
thf(2339,plain,
v5_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[2335]) ).
thf(5277,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( v1_funct_2 @ sk407 @ f1_s11_funct_2 @ f2_s11_funct_2 ) ),
inference(cnf,[status(esa)],[5274]) ).
thf(5284,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( v1_funct_2 @ sk407 @ f1_s11_funct_2 @ f2_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5277]) ).
thf(261,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/sandbox2/benchmark/theBenchmark.p',t118_funct_2) ).
thf(2501,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)],[261]) ).
thf(7935,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk216 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3112,6496]) ).
thf(7936,plain,
( ~ ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7935:[bind(A,$thf( sk216 ))]]) ).
thf(11116,plain,
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,7936]) ).
thf(11178,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk216 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11116]) ).
thf(11117,plain,
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,6582]) ).
thf(11200,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk71 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11117]) ).
thf(799,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_tarski @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).
thf(5182,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_tarski @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(3845,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)],[511]) ).
thf(364,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_subset_1) ).
thf(3089,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
=> ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_1) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
=> ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
= ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(2897,plain,
v3_filter_0 @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(178,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_group_1 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattice2) ).
thf(1992,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_group_1 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(746,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v11_lattices @ A )
=> ( v11_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_0) ).
thf(4984,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)],[746]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(1462,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(1130,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ( ( k1_relat_1 @ B )
!= ( k1_relat_1 @ C ) )
| ( ( k2_relat_1 @ B )
!= ( k1_tarski @ A ) )
| ( ( k2_relat_1 @ C )
!= ( k1_tarski @ A ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[1130]) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= ( k1_relat_1 @ C ) )
| ( ( k2_relat_1 @ B )
!= ( k1_tarski @ A ) )
| ( ( k2_relat_1 @ C )
!= ( k1_tarski @ A ) )
| ( B = C )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C ) ),
inference(lifteq,[status(thm)],[1131]) ).
thf(816,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_0_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).
thf(5256,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_0_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s7_domain_1 )
& ( A = B )
& ( p1_s7_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_funct_2) ).
thf(1144,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
| ( ( k1_relat_1 @ C )
= A ) ),
inference(cnf,[status(esa)],[1144]) ).
thf(1147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ C )
= A )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ),
inference(lifteq,[status(thm)],[1146]) ).
thf(8306,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk315 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4355,6524]) ).
thf(8307,plain,
( ~ ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[8306:[bind(A,$thf( sk315 ))]]) ).
thf(11126,plain,
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 )
!= ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,8307]) ).
thf(11205,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk315 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11126]) ).
thf(11247,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11205]) ).
thf(259,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_subset_1) ).
thf(2482,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(2483,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
inference(cnf,[status(esa)],[2482]) ).
thf(2484,plain,
! [A: $i] :
( ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) )
= ( k1_subset_1 @ A ) ),
inference(lifteq,[status(thm)],[2483]) ).
thf(248,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(2406,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(2407,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(cnf,[status(esa)],[2406]) ).
thf(2408,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(lifteq,[status(thm)],[2407]) ).
thf(34172,plain,
! [A: $i] :
( ( k3_subset_1 @ A @ A )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[2484,2408,2908]) ).
thf(25697,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk216 ) ),
inference(paramod_ordered,[status(thm)],[1266,14414]) ).
thf(25698,plain,
( ( v1_relat_1 @ ( sk19 @ sk216 ) )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25697:[bind(A,$thf( sk216 ))]]) ).
thf(600,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(4265,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)],[600]) ).
thf(2989,plain,
v10_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[2980]) ).
thf(8271,plain,
( ( v1_xboole_0 @ sk296 )
!= ( v1_xboole_0 @ sk218 ) ),
inference(paramod_ordered,[status(thm)],[4082,3123]) ).
thf(8278,plain,
sk296 != sk218,
inference(simp,[status(thm)],[8271]) ).
thf(834,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/sandbox2/benchmark/theBenchmark.p',t60_nat_lat) ).
thf(5337,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)],[834]) ).
thf(5338,plain,
l3_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[5337]) ).
thf(569,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) @ D )
= ( k4_lattices @ A @ ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattice4) ).
thf(4119,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)],[569]) ).
thf(545,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/sandbox2/benchmark/theBenchmark.p',dt_k15_filter_2) ).
thf(3998,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)],[545]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_2) ).
thf(2857,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(968,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) )
= ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattices) ).
thf(5866,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)],[968]) ).
thf(2403,plain,
v2_funct_1 @ sk138,
inference(cnf,[status(esa)],[2402]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(3638,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)],[466]) ).
thf(582,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/sandbox2/benchmark/theBenchmark.p',t17_filter_2) ).
thf(4194,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)],[582]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(5127,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)],[781]) ).
thf(577,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) )
= ( k3_lattices @ A @ ( k1_lattice4 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice4) ).
thf(4179,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)],[577]) ).
thf(905,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_filter_0) ).
thf(5604,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)],[905]) ).
thf(302,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/sandbox2/benchmark/theBenchmark.p',t119_funct_2) ).
thf(2767,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)],[302]) ).
thf(69,axiom,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(1332,plain,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1333,plain,
~ ? [A: $i,B: $i] :
( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(miniscope,[status(thm)],[1332]) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_funct_1 @ ( sk25 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1333]) ).
thf(1346,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_funct_1 @ ( sk25 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[1339]) ).
thf(1347,plain,
! [A: $i] : ( v1_funct_1 @ ( sk25 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[1346]) ).
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 ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_0) ).
thf(5397,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)],[849]) ).
thf(911,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_0) ).
thf(5622,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)],[911]) ).
thf(871,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/sandbox2/benchmark/theBenchmark.p',t28_lattice2) ).
thf(5480,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)],[871]) ).
thf(987,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_filter_2) ).
thf(5925,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)],[987]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(1741,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)],[125]) ).
thf(710,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k6_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k2_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice4) ).
thf(4830,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)],[710]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(4368,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ D @ C ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice2) ).
thf(2520,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ D @ C ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(737,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(4952,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)],[737]) ).
thf(295,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v3_filter_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice2) ).
thf(2730,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v3_filter_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(25660,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A != sk218 ) ),
inference(paramod_ordered,[status(thm)],[1266,7549]) ).
thf(25661,plain,
v1_relat_1 @ ( sk19 @ sk218 ),
inference(pattern_uni,[status(thm)],[25660:[bind(A,$thf( sk218 ))]]) ).
thf(28998,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ ( sk19 @ sk218 ) )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25661,1125]) ).
thf(28999,plain,
( ( k9_relat_1 @ ( sk19 @ sk218 ) @ ( k1_relat_1 @ ( sk19 @ sk218 ) ) )
= ( k2_relat_1 @ ( sk19 @ sk218 ) ) ),
inference(pattern_uni,[status(thm)],[28998:[bind(A,$thf( sk19 @ sk218 ))]]) ).
thf(534,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/sandbox2/benchmark/theBenchmark.p',t59_domain_1) ).
thf(3951,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)],[534]) ).
thf(12698,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ ( k1_relat_1 @ sk315 ) @ f1_s4_funct_2 )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12682,1074]) ).
thf(12699,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ sk315 ) @ A ) @ f1_s4_funct_2 ),
inference(pattern_uni,[status(thm)],[12698:[bind(A,$thf( k1_relat_1 @ sk315 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(12743,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ sk315 ) @ A ) @ f1_s4_funct_2 ),
inference(simp,[status(thm)],[12699]) ).
thf(13436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ sk315 ) @ A ) @ f1_s4_funct_2 )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12743,1074]) ).
thf(13437,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k4_xboole_0 @ ( k1_relat_1 @ sk315 ) @ B ) @ A ) @ f1_s4_funct_2 ),
inference(pattern_uni,[status(thm)],[13436:[bind(A,$thf( F )),bind(B,$thf( k4_xboole_0 @ ( k1_relat_1 @ sk315 ) @ F )),bind(C,$thf( f1_s4_funct_2 )),bind(D,$thf( D ))]]) ).
thf(13489,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k4_xboole_0 @ ( k1_relat_1 @ sk315 ) @ B ) @ A ) @ f1_s4_funct_2 ),
inference(simp,[status(thm)],[13437]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(1815,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)],[136]) ).
thf(4390,plain,
l3_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(770,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v14_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_0) ).
thf(5091,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)],[770]) ).
thf(755,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/sandbox2/benchmark/theBenchmark.p',d1_filter_2) ).
thf(5020,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)],[755]) ).
thf(451,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_struct_0 @ A )
<=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
thf(3557,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)],[451]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(4400,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)],[632]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( g2_struct_0 @ A @ B )
= ( g2_struct_0 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(5493,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( g2_struct_0 @ A @ B )
= ( g2_struct_0 @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(611,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/sandbox2/benchmark/theBenchmark.p',t80_lattice2) ).
thf(4302,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)],[611]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
<=> ( B
= ( k2_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_subset_1) ).
thf(2388,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
=> ( B
= ( k2_subset_1 @ A ) ) )
& ( ( B
= ( k2_subset_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(909,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k6_lattices @ A ) @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattices) ).
thf(5617,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)],[909]) ).
thf(668,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s14_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s14_funct_2 )
& ( p1_s14_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s14_funct_2 )
=> ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s14_funct_2) ).
thf(4595,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s14_funct_2 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f2_s14_funct_2 )
& ( p1_s14_funct_2 @ A @ B ) ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s14_funct_2 )
=> ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(256,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( a_2_0_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_domain_1) ).
thf(2456,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( k2_zfmisc_1 @ A @ B )
= ( a_2_0_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(211,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(2178,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',t9_filter_2) ).
thf(3431,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)],[427]) ).
thf(3122,plain,
v1_relat_1 @ sk218,
inference(cnf,[status(esa)],[3121]) ).
thf(8128,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) )
| ( ( v1_relat_1 @ sk218 )
!= ( v1_relat_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3122,1045]) ).
thf(8129,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk218 @ A ) @ ( k9_relat_1 @ sk218 @ ( k1_relat_1 @ sk218 ) ) ),
inference(pattern_uni,[status(thm)],[8128:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).
thf(13758,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk218 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3122,1125]) ).
thf(13759,plain,
( ( k9_relat_1 @ sk218 @ ( k1_relat_1 @ sk218 ) )
= ( k2_relat_1 @ sk218 ) ),
inference(pattern_uni,[status(thm)],[13758:[bind(A,$thf( sk218 ))]]) ).
thf(21476,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk218 @ A ) @ ( k2_relat_1 @ sk218 ) ),
inference(rewrite,[status(thm)],[8129,13759]) ).
thf(2880,plain,
v6_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(2777,plain,
v6_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1183,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)],[39]) ).
thf(496,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/sandbox2/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(3771,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)],[496]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(2950,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)],[336]) ).
thf(585,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
thf(4205,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(4396,plain,
v10_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(2307,plain,
~ ? [A: $i,B: $i] : ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(miniscope,[status(thm)],[2306]) ).
thf(2308,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[2307]) ).
thf(7264,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk152 ) ),
inference(paramod_ordered,[status(thm)],[2510,2308]) ).
thf(7268,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk152 ),
inference(simp,[status(thm)],[7264]) ).
thf(733,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(4934,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(4935,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(miniscope,[status(thm)],[4934]) ).
thf(4936,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[4935]) ).
thf(8277,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk296 ) ),
inference(paramod_ordered,[status(thm)],[4082,4936]) ).
thf(8284,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk296 ),
inference(simp,[status(thm)],[8277]) ).
thf(919,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/sandbox2/benchmark/theBenchmark.p',t26_lattice2) ).
thf(5663,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)],[919]) ).
thf(7541,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2933,3790]) ).
thf(7544,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[7541]) ).
thf(10640,plain,
! [A: $i] :
( ( ( k1_tarski @ k1_xboole_0 )
!= k1_xboole_0 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1868,7544]) ).
thf(10641,plain,
( ( k1_tarski @ k1_xboole_0 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[10640:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(2794,plain,
v3_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(975,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattices) ).
thf(5888,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)],[975]) ).
thf(531,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
<=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_0) ).
thf(3934,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)],[531]) ).
thf(767,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/sandbox2/benchmark/theBenchmark.p',dt_k19_filter_2) ).
thf(5084,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)],[767]) ).
thf(665,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) )
<=> ( v1_filter_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_0) ).
thf(4578,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)],[665]) ).
thf(2105,plain,
l3_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(3393,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)],[422]) ).
thf(966,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/sandbox2/benchmark/theBenchmark.p',d12_lattice4) ).
thf(5861,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)],[966]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(1373,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)],[72]) ).
thf(346,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/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(2996,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)],[346]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_lattices @ A @ B @ C )
= ( g3_lattices @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(1911,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)],[159]) ).
thf(2782,plain,
v15_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ( ( k1_relat_1 @ C )
!= A )
| ( r2_hidden @ ( sk4 @ C @ B @ A ) @ A )
| ( sk3 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[1031]) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ C )
!= A )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ( r2_hidden @ ( sk4 @ C @ B @ A ) @ A )
| ( sk3 @ C @ A @ B ) ),
inference(lifteq,[status(thm)],[1032]) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( r2_hidden @ ( sk4 @ B @ A @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ B ) )
| ( sk3 @ B @ ( k1_relat_1 @ B ) @ A ) ),
inference(simp,[status(thm)],[1039]) ).
thf(2893,plain,
v9_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(4297,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)],[609]) ).
thf(832,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k20_filter_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_2) ).
thf(5333,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k20_filter_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(4820,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)],[706]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(3163,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)],[378]) ).
thf(964,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k6_lattices @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattices) ).
thf(5856,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)],[964]) ).
thf(431,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/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_2) ).
thf(3453,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)],[431]) ).
thf(218,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k5_finsub_1 @ A )
= ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(2236,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k5_finsub_1 @ A )
= ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(893,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/sandbox2/benchmark/theBenchmark.p',d13_lattice4) ).
thf(5558,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)],[893]) ).
thf(14305,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,7936]) ).
thf(14375,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( sk216 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14305]) ).
thf(14408,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( sk216 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14375]) ).
thf(201,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_lattices @ A )
& ( l1_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u1_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 ) )
& ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_lattice2) ).
thf(2122,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_lattices @ A )
& ( l1_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u1_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 ) )
& ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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)],[201]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ A ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ B ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(1828,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= k1_xboole_0 )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ A ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k1_tarski @ B ) )
& ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
!= ( k2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(11672,plain,
! [A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,7451]) ).
thf(11682,plain,
! [A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[11672]) ).
thf(11691,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[11682]) ).
thf(173,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 ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t165_funct_2) ).
thf(1978,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 ) )
=> ( ( r1_tarski @ D @ C )
=> ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(2291,plain,
v5_lattices @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(949,axiom,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( r2_hidden @ A @ f2_s4_subset_1 )
<=> ( p1_s4_subset_1 @ A ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( r2_hidden @ A @ f3_s4_subset_1 )
<=> ( p1_s4_subset_1 @ A ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_subset_1) ).
thf(5788,plain,
( ( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( ( r2_hidden @ A @ f2_s4_subset_1 )
=> ( p1_s4_subset_1 @ A ) )
& ( ( p1_s4_subset_1 @ A )
=> ( r2_hidden @ A @ f2_s4_subset_1 ) ) ) )
& ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s4_subset_1 )
=> ( ( ( r2_hidden @ A @ f3_s4_subset_1 )
=> ( p1_s4_subset_1 @ A ) )
& ( ( p1_s4_subset_1 @ A )
=> ( r2_hidden @ A @ f3_s4_subset_1 ) ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(5795,plain,
( sk446
| ( m1_subset_1 @ sk448 @ f1_s4_subset_1 )
| ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(cnf,[status(esa)],[5788]) ).
thf(5805,plain,
( ( f3_s4_subset_1 = f2_s4_subset_1 )
| sk446
| ( m1_subset_1 @ sk448 @ f1_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[5795]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(3923,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(3300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(943,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m3_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice4) ).
thf(5761,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)],[943]) ).
thf(683,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(4686,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(2017,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)],[183]) ).
thf(958,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/sandbox2/benchmark/theBenchmark.p',d7_filter_2) ).
thf(5834,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)],[958]) ).
thf(6856,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk71 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1886,6539]) ).
thf(6857,plain,
( ~ ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6856:[bind(A,$thf( sk71 ))]]) ).
thf(11160,plain,
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,6857]) ).
thf(11168,plain,
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk315 != sk71 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11160]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(2058,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)],[193]) ).
thf(946,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v2_filter_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_0) ).
thf(5773,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)],[946]) ).
thf(839,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 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k7_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k7_lattices @ A @ B ) )
& ( ( k7_lattices @ A @ ( k6_filter_2 @ A @ C ) )
= ( k7_lattices @ ( k1_lattice2 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_2) ).
thf(5353,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 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k7_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k7_lattices @ A @ B ) )
& ( ( k7_lattices @ A @ ( k6_filter_2 @ A @ C ) )
= ( k7_lattices @ ( k1_lattice2 @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(551,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_lattices @ A @ B @ C )
<=> ( ( ( k1_lattices @ A @ B @ C )
= ( k6_lattices @ A ) )
& ( ( k1_lattices @ A @ C @ B )
= ( k6_lattices @ A ) )
& ( ( k2_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
& ( ( k2_lattices @ A @ C @ B )
= ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_lattices) ).
thf(4033,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_lattices @ A @ B @ C )
=> ( ( ( k1_lattices @ A @ B @ C )
= ( k6_lattices @ A ) )
& ( ( k1_lattices @ A @ C @ B )
= ( k6_lattices @ A ) )
& ( ( k2_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
& ( ( k2_lattices @ A @ C @ B )
= ( k5_lattices @ A ) ) ) )
& ( ( ( ( k1_lattices @ A @ B @ C )
= ( k6_lattices @ A ) )
& ( ( k1_lattices @ A @ C @ B )
= ( k6_lattices @ A ) )
& ( ( k2_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
& ( ( k2_lattices @ A @ C @ B )
= ( k5_lattices @ A ) ) )
=> ( r2_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(914,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/sandbox2/benchmark/theBenchmark.p',redefinition_k13_filter_2) ).
thf(5643,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)],[914]) ).
thf(481,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ ( k4_lattice4 @ A @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ ( k4_lattice4 @ A @ B ) )
& ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) )
= ( k2_lattice4 @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice4) ).
thf(3712,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)],[481]) ).
thf(25646,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v6_lattices @ k1_xboole_0 )
| ( A != k13_nat_lat ) ),
inference(paramod_ordered,[status(thm)],[1266,2336]) ).
thf(25647,plain,
( ( v1_relat_1 @ ( sk19 @ k13_nat_lat ) )
| ( v6_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25646:[bind(A,$thf( k13_nat_lat ))]]) ).
thf(978,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r2_lattice4 @ A @ B @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lattice4) ).
thf(5897,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)],[978]) ).
thf(515,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
<=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v15_lattices @ ( k1_lattice2 @ A ) )
& ( v16_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_2) ).
thf(3870,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v15_lattices @ ( k1_lattice2 @ A ) )
& ( v16_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v15_lattices @ ( k1_lattice2 @ A ) )
& ( v16_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(35,axiom,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(1166,plain,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1167,plain,
~ ? [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
inference(miniscope,[status(thm)],[1166]) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ),
inference(cnf,[status(esa)],[1167]) ).
thf(1169,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ),
inference(lifteq,[status(thm)],[1168]) ).
thf(937,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/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_2) ).
thf(5738,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)],[937]) ).
thf(1951,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
inference(cnf,[status(esa)],[1950]) ).
thf(1952,plain,
! [A: $i] :
( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
= ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(lifteq,[status(thm)],[1951]) ).
thf(3368,plain,
( ! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_tarski @ A @ B ) )
=> ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ! [D: $i] :
( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ! [D: $i] :
( ( ( D = A )
| ( D = B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_tarski @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[3367]) ).
thf(3373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( k2_tarski @ A @ B ) )
| ( D != A )
| ( r2_hidden @ D @ C ) ),
inference(cnf,[status(esa)],[3368]) ).
thf(3391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( k2_tarski @ A @ B ) )
| ( D != A )
| ( r2_hidden @ D @ C ) ),
inference(lifteq,[status(thm)],[3373]) ).
thf(3392,plain,
! [B: $i,A: $i] : ( r2_hidden @ A @ ( k2_tarski @ A @ B ) ),
inference(simp,[status(thm)],[3391]) ).
thf(24537,plain,
! [C: $i,B: $i,A: $i] :
( ( r2_hidden @ B @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1952,3392]) ).
thf(24538,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[24537:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(24566,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[24538]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(1213,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( A != C ) )
=> ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1214,plain,
( ! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( A != C ) )
=> ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[1213]) ).
thf(1217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
| ( A != C ) ),
inference(cnf,[status(esa)],[1214]) ).
thf(1220,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ),
inference(lifteq,[status(thm)],[1217]) ).
thf(1221,plain,
! [B: $i,A: $i] :
~ ( r2_hidden @ B @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ),
inference(simp,[status(thm)],[1220]) ).
thf(33842,plain,
! [C: $i,B: $i,A: $i] :
( ( r2_hidden @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
!= ( r2_hidden @ C @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[24566,1221]) ).
thf(33866,plain,
! [C: $i,B: $i,A: $i] :
( ( k1_xboole_0 != C )
| ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ),
inference(simp,[status(thm)],[33842]) ).
thf(33881,plain,
! [B: $i,A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= ( k4_xboole_0 @ B @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(simp,[status(thm)],[33866]) ).
thf(7837,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk207 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3010,6496]) ).
thf(7838,plain,
( ~ ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7837:[bind(A,$thf( sk207 ))]]) ).
thf(14312,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,7838]) ).
thf(14377,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( sk207 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14312]) ).
thf(14410,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( sk207 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14377]) ).
thf(478,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/sandbox2/benchmark/theBenchmark.p',redefinition_k10_filter_2) ).
thf(3685,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)],[478]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).
thf(3036,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(267,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relat_1) ).
thf(2523,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)],[267]) ).
thf(132,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(1796,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(11712,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk251 @ A ) )
!= ( v1_xboole_0 @ ( k4_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3555,2308]) ).
thf(11723,plain,
! [C: $i,B: $i,A: $i] :
( ( sk251 @ A )
!= ( k4_tarski @ B @ C ) ),
inference(simp,[status(thm)],[11712]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v1_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_funct_2) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( v1_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(825,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_0) ).
thf(5296,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)],[825]) ).
thf(2772,plain,
v4_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(829,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_0) ).
thf(5321,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)],[829]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).
thf(4307,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(6690,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk71 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1886,6524]) ).
thf(6691,plain,
( ~ ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6690:[bind(A,$thf( sk71 ))]]) ).
thf(7074,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1059,6691]) ).
thf(7100,plain,
! [B: $i,A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( B != sk71 )
| ( A != sk1 )
| ( ( k2_relat_1 @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7074]) ).
thf(7122,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ sk71 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7100]) ).
thf(8685,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7122,1887]) ).
thf(8686,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[8685]) ).
thf(794,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ! [G: $i] :
( ( m1_filter_0 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( u1_struct_0 @ A ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( u1_struct_0 @ A ) )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r1_filter_0 @ C @ G @ D @ E )
& ( r1_filter_0 @ C @ G @ E @ F ) )
=> ( r1_filter_0 @ C @ G @ D @ F ) )
& ( ( ( r1_filter_0 @ A @ B @ H @ I )
& ( r1_filter_0 @ A @ B @ I @ J ) )
=> ( r1_filter_0 @ A @ B @ H @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_filter_0) ).
thf(5169,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)],[794]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(2002,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)],[179]) ).
thf(1006,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice4) ).
thf(6021,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)],[1006]) ).
thf(308,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(2809,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)],[308]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(2799,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)],[306]) ).
thf(2286,plain,
~ ( v3_struct_0 @ sk118 ),
inference(cnf,[status(esa)],[2285]) ).
thf(2103,plain,
v7_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(2750,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)],[299]) ).
thf(920,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ C ) @ ( k18_filter_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_2) ).
thf(5665,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 ) ) ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ C ) @ ( k18_filter_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_relat_1 @ B )
!= k1_xboole_0 )
| ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[1100]) ).
thf(1104,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[1101]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(1242,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(464,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/sandbox2/benchmark/theBenchmark.p',t22_filter_2) ).
thf(3606,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)],[464]) ).
thf(385,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(3211,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)],[385]) ).
thf(954,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(5824,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(521,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/sandbox2/benchmark/theBenchmark.p',t38_lattice2) ).
thf(3906,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)],[521]) ).
thf(647,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ D )
=> ( r3_lattices @ A @ ( k3_lattice2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_lattice2) ).
thf(4475,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)],[647]) ).
thf(2586,plain,
v11_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(2982,plain,
v4_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[2980]) ).
thf(2884,plain,
v14_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(557,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m3_lattice4 @ C @ A )
=> ( ( C
= ( k3_lattice4 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattice4) ).
thf(4065,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)],[557]) ).
thf(114,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 ) )
| ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_2) ).
thf(1651,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 ) )
| ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(996,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_nat_lat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_nat_lat) ).
thf(5961,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)],[996]) ).
thf(459,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_0) ).
thf(3582,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)],[459]) ).
thf(789,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_2) ).
thf(5157,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)],[789]) ).
thf(752,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_lattices @ A @ B @ C )
& ( r1_lattices @ A @ C @ D ) )
=> ( r1_lattices @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattices) ).
thf(5012,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_lattices @ A @ B @ C )
& ( r1_lattices @ A @ C @ D ) )
=> ( r1_lattices @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(27616,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1266,1023]) ).
thf(27617,plain,
( ( v1_relat_1 @ ( sk19 @ sk1 ) )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[27616:[bind(A,$thf( sk1 ))]]) ).
thf(8077,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk216 ) ),
inference(paramod_ordered,[status(thm)],[3113,4936]) ).
thf(8078,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk216 ),
inference(simp,[status(thm)],[8077]) ).
thf(754,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
thf(5017,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ C )
= ( k2_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(888,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/sandbox2/benchmark/theBenchmark.p',dt_k18_filter_2) ).
thf(5545,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)],[888]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(1056,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1057,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ),
inference(cnf,[status(esa)],[1056]) ).
thf(6874,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk138 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2404,6539]) ).
thf(6875,plain,
( ~ ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6874:[bind(A,$thf( sk138 ))]]) ).
thf(6993,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1057,6875]) ).
thf(7014,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( B != sk138 )
| ( ( k1_relat_1 @ B )
!= sk1 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[6993]) ).
thf(7017,plain,
( ~ ( v1_relat_1 @ sk138 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(simp,[status(thm)],[7014]) ).
thf(7409,plain,
( ~ $true
| ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[7017,2405]) ).
thf(7410,plain,
( ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(simp,[status(thm)],[7409]) ).
thf(21102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ ( k9_relat_1 @ sk216 @ A ) @ ( k2_relat_1 @ sk216 ) )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21086,1074]) ).
thf(21103,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk216 @ B ) @ A ) @ ( k2_relat_1 @ sk216 ) ),
inference(pattern_uni,[status(thm)],[21102:[bind(A,$thf( F )),bind(B,$thf( k9_relat_1 @ sk216 @ F )),bind(C,$thf( k2_relat_1 @ sk216 )),bind(D,$thf( D ))]]) ).
thf(21174,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk216 @ B ) @ A ) @ ( k2_relat_1 @ sk216 ) ),
inference(simp,[status(thm)],[21103]) ).
thf(2790,plain,
v10_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(826,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v8_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).
thf(5298,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v8_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ C )
= C ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ C )
= C ) ) )
=> ( v8_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(1863,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)],[145]) ).
thf(25622,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v5_lattices @ k1_xboole_0 )
| ( A != sk188 ) ),
inference(paramod_ordered,[status(thm)],[1266,2787]) ).
thf(25623,plain,
( ( v1_relat_1 @ ( sk19 @ sk188 ) )
| ( v5_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25622:[bind(A,$thf( sk188 ))]]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
<=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(2204,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)],[212]) ).
thf(405,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v14_lattices @ A )
& ( r2_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattice4) ).
thf(3303,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)],[405]) ).
thf(7389,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk152 ) ),
inference(paramod_ordered,[status(thm)],[2510,2940]) ).
thf(7393,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk152 ),
inference(simp,[status(thm)],[7389]) ).
thf(727,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k5_filter_0 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k4_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_0) ).
thf(4888,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)],[727]) ).
thf(960,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/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
thf(5839,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)],[960]) ).
thf(483,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/sandbox2/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
thf(3720,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)],[483]) ).
thf(541,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v11_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( r2_hidden @ G @ B )
=> ( ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ G )
= ( k4_lattices @ C @ F @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ G ) ) ) ) )
=> ( ( k4_lattices @ C @ F @ ( k2_lattice2 @ A @ C @ B @ E ) )
= ( k2_lattice2 @ A @ C @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_lattice2) ).
thf(3984,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)],[541]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).
thf(3531,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ B )
& ( m1_subset_1 @ E @ C )
& ( A
= ( k1_domain_1 @ B @ C @ D @ E ) )
& ( p1_s2_domain_1 @ D @ E ) )
=> ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(465,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) @ D )
= ( k3_lattices @ A @ ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_lattice4) ).
thf(3635,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)],[465]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(2364,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)],[240]) ).
thf(858,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_0) ).
thf(5438,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)],[858]) ).
thf(380,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(3186,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(229,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(2296,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
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 ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ F @ D )
& ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) )
=> ( r3_lattices @ A @ B @ ( k2_lattice2 @ C @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice2) ).
thf(4576,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)],[664]) ).
thf(881,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_0) ).
thf(5519,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)],[881]) ).
thf(10638,plain,
! [A: $i] :
( ( ( k1_tarski @ k1_xboole_0 )
!= sk152 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1868,6851]) ).
thf(10639,plain,
( ( k1_tarski @ k1_xboole_0 )
!= sk152 ),
inference(pattern_uni,[status(thm)],[10638:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(2773,plain,
v14_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(5279,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ sk407 @ f3_s11_funct_2 )
= f5_s11_funct_2 ) ),
inference(cnf,[status(esa)],[5274]) ).
thf(5281,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ sk407 @ f3_s11_funct_2 )
= f5_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5279]) ).
thf(780,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ B @ C )
<=> ( ( k1_lattices @ A @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
thf(5122,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_lattices @ A @ B @ C )
=> ( ( k1_lattices @ A @ B @ C )
= C ) )
& ( ( ( k1_lattices @ A @ B @ C )
= C )
=> ( r1_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(426,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 @ 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 ) )
=> ( ( ( k1_lattices @ A @ C @ D )
= ( k1_lattices @ B @ E @ F ) )
& ( ( k2_lattices @ A @ C @ D )
= ( k2_lattices @ B @ E @ F ) )
& ( ( r1_lattices @ A @ C @ D )
=> ( r1_lattices @ B @ E @ F ) )
& ( ( r1_lattices @ B @ E @ F )
=> ( r1_lattices @ A @ C @ D ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_filter_2) ).
thf(3418,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 @ 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 ) )
=> ( ( ( k1_lattices @ A @ C @ D )
= ( k1_lattices @ B @ E @ F ) )
& ( ( k2_lattices @ A @ C @ D )
= ( k2_lattices @ B @ E @ F ) )
& ( ( r1_lattices @ A @ C @ D )
=> ( r1_lattices @ B @ E @ F ) )
& ( ( r1_lattices @ B @ E @ F )
=> ( r1_lattices @ A @ C @ D ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(732,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( m1_lattice4 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice4) ).
thf(4925,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)],[732]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(1088,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ( ( k1_relat_1 @ D )
!= ( k1_tarski @ A ) )
| ~ ( r2_hidden @ A @ B )
| ~ ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C )
| ( m2_relset_1 @ D @ B @ C ) ),
inference(cnf,[status(esa)],[1088]) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ D )
!= ( k1_tarski @ A ) )
| ~ ( v1_relat_1 @ D )
| ~ ( v1_funct_1 @ D )
| ~ ( r2_hidden @ A @ B )
| ~ ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C )
| ( m2_relset_1 @ D @ B @ C ) ),
inference(lifteq,[status(thm)],[1089]) ).
thf(251,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 ) )
=> ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
thf(2428,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 ) )
=> ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ D @ C ) @ E )
= E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice2) ).
thf(2541,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ D @ C ) @ E )
= E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(4397,plain,
v16_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(27195,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1266,1022]) ).
thf(27196,plain,
( ( v1_relat_1 @ ( sk19 @ sk1 ) )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[27195:[bind(A,$thf( sk1 ))]]) ).
thf(11154,plain,
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 )
!= ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,8299]) ).
thf(11163,plain,
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk315 != sk315 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11154]) ).
thf(11217,plain,
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11163]) ).
thf(2890,plain,
v13_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(759,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/sandbox2/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
thf(5049,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)],[759]) ).
thf(2589,plain,
v6_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',t27_binop_1) ).
thf(2705,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)],[291]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(2409,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)],[249]) ).
thf(2509,plain,
v1_relat_1 @ sk152,
inference(cnf,[status(esa)],[2508]) ).
thf(6189,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) )
| ( ( v1_relat_1 @ sk152 )
!= ( v1_relat_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2509,1045]) ).
thf(6190,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk152 @ A ) @ ( k9_relat_1 @ sk152 @ ( k1_relat_1 @ sk152 ) ) ),
inference(pattern_uni,[status(thm)],[6189:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).
thf(13760,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk152 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2509,1125]) ).
thf(13761,plain,
( ( k9_relat_1 @ sk152 @ ( k1_relat_1 @ sk152 ) )
= ( k2_relat_1 @ sk152 ) ),
inference(pattern_uni,[status(thm)],[13760:[bind(A,$thf( sk152 ))]]) ).
thf(18965,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk152 @ A ) @ ( k2_relat_1 @ sk152 ) ),
inference(rewrite,[status(thm)],[6190,13761]) ).
thf(395,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(3261,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(922,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/sandbox2/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(5670,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)],[922]) ).
thf(1337,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( r1_tarski @ ( k2_relat_1 @ ( sk25 @ B @ A ) ) @ A ) ),
inference(cnf,[status(esa)],[1333]) ).
thf(1342,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( r1_tarski @ ( k2_relat_1 @ ( sk25 @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[1337]) ).
thf(1343,plain,
! [A: $i] : ( r1_tarski @ ( k2_relat_1 @ ( sk25 @ k1_xboole_0 @ A ) ) @ A ),
inference(simp,[status(thm)],[1342]) ).
thf(538,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_0) ).
thf(3972,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)],[538]) ).
thf(463,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ( ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ D @ B )
= ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ E @ B ) )
=> ( ( k3_lattice2 @ A @ C @ B @ D )
= ( k3_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_lattice2) ).
thf(3603,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)],[463]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(1580,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)],[103]) ).
thf(6032,plain,
l3_lattices @ sk469,
inference(cnf,[status(esa)],[6031]) ).
thf(225,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(2277,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(628,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4375,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(639,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v3_lattice4 @ C @ B @ A )
=> ( ( v3_filter_0 @ A )
& ( r1_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice4) ).
thf(4434,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)],[639]) ).
thf(725,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/sandbox2/benchmark/theBenchmark.p',d1_lattice2) ).
thf(4878,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)],[725]) ).
thf(898,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r4_lattice4 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice4) ).
thf(5579,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)],[898]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(1570,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(748,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v8_lattices @ A )
& ( v9_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 ) )
=> ( ( r1_lattices @ A @ B @ C )
<=> ( ( k2_lattices @ A @ B @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattices) ).
thf(4989,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v8_lattices @ A )
& ( v9_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 ) )
=> ( ( ( r1_lattices @ A @ B @ C )
=> ( ( k2_lattices @ A @ B @ C )
= B ) )
& ( ( ( k2_lattices @ A @ B @ C )
= B )
=> ( r1_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(11715,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk251 @ A ) )
!= ( v1_xboole_0 @ ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3555,3790]) ).
thf(11719,plain,
! [B: $i,A: $i] :
( ( sk251 @ A )
!= ( k1_zfmisc_1 @ B ) ),
inference(simp,[status(thm)],[11715]) ).
thf(994,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/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_2) ).
thf(5956,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)],[994]) ).
thf(952,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v16_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattices @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_lattices) ).
thf(5815,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)],[952]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).
thf(2969,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)],[340]) ).
thf(563,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/sandbox2/benchmark/theBenchmark.p',d3_lattice2) ).
thf(4091,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)],[563]) ).
thf(657,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(4521,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)],[657]) ).
thf(360,axiom,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(3069,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ E )
=> ( ( k1_funct_1 @ C @ F )
= ( k1_funct_1 @ D @ F ) ) ) )
=> ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ C @ E ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_lattice2) ).
thf(3233,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ E )
=> ( ( k1_funct_1 @ C @ F )
= ( k1_funct_1 @ D @ F ) ) ) )
=> ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ C @ E ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(25811,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( A != sk138 ) ),
inference(paramod_ordered,[status(thm)],[1266,12244]) ).
thf(25812,plain,
( ( v1_relat_1 @ ( sk19 @ sk138 ) )
| ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25811:[bind(A,$thf( sk138 ))]]) ).
thf(332,axiom,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(2935,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(2936,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2935]) ).
thf(2937,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2936]) ).
thf(8072,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk216 ) ),
inference(paramod_ordered,[status(thm)],[3113,2308]) ).
thf(8081,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk216 ),
inference(simp,[status(thm)],[8072]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(3134,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)],[374]) ).
thf(942,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v9_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ B @ C ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattices) ).
thf(5754,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v9_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ B @ C ) )
= B ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ B @ C ) )
= B ) ) )
=> ( v9_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( r1_lattices @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(4284,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( r1_lattices @ A @ B @ C ) )
& ( ( r1_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(2986,plain,
v9_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[2980]) ).
thf(6176,plain,
( ( v1_xboole_0 @ sk364 )
!= ( v1_xboole_0 @ sk152 ) ),
inference(paramod_ordered,[status(thm)],[2510,4871]) ).
thf(6178,plain,
sk364 != sk152,
inference(simp,[status(thm)],[6176]) ).
thf(680,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(4661,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(2528,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)],[269]) ).
thf(552,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ C ) @ ( k2_lattice2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice2) ).
thf(4044,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)],[552]) ).
thf(401,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
<=> ( v1_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_2) ).
thf(3286,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( r2_filter_2 @ A @ B )
=> ( v1_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) )
& ( ( v1_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) )
=> ( r2_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(14309,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,7842]) ).
thf(14369,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk207 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14309]) ).
thf(14401,plain,
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk207 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14369]) ).
thf(688,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(4725,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(184,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2019,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(2020,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ~ ? [C: $i] :
( ( r2_hidden @ C @ B )
& ~ ? [D: $i] :
( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ~ ? [C: $i] :
( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(miniscope,[status(thm)],[2019]) ).
thf(2022,plain,
! [A: $i] : ( r2_hidden @ A @ ( sk80 @ A ) ),
inference(cnf,[status(esa)],[2020]) ).
thf(318,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(2849,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)],[318]) ).
thf(2850,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( r2_hidden @ B @ A ) )
& ! [A: $i] :
( ~ ? [B: $i] : ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[2849]) ).
thf(2852,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[2850]) ).
thf(2855,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(lifteq,[status(thm)],[2852]) ).
thf(2856,plain,
! [A: $i] :
~ ( r2_hidden @ A @ k1_xboole_0 ),
inference(simp,[status(thm)],[2855]) ).
thf(13600,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ A @ ( sk80 @ A ) )
!= ( r2_hidden @ B @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2022,2856]) ).
thf(13606,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( sk80 @ A )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[13600]) ).
thf(13612,plain,
! [A: $i] :
( ( sk80 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[13606]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(1888,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(615,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r2_hidden @ ( k6_lattices @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_filter_0) ).
thf(4327,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)],[615]) ).
thf(758,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( v14_lattices @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattices) ).
thf(5038,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( ( v14_lattices @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) )
=> ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(744,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ D @ C )
= ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ E @ C ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_lattice2 @ B @ A @ C @ D )
= ( k2_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice2) ).
thf(4979,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)],[744]) ).
thf(236,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u2_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 ) )
& ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattice2) ).
thf(2327,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u2_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 ) )
& ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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)],[236]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(2741,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)],[296]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relat_1) ).
thf(2112,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(1573,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ~ ( v1_xboole_0 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(462,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/sandbox2/benchmark/theBenchmark.p',t15_filter_2) ).
thf(3595,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)],[462]) ).
thf(556,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(4063,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(379,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/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(3166,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)],[379]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',t57_domain_1) ).
thf(2445,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)],[253]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m1_lattice4 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(5826,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)],[955]) ).
thf(847,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( k3_filter_0 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_0) ).
thf(5391,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)],[847]) ).
thf(2873,plain,
v5_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(625,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(4365,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(4366,plain,
~ ? [A: $i,B: $i] : ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(miniscope,[status(thm)],[4365]) ).
thf(4367,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[4366]) ).
thf(7398,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk152 ) ),
inference(paramod_ordered,[status(thm)],[2510,4367]) ).
thf(7404,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk152 ),
inference(simp,[status(thm)],[7398]) ).
thf(23727,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk152 )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1952,7404]) ).
thf(23728,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk152 ),
inference(pattern_uni,[status(thm)],[23727:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(23776,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk152 ),
inference(simp,[status(thm)],[23728]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(1920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(666,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( v5_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 ) )
=> ( ( k1_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattices) ).
thf(4585,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( ( v5_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 ) )
=> ( ( k1_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) )
=> ( v5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(8076,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk216 ) ),
inference(paramod_ordered,[status(thm)],[3113,4367]) ).
thf(8085,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk216 ),
inference(simp,[status(thm)],[8076]) ).
thf(3372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( k2_tarski @ A @ B ) )
| ( D != B )
| ( r2_hidden @ D @ C ) ),
inference(cnf,[status(esa)],[3368]) ).
thf(3385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( k2_tarski @ A @ B ) )
| ( D != B )
| ( r2_hidden @ D @ C ) ),
inference(lifteq,[status(thm)],[3372]) ).
thf(3386,plain,
! [B: $i,A: $i] : ( r2_hidden @ B @ ( k2_tarski @ A @ B ) ),
inference(simp,[status(thm)],[3385]) ).
thf(24347,plain,
! [C: $i,B: $i,A: $i] :
( ( r2_hidden @ C @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1952,3386]) ).
thf(24348,plain,
! [A: $i] : ( r2_hidden @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[24347:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(24377,plain,
! [A: $i] : ( r2_hidden @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[24348]) ).
thf(6595,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk138 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2404,6496]) ).
thf(6596,plain,
( ~ ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[6595:[bind(A,$thf( sk138 ))]]) ).
thf(6934,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1057,6596]) ).
thf(6946,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( B != sk138 )
| ( ( k1_relat_1 @ B )
!= sk1 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[6934]) ).
thf(6953,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ sk138 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(simp,[status(thm)],[6946]) ).
thf(7184,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[6953,2405]) ).
thf(7185,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(simp,[status(thm)],[7184]) ).
thf(749,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(4994,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)],[749]) ).
thf(375,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_group_1 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v3_filter_0 @ A )
& ( v1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattice2) ).
thf(3137,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_group_1 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v3_filter_0 @ A )
& ( v1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(3499,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)],[440]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(3059,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)],[359]) ).
thf(3060,plain,
( ! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[3059]) ).
thf(3061,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[3060]) ).
thf(3064,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3061]) ).
thf(3065,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3064]) ).
thf(3556,plain,
! [A: $i] : ( m1_subset_1 @ ( sk251 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[3554]) ).
thf(458,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ E ) ) )
=> ( r3_lattices @ C @ ( k2_lattice2 @ A @ C @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_lattice2) ).
thf(3578,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)],[458]) ).
thf(1175,plain,
! [B: $i,A: $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 )
| ( ( k1_binop_1 @ B @ ( sk12 @ B @ A ) @ ( sk12 @ B @ A ) )
!= ( sk12 @ B @ A ) )
| ( v3_binop_1 @ B @ A ) ),
inference(cnf,[status(esa)],[1173]) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( ( k1_binop_1 @ B @ ( sk12 @ B @ A ) @ ( sk12 @ B @ A ) )
!= ( sk12 @ B @ A ) )
| ~ ( 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 ) ),
inference(lifteq,[status(thm)],[1175]) ).
thf(4385,plain,
v4_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(7532,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2933,2940]) ).
thf(7545,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[7532]) ).
thf(11121,plain,
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,7838]) ).
thf(11174,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk207 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11121]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(3028,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(2345,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)],[239]) ).
thf(1128,plain,
! [C: $i,B: $i,A: $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 )
| ~ ( m1_realset1 @ C @ A @ B )
| ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ),
inference(cnf,[status(esa)],[1126]) ).
thf(566,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/sandbox2/benchmark/theBenchmark.p',dt_k24_filter_2) ).
thf(4104,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)],[566]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_partfun1) ).
thf(2547,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(2344,plain,
v7_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[2335]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_2) ).
thf(4732,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(26176,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A
!= ( k1_tarski @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1266,10641]) ).
thf(26177,plain,
v1_relat_1 @ ( sk19 @ ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26176:[bind(A,$thf( k1_tarski @ k1_xboole_0 ))]]) ).
thf(29236,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ ( sk19 @ ( k1_tarski @ k1_xboole_0 ) ) )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26177,1125]) ).
thf(29237,plain,
( ( k9_relat_1 @ ( sk19 @ ( k1_tarski @ k1_xboole_0 ) ) @ ( k1_relat_1 @ ( sk19 @ ( k1_tarski @ k1_xboole_0 ) ) ) )
= ( k2_relat_1 @ ( sk19 @ ( k1_tarski @ k1_xboole_0 ) ) ) ),
inference(pattern_uni,[status(thm)],[29236:[bind(A,$thf( sk19 @ ( k1_tarski @ k1_xboole_0 ) ))]]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(3105,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)],[367]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
& ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(2157,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)],[205]) ).
thf(2100,plain,
v9_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(2801,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)],[307]) ).
thf(513,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(3860,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(3862,plain,
l1_struct_0 @ sk279,
inference(cnf,[status(esa)],[3860]) ).
thf(637,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/sandbox2/benchmark/theBenchmark.p',t25_filter_2) ).
thf(4429,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)],[637]) ).
thf(8294,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk315 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4355,6496]) ).
thf(8295,plain,
( ~ ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[8294:[bind(A,$thf( sk315 ))]]) ).
thf(14350,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,8295]) ).
thf(14380,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( sk315 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14350]) ).
thf(14413,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( sk315 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14380]) ).
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 )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
<=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k10_filter_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_filter_0) ).
thf(5081,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)],[766]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_2) ).
thf(3916,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(3968,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ! [C: $i] :
( ( m3_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)],[537]) ).
thf(220,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(2243,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)],[220]) ).
thf(2245,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( sk111 @ B @ A ) ),
inference(cnf,[status(esa)],[2243]) ).
thf(26534,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A
!= ( k1_funct_2 @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1266,7545]) ).
thf(26535,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( k1_funct_2 @ A @ A ) ) ),
inference(pattern_uni,[status(thm)],[26534:[bind(A,$thf( k1_funct_2 @ D @ D )),bind(B,$thf( D ))]]) ).
thf(28681,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( k1_funct_2 @ A @ A ) ) ),
inference(simp,[status(thm)],[26535]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(3782,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)],[498]) ).
thf(5904,plain,
~ ( v3_struct_0 @ sk456 ),
inference(cnf,[status(esa)],[5902]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',d6_binop_1) ).
thf(1234,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)],[52]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_realset1 @ A @ B @ C )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).
thf(1983,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_realset1 @ A @ B @ C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
=> ( r1_realset1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(739,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k5_lattices @ A ) )
= ( k6_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice4) ).
thf(4957,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)],[739]) ).
thf(773,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice2) ).
thf(5098,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)],[773]) ).
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 @ D @ C )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_binop_1) ).
thf(2990,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)],[345]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ~ ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(1953,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)],[169]) ).
thf(923,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/sandbox2/benchmark/theBenchmark.p',t30_lattice2) ).
thf(5673,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)],[923]) ).
thf(836,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_filter_0) ).
thf(5345,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)],[836]) ).
thf(2895,plain,
~ ( v3_struct_0 @ sk197 ),
inference(cnf,[status(esa)],[2887]) ).
thf(597,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_filter_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
<=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_0) ).
thf(4248,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)],[597]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
<=> ( ( A = C )
& ( r2_hidden @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(2841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
=> ( ( A = C )
& ( r2_hidden @ B @ D ) ) )
& ( ( ( A = C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1008,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/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
thf(6028,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)],[1008]) ).
thf(8276,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk296 ) ),
inference(paramod_ordered,[status(thm)],[4082,4367]) ).
thf(8282,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk296 ),
inference(simp,[status(thm)],[8276]) ).
thf(1797,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1796]) ).
thf(1798,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1797]) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[1183]) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1184]) ).
thf(1186,plain,
! [B: $i,A: $i] :
( ( sk13 @ A @ ( k4_xboole_0 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk13])]) ).
thf(34007,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1798,1186]) ).
thf(34008,plain,
! [A: $i] :
( ( sk13 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[34007:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',d5_binop_1) ).
thf(1060,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)],[11]) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ A )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( ( k1_binop_1 @ C @ B @ ( sk6 @ C @ B @ A ) )
!= ( sk6 @ C @ B @ A ) )
| ( r1_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1060]) ).
thf(1064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_binop_1 @ C @ B @ ( sk6 @ C @ B @ A ) )
!= ( sk6 @ C @ B @ A ) )
| ~ ( m1_subset_1 @ B @ A )
| ~ ( 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 ) ),
inference(lifteq,[status(thm)],[1062]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(1111,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(879,axiom,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(5502,plain,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(676,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s12_funct_2 )
=> ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s12_funct_2 )
=> ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
= ( f3_s12_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s12_funct_2) ).
thf(4636,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s12_funct_2 )
=> ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s12_funct_2 )
=> ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
= ( f3_s12_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(15054,plain,
! [B: $i,A: $i] :
( ( r2_hidden @ A @ ( sk352 @ A ) )
!= ( r2_hidden @ B @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[4711,2856]) ).
thf(15059,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( sk352 @ A )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[15054]) ).
thf(15065,plain,
! [A: $i] :
( ( sk352 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15059]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(2694,plain,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(716,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/sandbox2/benchmark/theBenchmark.p',t21_filter_2) ).
thf(4845,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)],[716]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).
thf(2631,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)],[284]) ).
thf(224,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 )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) )
<=> ( ( k2_relat_1 @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_2) ).
thf(2268,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 )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) )
=> ( ( k2_relat_1 @ C )
= B ) )
& ( ( ( k2_relat_1 @ C )
= B )
=> ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(590,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ E @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) ) ) )
=> ( r3_lattices @ C @ E @ ( k3_lattice2 @ A @ C @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_lattice2) ).
thf(4219,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)],[590]) ).
thf(868,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(5475,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)],[868]) ).
thf(992,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 )
=> ( ( r2_hidden @ B @ ( k22_filter_2 @ A @ B @ C ) )
& ( r2_hidden @ C @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_2) ).
thf(5951,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 )
=> ( ( r2_hidden @ B @ ( k22_filter_2 @ A @ B @ C ) )
& ( r2_hidden @ C @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(99,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ B @ A )
=> ( ( k1_funct_4 @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice2) ).
thf(1567,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ B @ A )
=> ( ( k1_funct_4 @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(26809,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A
!= ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1266,7544]) ).
thf(26810,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( k1_zfmisc_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26809:[bind(A,$thf( k1_zfmisc_1 @ C )),bind(B,$thf( C ))]]) ).
thf(28314,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( k1_zfmisc_1 @ A ) ) ),
inference(simp,[status(thm)],[26810]) ).
thf(25715,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v3_lattices @ k1_xboole_0 )
| ( A != sk317 ) ),
inference(paramod_ordered,[status(thm)],[1266,4391]) ).
thf(25716,plain,
( ( v1_relat_1 @ ( sk19 @ sk317 ) )
| ( v3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25715:[bind(A,$thf( sk317 ))]]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(5075,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(654,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( v1_relat_1 @ ( k10_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_0) ).
thf(4513,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)],[654]) ).
thf(23725,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk296 )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1952,8282]) ).
thf(23726,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk296 ),
inference(pattern_uni,[status(thm)],[23725:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(23775,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk296 ),
inference(simp,[status(thm)],[23726]) ).
thf(2108,plain,
v5_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m2_lattice4 @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_1_lattice4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k2_lattice4 @ B @ D ) )
& ( r1_tarski @ D @ ( k4_lattice4 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).
thf(4736,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)],[692]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(3573,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)],[456]) ).
thf(2781,plain,
v5_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] : ( m1_struct_0 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_struct_0) ).
thf(4333,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] : ( m1_struct_0 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(3954,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)],[535]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(1329,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1152,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( k1_funct_1 @ B @ ( sk11 @ B @ A ) )
!= ( sk10 @ B @ A ) )
| ( ( k1_funct_1 @ A @ ( sk10 @ B @ A ) )
!= ( sk11 @ B @ A ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1148]) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( k1_funct_1 @ B @ ( sk11 @ B @ A ) )
!= ( sk10 @ B @ A ) )
| ( ( sk11 @ B @ A )
!= ( k1_funct_1 @ A @ ( sk10 @ B @ A ) ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1152]) ).
thf(2877,plain,
l3_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(1025,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ E )
| ( E
!= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
| ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) ) ),
inference(cnf,[status(esa)],[1024]) ).
thf(1027,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
!= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
| ( ( k2_relat_1 @ E )
= ( k2_tarski @ B @ D ) )
| ~ ( v1_relat_1 @ E ) ),
inference(lifteq,[status(thm)],[1025]) ).
thf(1028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k2_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
= ( k2_tarski @ B @ D ) )
| ~ ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ) ),
inference(simp,[status(thm)],[1027]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k2_tarski @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).
thf(4518,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( ( k7_domain_1 @ A @ B @ C )
= ( k2_tarski @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1078,plain,
! [C: $i,B: $i,A: $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_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( ( k1_binop_1 @ B @ ( sk7 @ C @ B @ A ) @ ( k1_binop_1 @ C @ ( sk8 @ C @ B @ A ) @ ( sk9 @ C @ B @ A ) ) )
!= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) ) @ ( k1_binop_1 @ B @ ( sk7 @ C @ B @ A ) @ ( sk9 @ C @ B @ A ) ) ) )
| ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) ) @ ( sk9 @ C @ B @ A ) )
!= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ ( sk7 @ C @ B @ A ) @ ( sk9 @ C @ B @ A ) ) @ ( k1_binop_1 @ B @ ( sk8 @ C @ B @ A ) @ ( sk9 @ C @ B @ A ) ) ) )
| ( r6_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1075]) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_binop_1 @ B @ ( sk7 @ C @ B @ A ) @ ( k1_binop_1 @ C @ ( sk8 @ C @ B @ A ) @ ( sk9 @ C @ B @ A ) ) )
!= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) ) @ ( k1_binop_1 @ B @ ( sk7 @ C @ B @ A ) @ ( sk9 @ C @ B @ A ) ) ) )
| ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) ) @ ( sk9 @ C @ B @ A ) )
!= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ ( sk7 @ C @ B @ A ) @ ( sk9 @ C @ B @ A ) ) @ ( k1_binop_1 @ B @ ( sk8 @ C @ B @ A ) @ ( sk9 @ C @ B @ A ) ) ) )
| ~ ( 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_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 ) ),
inference(lifteq,[status(thm)],[1078]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(3326,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(793,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_0) ).
thf(5166,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)],[793]) ).
thf(170,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_group_1 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattice2) ).
thf(1964,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_group_1 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',t6_relset_1) ).
thf(1942,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)],[166]) ).
thf(931,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_filter_0 @ A @ B ) @ C ) ) )
& ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_filter_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_0) ).
thf(5694,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)],[931]) ).
thf(347,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/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(3000,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)],[347]) ).
thf(917,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_2_domain_1 )
<=> ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).
thf(5651,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_2_domain_1 )
=> ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) ) )
& ( ? [B: $i,C: $i] :
( ( m1_subset_1 @ B @ f1_s9_domain_1 )
& ( m1_subset_1 @ C @ f2_s9_domain_1 )
& ( A
= ( f4_s9_domain_1 @ B @ C ) )
& ( p1_s9_domain_1 @ B @ C ) )
=> ( r2_hidden @ A @ a_0_2_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(2561,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)],[278]) ).
thf(776,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ C @ E @ D @ D )
& ( r1_filter_0 @ A @ B @ F @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_filter_0) ).
thf(5107,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)],[776]) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_realset1 @ C @ A @ B )
| ( v1_funct_1 @ C ) ),
inference(cnf,[status(esa)],[1179]) ).
thf(910,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/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_2) ).
thf(5620,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)],[910]) ).
thf(4389,plain,
v14_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(634,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ C @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) ) @ ( k5_lattice4 @ A ) )
= ( k4_lattices @ A @ ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice4) ).
thf(4421,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)],[634]) ).
thf(864,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/sandbox2/benchmark/theBenchmark.p',dt_m2_nat_lat) ).
thf(5464,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)],[864]) ).
thf(695,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/sandbox2/benchmark/theBenchmark.p',t5_filter_2) ).
thf(4750,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)],[695]) ).
thf(815,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(5253,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)],[815]) ).
thf(948,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(5786,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)],[948]) ).
thf(11149,plain,
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 )
!= ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,8295]) ).
thf(11197,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk315 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11149]) ).
thf(11243,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11197]) ).
thf(219,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(2239,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)],[219]) ).
thf(2240,plain,
! [B: $i,A: $i] : ( v1_funct_1 @ ( sk110 @ B @ A ) ),
inference(cnf,[status(esa)],[2239]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_0 @ ( k3_filter_0 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(5547,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)],[889]) ).
thf(693,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(4744,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(989,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattices) ).
thf(5932,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)],[989]) ).
thf(719,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).
thf(4861,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)],[719]) ).
thf(554,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/sandbox2/benchmark/theBenchmark.p',redefinition_k4_filter_2) ).
thf(4054,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)],[554]) ).
thf(46,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(1207,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(721,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_lattices @ A @ ( k2_lattice2 @ C @ A @ D @ E ) @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice2) ).
thf(4867,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)],[721]) ).
thf(641,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k6_lattices @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattices) ).
thf(4444,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( B
= ( k6_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(5905,plain,
l3_lattices @ sk456,
inference(cnf,[status(esa)],[5902]) ).
thf(643,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F )
= B ) ) )
=> ( ( D = k1_xboole_0 )
| ( ( k2_lattice2 @ C @ A @ D @ E )
= B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice2) ).
thf(4457,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)],[643]) ).
thf(4384,plain,
v15_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(447,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( k5_lattice4 @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice4) ).
thf(3541,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)],[447]) ).
thf(490,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v14_lattices @ A )
=> ( v14_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_0) ).
thf(3743,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)],[490]) ).
thf(927,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattice4 @ A @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattice4) ).
thf(5683,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)],[927]) ).
thf(684,axiom,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s13_funct_2 )
=> ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s13_funct_2 )
=> ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
= ( f3_s13_funct_2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s13_funct_2) ).
thf(4689,plain,
( ! [A: $i] :
( ( m1_subset_1 @ A @ f1_s13_funct_2 )
=> ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
=> ? [A: $i] :
( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s13_funct_2 )
=> ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
= ( f3_s13_funct_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(3070,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[3069]) ).
thf(15934,plain,
! [A: $i] : ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ A ) ),
inference(rewrite,[status(thm)],[3070,2408]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(4223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(813,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( v14_lattices @ A )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ ( k17_filter_2 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_2) ).
thf(5245,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( v14_lattices @ A )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ ( k17_filter_2 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(702,axiom,
? [A: $i] : ( l2_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(4804,plain,
? [A: $i] : ( l2_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(3242,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)],[392]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(1114,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)],[23]) ).
thf(962,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice4) ).
thf(5850,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)],[962]) ).
thf(472,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k6_lattices @ A )
= ( k5_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_lattice2) ).
thf(3656,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)],[472]) ).
thf(7947,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ sk216 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3112,6524]) ).
thf(7948,plain,
( ~ ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7947:[bind(A,$thf( sk216 ))]]) ).
thf(471,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(3654,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(787,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r8_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_filter_0) ).
thf(5149,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)],[787]) ).
thf(1010,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_2) ).
thf(6033,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(2836,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)],[315]) ).
thf(652,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( k1_lattice2 @ A )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice2) ).
thf(4508,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)],[652]) ).
thf(2900,plain,
v5_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(1231,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)],[51]) ).
thf(808,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 )
=> ( ( k22_filter_2 @ A @ B @ C )
= ( a_3_2_filter_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_filter_2) ).
thf(5234,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 )
=> ( ( k22_filter_2 @ A @ B @ C )
= ( a_3_2_filter_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(1974,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(25642,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v6_lattices @ k1_xboole_0 )
| ( A != sk118 ) ),
inference(paramod_ordered,[status(thm)],[1266,2295]) ).
thf(25643,plain,
( ( v1_relat_1 @ ( sk19 @ sk118 ) )
| ( v6_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25642:[bind(A,$thf( sk118 ))]]) ).
thf(877,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/sandbox2/benchmark/theBenchmark.p',t40_lattice2) ).
thf(5498,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)],[877]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(1932,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(2581,plain,
v9_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(180,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(2006,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(1799,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(532,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( B
!= ( k5_lattices @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_0) ).
thf(3937,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)],[532]) ).
thf(144,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_filter_0) ).
thf(1852,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v12_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(309,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A ) )
=> ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice2) ).
thf(2813,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A ) )
=> ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',d17_binop_1) ).
thf(3115,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)],[370]) ).
thf(827,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( v1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
<=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice4) ).
thf(5305,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)],[827]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',t16_binop_1) ).
thf(1429,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)],[82]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(2862,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)],[321]) ).
thf(290,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(2697,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(5792,plain,
( sk446
| ( r2_hidden @ sk448 @ f3_s4_subset_1 )
| ( p1_s4_subset_1 @ sk448 )
| ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(cnf,[status(esa)],[5788]) ).
thf(5801,plain,
( ( f3_s4_subset_1 = f2_s4_subset_1 )
| sk446
| ( r2_hidden @ sk448 @ f3_s4_subset_1 )
| ( p1_s4_subset_1 @ sk448 ) ),
inference(lifteq,[status(thm)],[5792]) ).
thf(120,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(1720,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(598,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/sandbox2/benchmark/theBenchmark.p',t10_filter_2) ).
thf(4259,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)],[598]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k11_filter_0 @ A @ B )
= ( k10_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).
thf(3920,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)],[526]) ).
thf(420,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( a_2_1_lattice4 @ A @ B )
= ( k3_lattice4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice4) ).
thf(3364,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)],[420]) ).
thf(11708,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk251 @ A ) )
!= ( v1_xboole_0 @ ( k1_funct_2 @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3555,2940]) ).
thf(11725,plain,
! [B: $i,A: $i] :
( ( sk251 @ A )
!= ( k1_funct_2 @ B @ B ) ),
inference(simp,[status(thm)],[11708]) ).
thf(677,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v2_lattice4 @ C @ A @ B )
<=> ( ( k2_relat_1 @ C )
= ( u1_struct_0 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice4) ).
thf(4644,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)],[677]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(3563,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)],[453]) ).
thf(588,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k6_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_0) ).
thf(4212,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)],[588]) ).
thf(8068,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk216 ) ),
inference(paramod_ordered,[status(thm)],[3113,2940]) ).
thf(8080,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk216 ),
inference(simp,[status(thm)],[8068]) ).
thf(2883,plain,
v15_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(856,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( C
= ( k7_lattices @ A @ B ) )
<=> ( r2_lattices @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattices) ).
thf(5417,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)],[856]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',t18_binop_1) ).
thf(1895,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)],[154]) ).
thf(1012,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( v3_lattice4 @ C @ A @ B )
<=> ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice4) ).
thf(6038,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)],[1012]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattices) ).
thf(4572,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(2909,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(21008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ ( k9_relat_1 @ sk207 @ A ) @ ( k2_relat_1 @ sk207 ) )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20993,1074]) ).
thf(21009,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk207 @ B ) @ A ) @ ( k2_relat_1 @ sk207 ) ),
inference(pattern_uni,[status(thm)],[21008:[bind(A,$thf( F )),bind(B,$thf( k9_relat_1 @ sk207 @ F )),bind(C,$thf( k2_relat_1 @ sk207 )),bind(D,$thf( D ))]]) ).
thf(21074,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk207 @ B ) @ A ) @ ( k2_relat_1 @ sk207 ) ),
inference(simp,[status(thm)],[21009]) ).
thf(6846,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk71 ) ),
inference(paramod_ordered,[status(thm)],[1884,3790]) ).
thf(6850,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk71 ),
inference(simp,[status(thm)],[6846]) ).
thf(10650,plain,
! [A: $i] :
( ( ( k1_tarski @ k1_xboole_0 )
!= sk71 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1868,6850]) ).
thf(10651,plain,
( ( k1_tarski @ k1_xboole_0 )
!= sk71 ),
inference(pattern_uni,[status(thm)],[10650:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_lattice4) ).
thf(3824,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)],[507]) ).
thf(778,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/sandbox2/benchmark/theBenchmark.p',t26_filter_2) ).
thf(5112,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)],[778]) ).
thf(520,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/sandbox2/benchmark/theBenchmark.p',t37_lattice2) ).
thf(3903,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)],[520]) ).
thf(579,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/sandbox2/benchmark/theBenchmark.p',t36_lattice2) ).
thf(4184,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)],[579]) ).
thf(2788,plain,
v8_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(25713,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v13_lattices @ k1_xboole_0 )
| ( A != sk187 ) ),
inference(paramod_ordered,[status(thm)],[1266,2776]) ).
thf(25714,plain,
( ( v1_relat_1 @ ( sk19 @ sk187 ) )
| ( v13_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25713:[bind(A,$thf( sk187 ))]]) ).
thf(98,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/sandbox2/benchmark/theBenchmark.p',d7_binop_1) ).
thf(1563,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)],[98]) ).
thf(855,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_0) ).
thf(5415,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)],[855]) ).
thf(192,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(2056,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(2057,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[2056]) ).
thf(406,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( B
!= ( k17_filter_2 @ A ) )
& ( v1_filter_2 @ B @ A ) )
<=> ( r2_filter_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_2) ).
thf(3306,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( ( B
!= ( k17_filter_2 @ A ) )
& ( v1_filter_2 @ B @ A ) )
=> ( r2_filter_2 @ A @ B ) )
& ( ( r2_filter_2 @ A @ B )
=> ( ( B
!= ( k17_filter_2 @ A ) )
& ( v1_filter_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(8270,plain,
( ( v1_xboole_0 @ sk364 )
!= ( v1_xboole_0 @ sk296 ) ),
inference(paramod_ordered,[status(thm)],[4082,4871]) ).
thf(8279,plain,
sk364 != sk296,
inference(simp,[status(thm)],[8270]) ).
thf(461,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/sandbox2/benchmark/theBenchmark.p',redefinition_k16_filter_2) ).
thf(3592,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)],[461]) ).
thf(1054,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ A @ B )
| ~ ( m2_relset_1 @ D @ A @ B )
| ~ ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
| ( m1_subset_1 @ ( sk5 @ E @ D @ C @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[1051]) ).
thf(1003,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/sandbox2/benchmark/theBenchmark.p',t33_lattice2) ).
thf(6011,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)],[1003]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(1170,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( sk3 @ C @ A @ B )
| ( m2_relset_1 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[1031]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C )
& ! [E: $i,F: $i] :
( ( ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) )
=> ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) ) )
& ( ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) )
=> ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).
thf(2368,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C )
& ! [E: $i,F: $i] :
( ( ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) )
=> ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) ) )
& ( ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) )
=> ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(88,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(1466,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_2) ).
thf(1069,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1070,plain,
! [B: $i,A: $i] :
( ~ ( v1_funct_1 @ B )
| ~ ( v1_funct_2 @ B @ A @ A )
| ~ ( m2_relset_1 @ B @ A @ A )
| ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A ) ),
inference(cnf,[status(esa)],[1069]) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
= A )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_funct_2 @ B @ A @ A )
| ~ ( m2_relset_1 @ B @ A @ A ) ),
inference(lifteq,[status(thm)],[1070]) ).
thf(25741,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk315 ) ),
inference(paramod_ordered,[status(thm)],[1266,14409]) ).
thf(25742,plain,
( ( v1_relat_1 @ ( sk19 @ sk315 ) )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25741:[bind(A,$thf( sk315 ))]]) ).
thf(2793,plain,
l3_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(382,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).
thf(3190,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(814,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 )
=> ( ( r2_hidden @ D @ ( k22_filter_2 @ A @ B @ C ) )
<=> ( ( r3_lattices @ A @ B @ D )
& ( r3_lattices @ A @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_filter_2) ).
thf(5249,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 )
=> ( ( ( r2_hidden @ D @ ( k22_filter_2 @ A @ B @ C ) )
=> ( ( r3_lattices @ A @ B @ D )
& ( r3_lattices @ A @ D @ C ) ) )
& ( ( ( r3_lattices @ A @ B @ D )
& ( r3_lattices @ A @ D @ C ) )
=> ( r2_hidden @ D @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(288,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/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(2662,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)],[288]) ).
thf(2338,plain,
v10_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[2335]) ).
thf(969,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( ( k3_filter_0 @ A @ C )
= ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_0) ).
thf(5872,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)],[969]) ).
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] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',d9_binop_1) ).
thf(1727,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)],[122]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(2176,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)],[210]) ).
thf(2585,plain,
v3_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(863,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
<=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_lattice2) ).
thf(5451,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)],[863]) ).
thf(58,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relat_1) ).
thf(1273,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(334,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/sandbox2/benchmark/theBenchmark.p',d16_binop_1) ).
thf(2941,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)],[334]) ).
thf(850,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattices) ).
thf(5400,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)],[850]) ).
thf(811,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k5_lattices @ A ) @ B )
= ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattices) ).
thf(5241,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)],[811]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v2_struct_0 @ ( g2_struct_0 @ A @ B ) )
& ( l2_struct_0 @ ( g2_struct_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g2_struct_0) ).
thf(3343,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v2_struct_0 @ ( g2_struct_0 @ A @ B ) )
& ( l2_struct_0 @ ( g2_struct_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(731,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ F ) ) ) )
=> ( r3_lattices @ C @ ( k3_lattice2 @ A @ C @ B @ D ) @ ( k3_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_lattice2) ).
thf(4921,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)],[731]) ).
thf(15426,plain,
! [B: $i,A: $i] :
( ( ( sk251 @ A )
!= ( k1_tarski @ k1_xboole_0 ) )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1868,11719]) ).
thf(15427,plain,
! [A: $i] :
( ( sk251 @ A )
!= ( k1_tarski @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[15426:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(55,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(1251,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)],[55]) ).
thf(872,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice4 @ A @ ( k1_setwiseo @ ( u1_struct_0 @ A ) ) )
= ( k5_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattice4) ).
thf(5483,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)],[872]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(3130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1001,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 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k7_lattices @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l70_filter_2) ).
thf(5996,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 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k7_lattices @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(1017,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/sandbox2/benchmark/theBenchmark.p',t27_filter_2) ).
thf(6053,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)],[1017]) ).
thf(572,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4131,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(934,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v16_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_filter_0) ).
thf(5722,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)],[934]) ).
thf(7090,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1059,6596]) ).
thf(7103,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( B != sk138 )
| ( A != sk1 )
| ( ( k2_relat_1 @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7090]) ).
thf(7126,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ sk138 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7103]) ).
thf(8996,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7126,2405]) ).
thf(8997,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[8996]) ).
thf(11671,plain,
! [A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,8997]) ).
thf(11683,plain,
! [A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[11671]) ).
thf(11692,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[11683]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(4470,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)],[646]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
<=> ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(1754,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) )
=> ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) ) )
& ( ( ~ ( r2_hidden @ A @ C )
& ~ ( r2_hidden @ B @ C ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k2_tarski @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(2292,plain,
v8_lattices @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(7096,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1059,6857]) ).
thf(7097,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( B != sk71 )
| ( A != sk1 )
| ( ( k2_relat_1 @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7096]) ).
thf(7119,plain,
( ~ ( v1_relat_1 @ sk71 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7097]) ).
thf(7767,plain,
( ~ $true
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7119,1887]) ).
thf(7768,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7767]) ).
thf(11663,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,7768]) ).
thf(11679,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= k1_xboole_0 )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[11663]) ).
thf(11705,plain,
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[11679]) ).
thf(723,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/sandbox2/benchmark/theBenchmark.p',redefinition_k11_filter_2) ).
thf(4872,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)],[723]) ).
thf(10308,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= ( k2_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1098,7768]) ).
thf(10335,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[10308]) ).
thf(13626,plain,
( ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= ( k1_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1099,10335]) ).
thf(13655,plain,
( ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[13626]) ).
thf(13674,plain,
( ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[13655]) ).
thf(13725,plain,
( ~ $true
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[13674,1977]) ).
thf(13726,plain,
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[13725]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(2556,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(4354,plain,
v1_funct_2 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2,
inference(cnf,[status(esa)],[4351]) ).
thf(4393,plain,
v8_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(402,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k5_filter_0 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_0) ).
thf(3289,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)],[402]) ).
thf(7536,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2933,2308]) ).
thf(7551,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[7536]) ).
thf(27159,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A
!= ( k4_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1266,7551]) ).
thf(27160,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk19 @ ( k4_tarski @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[27159:[bind(A,$thf( k4_tarski @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(28372,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk19 @ ( k4_tarski @ A @ B ) ) ),
inference(simp,[status(thm)],[27160]) ).
thf(509,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_lattices @ A @ ( k1_lattice4 @ A @ B ) )
= ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k5_lattice4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice4) ).
thf(3839,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)],[509]) ).
thf(772,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_0) ).
thf(5095,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)],[772]) ).
thf(883,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattice2) ).
thf(5525,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)],[883]) ).
thf(2894,plain,
v4_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(933,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/sandbox2/benchmark/theBenchmark.p',fc2_filter_2) ).
thf(5720,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)],[933]) ).
thf(601,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ B @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattices) ).
thf(4268,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ B @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',t26_binop_1) ).
thf(1929,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)],[162]) ).
thf(570,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F )
= B ) ) )
=> ( ( D = k1_xboole_0 )
| ( ( k3_lattice2 @ C @ A @ D @ E )
= B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_lattice2) ).
thf(4122,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)],[570]) ).
thf(957,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 ) ) ) )
=> ( ( k20_filter_2 @ A @ B @ C )
= ( a_3_0_filter_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_2) ).
thf(5831,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 ) ) ) )
=> ( ( k20_filter_2 @ A @ B @ C )
= ( a_3_0_filter_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(519,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ C @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) ) @ ( k5_lattice4 @ A ) )
= ( k3_lattices @ A @ ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice4) ).
thf(3900,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)],[519]) ).
thf(970,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(5876,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)],[970]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(4381,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)],[630]) ).
thf(810,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice4) ).
thf(5239,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)],[810]) ).
thf(5503,plain,
~ ( v3_struct_0 @ sk421 ),
inference(cnf,[status(esa)],[5502]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',d11_binop_1) ).
thf(1488,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)],[93]) ).
thf(886,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_0) ).
thf(5535,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)],[886]) ).
thf(546,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 )
& ( B
!= ( k6_lattices @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( r2_filter_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_filter_2) ).
thf(4000,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 )
& ( B
!= ( k6_lattices @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( r2_filter_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(3187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(3741,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(4662,plain,
l1_lattices @ sk344,
inference(cnf,[status(esa)],[4661]) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(2048,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)],[190]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_partfun1) ).
thf(2859,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(867,axiom,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(5473,plain,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(5474,plain,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
inference(cnf,[status(esa)],[5473]) ).
thf(874,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/sandbox2/benchmark/theBenchmark.p',t23_filter_2) ).
thf(5488,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)],[874]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(1389,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)],[75]) ).
thf(2791,plain,
v7_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(3240,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(2789,plain,
v6_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(444,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/sandbox2/benchmark/theBenchmark.p',t35_lattice2) ).
thf(3519,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)],[444]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_realset1) ).
thf(2525,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(575,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( v4_lattices @ ( k1_lattice2 @ A ) )
& ( v5_lattices @ ( k1_lattice2 @ A ) )
& ( v6_lattices @ ( k1_lattice2 @ A ) )
& ( v7_lattices @ ( k1_lattice2 @ A ) )
& ( v8_lattices @ ( k1_lattice2 @ A ) )
& ( v9_lattices @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( v12_lattices @ ( k1_lattice2 @ A ) )
& ( v13_lattices @ ( k1_lattice2 @ A ) )
& ( v14_lattices @ ( k1_lattice2 @ A ) )
& ( v15_lattices @ ( k1_lattice2 @ A ) )
& ( v16_lattices @ ( k1_lattice2 @ A ) )
& ( v17_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_filter_2) ).
thf(4159,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( v4_lattices @ ( k1_lattice2 @ A ) )
& ( v5_lattices @ ( k1_lattice2 @ A ) )
& ( v6_lattices @ ( k1_lattice2 @ A ) )
& ( v7_lattices @ ( k1_lattice2 @ A ) )
& ( v8_lattices @ ( k1_lattice2 @ A ) )
& ( v9_lattices @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( v12_lattices @ ( k1_lattice2 @ A ) )
& ( v13_lattices @ ( k1_lattice2 @ A ) )
& ( v14_lattices @ ( k1_lattice2 @ A ) )
& ( v15_lattices @ ( k1_lattice2 @ A ) )
& ( v16_lattices @ ( k1_lattice2 @ A ) )
& ( v17_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(2981,plain,
v3_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[2980]) ).
thf(614,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(4309,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)],[614]) ).
thf(986,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ C ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_filter_0) ).
thf(5923,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)],[986]) ).
thf(128,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 ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( v1_partfun1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_partfun1) ).
thf(1752,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 ) )
=> ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
=> ( v1_partfun1 @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ C @ E ) @ D )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_lattice2) ).
thf(2514,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ C @ E ) @ D )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(2568,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)],[279]) ).
thf(743,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( k2_filter_0 @ A @ ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_0) ).
thf(4975,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)],[743]) ).
thf(673,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( m2_lattice4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattice4) ).
thf(4612,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)],[673]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k6_filter_0 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(5752,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)],[941]) ).
thf(697,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_filter_0 @ B @ A )
<=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_filter_0) ).
thf(4758,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)],[697]) ).
thf(651,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k5_lattices @ A )
= ( k6_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_lattice2) ).
thf(4505,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)],[651]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k1_funct_2 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_2) ).
thf(1669,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k1_funct_2 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(25650,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v7_lattices @ k1_xboole_0 )
| ( A != sk196 ) ),
inference(paramod_ordered,[status(thm)],[1266,2876]) ).
thf(25651,plain,
( ( v1_relat_1 @ ( sk19 @ sk196 ) )
| ( v7_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25650:[bind(A,$thf( sk196 ))]]) ).
thf(469,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_0) ).
thf(3646,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)],[469]) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(2753,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)],[300]) ).
thf(862,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/sandbox2/benchmark/theBenchmark.p',t39_lattice2) ).
thf(5449,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)],[862]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(2166,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)],[208]) ).
thf(718,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/sandbox2/benchmark/theBenchmark.p',d20_binop_1) ).
thf(4854,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)],[718]) ).
thf(936,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 ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k19_filter_2 @ A @ C ) @ ( k19_filter_2 @ A @ D ) ) )
& ( r1_tarski @ ( k19_filter_2 @ A @ ( k19_filter_2 @ A @ B ) ) @ ( k19_filter_2 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_2) ).
thf(5735,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 ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k19_filter_2 @ A @ C ) @ ( k19_filter_2 @ A @ D ) ) )
& ( r1_tarski @ ( k19_filter_2 @ A @ ( k19_filter_2 @ A @ B ) ) @ ( k19_filter_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(3090,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
inference(cnf,[status(esa)],[3089]) ).
thf(3091,plain,
! [A: $i] :
( ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ),
inference(lifteq,[status(thm)],[3090]) ).
thf(34365,plain,
! [A: $i] :
( ( k3_subset_1 @ A @ k1_xboole_0 )
= A ),
inference(rewrite,[status(thm)],[3091,2408,2908]) ).
thf(280,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(2573,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1016,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/sandbox2/benchmark/theBenchmark.p',t20_filter_2) ).
thf(6048,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)],[1016]) ).
thf(26130,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( A != sk216 ) ),
inference(paramod_ordered,[status(thm)],[1266,14408]) ).
thf(26131,plain,
( ( v1_relat_1 @ ( sk19 @ sk216 ) )
| ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26130:[bind(A,$thf( sk216 ))]]) ).
thf(389,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v3_filter_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice2) ).
thf(3223,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v3_filter_0 @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1135,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( 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_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( 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 ) )
| ~ ( r5_binop_1 @ A @ C @ D )
| ( r5_binop_1 @ B @ E @ F ) ),
inference(cnf,[status(esa)],[1133]) ).
thf(1138,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
!= ( k1_realset1 @ C @ B ) )
| ( F
!= ( k1_realset1 @ D @ B ) )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( 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_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( v1_funct_1 @ E )
| ~ ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( 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 ) ),
inference(lifteq,[status(thm)],[1135]) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( 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_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( 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 )
| ~ ( v1_funct_1 @ ( k1_realset1 @ D @ B ) )
| ~ ( v1_funct_2 @ ( k1_realset1 @ D @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( m2_relset_1 @ ( k1_realset1 @ D @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
| ~ ( r5_binop_1 @ A @ C @ D )
| ( r5_binop_1 @ B @ ( k1_realset1 @ C @ B ) @ ( k1_realset1 @ D @ B ) ) ),
inference(simp,[status(thm)],[1138]) ).
thf(800,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/sandbox2/benchmark/theBenchmark.p',t19_filter_2) ).
thf(5185,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)],[800]) ).
thf(26202,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( m1_subset_1 @ sk2 @ ( u1_struct_0 @ k1_xboole_0 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1266,1020]) ).
thf(26203,plain,
( ( v1_relat_1 @ ( sk19 @ sk1 ) )
| ( m1_subset_1 @ sk2 @ ( u1_struct_0 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[26202:[bind(A,$thf( sk1 ))]]) ).
thf(497,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 ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( ( ( k20_filter_2 @ A @ B @ C )
= ( k5_filter_0 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) @ ( k7_filter_2 @ A @ C ) ) )
& ( ( k20_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) @ ( k7_filter_2 @ A @ C ) )
= ( k5_filter_0 @ A @ B @ C ) )
& ( ( k20_filter_2 @ ( k1_lattice2 @ A ) @ D @ E )
= ( k5_filter_0 @ A @ ( k8_filter_2 @ A @ D ) @ ( k8_filter_2 @ A @ E ) ) )
& ( ( k20_filter_2 @ A @ ( k8_filter_2 @ A @ D ) @ ( k8_filter_2 @ A @ E ) )
= ( k5_filter_0 @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_2) ).
thf(3773,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 ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( ( ( k20_filter_2 @ A @ B @ C )
= ( k5_filter_0 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) @ ( k7_filter_2 @ A @ C ) ) )
& ( ( k20_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) @ ( k7_filter_2 @ A @ C ) )
= ( k5_filter_0 @ A @ B @ C ) )
& ( ( k20_filter_2 @ ( k1_lattice2 @ A ) @ D @ E )
= ( k5_filter_0 @ A @ ( k8_filter_2 @ A @ D ) @ ( k8_filter_2 @ A @ E ) ) )
& ( ( k20_filter_2 @ A @ ( k8_filter_2 @ A @ D ) @ ( k8_filter_2 @ A @ E ) )
= ( k5_filter_0 @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(185,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/sandbox2/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(2029,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)],[185]) ).
thf(580,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(4186,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)],[580]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_filter_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(5363,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)],[842]) ).
thf(2293,plain,
v9_lattices @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(5471,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(700,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) )
= ( k4_lattices @ A @ ( k2_lattice4 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice4) ).
thf(4796,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)],[700]) ).
thf(2891,plain,
v1_lattice2 @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(713,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_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 ) )
=> ( ( r1_lattices @ A @ B @ C )
=> ( r1_lattices @ A @ ( k2_lattices @ A @ B @ D ) @ ( k2_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattices) ).
thf(4837,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_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 ) )
=> ( ( r1_lattices @ A @ B @ C )
=> ( r1_lattices @ A @ ( k2_lattices @ A @ B @ D ) @ ( k2_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(362,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 ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( a_3_3_domain_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_domain_1) ).
thf(3077,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 ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( a_3_3_domain_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(981,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_lattice4 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(5908,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)],[981]) ).
thf(904,axiom,
! [A: $i] :
( ( r2_hidden @ A @ a_0_1_domain_1 )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).
thf(5595,plain,
! [A: $i] :
( ( ( r2_hidden @ A @ a_0_1_domain_1 )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ f1_s8_domain_1 )
& ( A
= ( f3_s8_domain_1 @ B ) )
& ( p1_s8_domain_1 @ B ) )
=> ( r2_hidden @ A @ a_0_1_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(470,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattices @ A @ ( k1_lattice4 @ A @ B ) @ ( k1_lattice4 @ A @ C ) )
= ( k1_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattice4) ).
thf(3651,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)],[470]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_0 @ ( k2_filter_0 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(5859,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)],[965]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ B )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(4099,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(7533,plain,
( ( v1_xboole_0 @ sk14 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2933,1196]) ).
thf(7548,plain,
sk14 != k1_xboole_0,
inference(simp,[status(thm)],[7533]) ).
thf(28215,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A != sk14 ) ),
inference(paramod_ordered,[status(thm)],[1266,7548]) ).
thf(28216,plain,
v1_relat_1 @ ( sk19 @ sk14 ),
inference(pattern_uni,[status(thm)],[28215:[bind(A,$thf( sk14 ))]]) ).
thf(29152,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ ( sk19 @ sk14 ) )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28216,1125]) ).
thf(29153,plain,
( ( k9_relat_1 @ ( sk19 @ sk14 ) @ ( k1_relat_1 @ ( sk19 @ sk14 ) ) )
= ( k2_relat_1 @ ( sk19 @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[29152:[bind(A,$thf( sk19 @ sk14 ))]]) ).
thf(5278,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( v1_funct_1 @ sk407 ) ),
inference(cnf,[status(esa)],[5274]) ).
thf(5282,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( v1_funct_1 @ sk407 ) ),
inference(lifteq,[status(thm)],[5278]) ).
thf(146,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(1865,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(707,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(4822,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(768,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/sandbox2/benchmark/theBenchmark.p',t41_lattice2) ).
thf(5086,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)],[768]) ).
thf(414,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).
thf(3340,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)],[414]) ).
thf(12098,plain,
! [A: $i] :
( ( m1_subset_1 @ k1_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1868,2057]) ).
thf(12099,plain,
m1_subset_1 @ k1_xboole_0 @ ( k1_tarski @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12098:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(947,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( r3_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_filter_0) ).
thf(5784,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)],[947]) ).
thf(87,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(1464,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
<=> ( ( r2_hidden @ A @ C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(2474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
=> ( ( r2_hidden @ A @ C )
& ( B = D ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( B = D ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',fc2_realset1) ).
thf(2311,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)],[233]) ).
thf(763,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/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(5071,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)],[763]) ).
thf(619,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_0) ).
thf(4337,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)],[619]) ).
thf(544,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_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 ) )
=> ( r1_lattices @ A @ B @ ( k1_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattices) ).
thf(3996,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_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 ) )
=> ( r1_lattices @ A @ B @ ( k1_lattices @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(394,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/sandbox2/benchmark/theBenchmark.p',t1_filter_2) ).
thf(3251,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)],[394]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',d18_binop_1) ).
thf(3155,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)],[377]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) )
<=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(4620,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)],[674]) ).
thf(2774,plain,
~ ( v3_struct_0 @ sk187 ),
inference(cnf,[status(esa)],[2770]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',d14_binop_1) ).
thf(2257,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)],[222]) ).
thf(875,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/sandbox2/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(5491,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)],[875]) ).
thf(907,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(5610,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)],[907]) ).
thf(2896,plain,
v6_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(11716,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk251 @ A ) )
!= ( v1_xboole_0 @ ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3555,4367]) ).
thf(11718,plain,
! [C: $i,B: $i,A: $i] :
( ( sk251 @ A )
!= ( k2_tarski @ B @ C ) ),
inference(simp,[status(thm)],[11716]) ).
thf(4388,plain,
~ ( v3_struct_0 @ sk317 ),
inference(cnf,[status(esa)],[4383]) ).
thf(11132,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,6705]) ).
thf(11169,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk138 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11132]) ).
thf(7543,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2933,4936]) ).
thf(7546,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[7543]) ).
thf(24536,plain,
! [C: $i,B: $i,A: $i] :
( ( r2_hidden @ A @ ( k2_tarski @ A @ B ) )
!= ( r2_hidden @ C @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[3392,2856]) ).
thf(24549,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( k2_tarski @ A @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[24536]) ).
thf(24556,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ B @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[24549]) ).
thf(27209,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A
!= ( k2_tarski @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1266,24556]) ).
thf(27210,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk19 @ ( k2_tarski @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[27209:[bind(A,$thf( k2_tarski @ D @ E )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).
thf(28379,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk19 @ ( k2_tarski @ A @ B ) ) ),
inference(simp,[status(thm)],[27210]) ).
thf(7397,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk71 ) ),
inference(paramod_ordered,[status(thm)],[1884,4367]) ).
thf(7403,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= sk71 ),
inference(simp,[status(thm)],[7397]) ).
thf(23735,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk71 )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1952,7403]) ).
thf(23736,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk71 ),
inference(pattern_uni,[status(thm)],[23735:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(23779,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk71 ),
inference(simp,[status(thm)],[23736]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v2_funct_1 @ C )
<=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(2084,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)],[196]) ).
thf(812,axiom,
m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s9_domain_1) ).
thf(5244,plain,
m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(495,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) ) )
=> ( ( D = k1_xboole_0 )
| ( r3_lattices @ A @ ( k2_lattice2 @ C @ A @ D @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice2) ).
thf(3764,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)],[495]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(5103,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(2987,plain,
v5_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[2980]) ).
thf(449,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 @ ( k3_lattices @ A @ B @ C ) @ ( k20_filter_2 @ A @ D @ E ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k20_filter_2 @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_2) ).
thf(3551,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 @ ( k3_lattices @ A @ B @ C ) @ ( k20_filter_2 @ A @ D @ E ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k20_filter_2 @ A @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1340,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( B
= ( k1_relat_1 @ ( sk25 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[1333]) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k1_relat_1 @ ( sk25 @ B @ A ) )
= B ) ),
inference(lifteq,[status(thm)],[1340]) ).
thf(1349,plain,
! [A: $i] :
( ( k1_relat_1 @ ( sk25 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1348]) ).
thf(963,axiom,
( ~ ( v3_struct_0 @ k13_nat_lat )
& ( v10_lattices @ k13_nat_lat )
& ( l3_lattices @ k13_nat_lat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_nat_lat) ).
thf(5852,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)],[963]) ).
thf(5853,plain,
l3_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[5852]) ).
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 ) )
=> ( ( 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/sandbox2/benchmark/theBenchmark.p',d15_binop_1) ).
thf(3270,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)],[398]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
<=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(1492,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
=> ~ ( r2_hidden @ B @ A ) )
& ( ~ ( r2_hidden @ B @ A )
=> ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(337,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/sandbox2/benchmark/theBenchmark.p',d12_binop_1) ).
thf(2955,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)],[337]) ).
thf(2246,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk111 @ B @ A ) ),
inference(cnf,[status(esa)],[2243]) ).
thf(121,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(1722,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(4805,plain,
l2_struct_0 @ sk360,
inference(cnf,[status(esa)],[4804]) ).
thf(13748,plain,
! [A: $i] :
( ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) )
| ( ( v1_relat_1 @ sk138 )
!= ( v1_relat_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2405,1125]) ).
thf(13749,plain,
( ( k9_relat_1 @ sk138 @ ( k1_relat_1 @ sk138 ) )
= ( k2_relat_1 @ sk138 ) ),
inference(pattern_uni,[status(thm)],[13748:[bind(A,$thf( sk138 ))]]) ).
thf(853,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k17_filter_2 @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_2) ).
thf(5407,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k17_filter_2 @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1042,plain,
! [B: $i,A: $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(cnf,[status(esa)],[1041]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_funct_2 @ B @ A @ A )
| ~ ( m2_relset_1 @ B @ A @ A ) ),
inference(lifteq,[status(thm)],[1042]) ).
thf(771,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5093,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(576,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(4176,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)],[576]) ).
thf(929,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r1_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_filter_0) ).
thf(5689,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)],[929]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
| ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
inference(cnf,[status(esa)],[1120]) ).
thf(1122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ),
inference(lifteq,[status(thm)],[1121]) ).
thf(845,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/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_2) ).
thf(5381,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)],[845]) ).
thf(648,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( v4_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ B @ C )
= ( k1_lattices @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattices) ).
thf(4477,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( ( v4_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ B @ C )
= ( k1_lattices @ A @ C @ B ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattices @ A @ B @ C )
= ( k1_lattices @ A @ C @ B ) ) ) )
=> ( v4_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(4107,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)],[567]) ).
thf(432,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v17_lattices @ A )
<=> ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_lattices) ).
thf(3456,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)],[432]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(5114,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)],[779]) ).
thf(2343,plain,
~ ( v3_struct_0 @ k13_nat_lat ),
inference(cnf,[status(esa)],[2335]) ).
thf(977,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/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).
thf(5894,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)],[977]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( v1_funct_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) )
& ( v1_funct_2 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B )
& ( m2_relset_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice2) ).
thf(1821,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( v1_funct_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) )
& ( v1_funct_2 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B )
& ( m2_relset_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(14323,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,7948]) ).
thf(14370,plain,
! [B: $i,A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( sk216 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14323]) ).
thf(14402,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( sk216 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14370]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(1838,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( B
= ( k1_funct_1 @ C @ A ) ) )
=> ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(2874,plain,
v9_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(974,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/sandbox2/benchmark/theBenchmark.p',d5_filter_2) ).
thf(5885,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)],[974]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
= ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_subset_1) ).
thf(2553,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
= ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(329,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_lattices) ).
thf(2911,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(388,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 ) )
=> ( ( m3_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_realset1) ).
thf(3219,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 ) )
=> ( ( ( m3_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( m3_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(895,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/sandbox2/benchmark/theBenchmark.p',t25_lattice2) ).
thf(5563,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)],[895]) ).
thf(492,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( v6_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ C )
= ( k2_lattices @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattices) ).
thf(3747,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( ( v6_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ C )
= ( k2_lattices @ A @ C @ B ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ C )
= ( k2_lattices @ A @ C @ B ) ) ) )
=> ( v6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(661,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/sandbox2/benchmark/theBenchmark.p',d10_filter_0) ).
thf(4541,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)],[661]) ).
thf(13118,plain,
! [C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) )
| ( ( r1_tarski @ ( k2_relat_1 @ sk315 ) @ f2_s4_funct_2 )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13107,1087]) ).
thf(13119,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ f2_s4_funct_2 ) @ ( k4_xboole_0 @ A @ ( k2_relat_1 @ sk315 ) ) ),
inference(pattern_uni,[status(thm)],[13118:[bind(A,$thf( k2_relat_1 @ sk315 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(13164,plain,
! [A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ f2_s4_funct_2 ) @ ( k4_xboole_0 @ A @ ( k2_relat_1 @ sk315 ) ) ),
inference(simp,[status(thm)],[13119]) ).
thf(1000,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/sandbox2/benchmark/theBenchmark.p',t73_lattice2) ).
thf(5994,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)],[1000]) ).
thf(2111,plain,
l2_struct_0 @ sk95,
inference(cnf,[status(esa)],[2109]) ).
thf(796,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 )
= B ) )
& ( ( k18_filter_2 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_filter_2) ).
thf(5175,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 )
= B ) )
& ( ( k18_filter_2 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(110,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(1630,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(705,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/sandbox2/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(4818,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)],[705]) ).
thf(833,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_2) ).
thf(5335,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(2780,plain,
v3_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(33989,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ B @ A )
= C )
| ( ( k4_xboole_0 @ A @ k1_xboole_0 )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1110,1186]) ).
thf(33990,plain,
! [A: $i] :
( ( sk13 @ k1_xboole_0 @ A )
= A ),
inference(pattern_uni,[status(thm)],[33989:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(455,axiom,
m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s7_domain_1) ).
thf(3572,plain,
m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(530,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(3932,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(158,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_lattices @ A )
& ( l1_lattices @ A ) )
=> ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattice2) ).
thf(1909,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v7_lattices @ A )
& ( l1_lattices @ A ) )
=> ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(1161,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1162,plain,
! [C: $i,B: $i,A: $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_realset1 @ C @ A @ B )
| ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[1161]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(4208,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)],[586]) ).
thf(2785,plain,
v9_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( r2_tarski @ A @ B )
<=> ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( D = F )
<=> ( E = G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tarski) ).
thf(2593,plain,
! [A: $i,B: $i] :
( ( ( r2_tarski @ A @ B )
=> ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( ( D = F )
=> ( E = G ) )
& ( ( E = G )
=> ( D = F ) ) ) ) ) )
& ( ? [C: $i] :
( ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ B )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
& ( r2_hidden @ ( k4_tarski @ F @ G ) @ C ) )
=> ( ( ( D = F )
=> ( E = G ) )
& ( ( E = G )
=> ( D = F ) ) ) ) )
=> ( r2_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(717,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 ) ) ) )
=> ( ( ( v14_lattices @ A )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ ( k17_filter_2 @ A ) )
& ( ( k19_filter_2 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_2) ).
thf(4850,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 ) ) ) )
=> ( ( ( v14_lattices @ A )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ ( k17_filter_2 @ A ) )
& ( ( k19_filter_2 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v2_funct_1 @ D )
& ( r2_hidden @ C @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).
thf(3006,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v2_funct_1 @ D )
& ( r2_hidden @ C @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(1014,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( m1_subset_1 @ ( k5_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(6044,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)],[1014]) ).
thf(2289,plain,
v7_lattices @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(798,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(5180,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)],[798]) ).
thf(3861,plain,
~ ( v3_struct_0 @ sk279 ),
inference(cnf,[status(esa)],[3860]) ).
thf(7899,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A )
!= ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1057,7842]) ).
thf(7920,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( B != sk207 )
| ( ( k1_relat_1 @ B )
!= sk1 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[7899]) ).
thf(7927,plain,
( ~ ( v1_relat_1 @ sk207 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk207 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk207 )
!= sk1 ) ),
inference(simp,[status(thm)],[7920]) ).
thf(32703,plain,
( ~ $true
| ~ ( r1_tarski @ ( k2_relat_1 @ sk207 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk207 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[7927,3011]) ).
thf(32704,plain,
( ~ ( r1_tarski @ ( k2_relat_1 @ sk207 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk207 )
!= sk1 ) ),
inference(simp,[status(thm)],[32703]) ).
thf(32819,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk207 )
!= sk1 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k2_relat_1 @ sk207 ) @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,32704]) ).
thf(32830,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk207 )
!= sk1 )
| ( ( k2_relat_1 @ sk207 )
!= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[32819]) ).
thf(32869,plain,
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk207 )
!= sk1 )
| ( ( k2_relat_1 @ sk207 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[32830]) ).
thf(1174,plain,
! [C: $i,B: $i,A: $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 )
| ~ ( m1_subset_1 @ C @ A )
| ( ( k1_binop_1 @ B @ C @ C )
= C ) ),
inference(cnf,[status(esa)],[1173]) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_binop_1 @ B @ C @ C )
= C )
| ~ ( 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 )
| ~ ( m1_subset_1 @ C @ A ) ),
inference(lifteq,[status(thm)],[1174]) ).
thf(342,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(2974,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(8069,plain,
( ( v1_xboole_0 @ sk216 )
!= ( v1_xboole_0 @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[3113,1196]) ).
thf(8079,plain,
sk216 != sk14,
inference(simp,[status(thm)],[8069]) ).
thf(854,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r3_lattice4 @ A @ B @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice4) ).
thf(5410,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)],[854]) ).
thf(8272,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk296 ) ),
inference(paramod_ordered,[status(thm)],[4082,2308]) ).
thf(8281,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk296 ),
inference(simp,[status(thm)],[8272]) ).
thf(1061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ A )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( m1_subset_1 @ ( sk6 @ C @ B @ A ) @ A )
| ( r1_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1060]) ).
thf(593,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k5_filter_0 @ A @ D @ E ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k5_filter_0 @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_0) ).
thf(4232,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)],[593]) ).
thf(11711,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( sk251 @ A ) )
!= ( v1_xboole_0 @ sk218 ) ),
inference(paramod_ordered,[status(thm)],[3555,3123]) ).
thf(11721,plain,
! [A: $i] :
( ( sk251 @ A )
!= sk218 ),
inference(simp,[status(thm)],[11711]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k2_lattices @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(3806,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k2_lattices @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1176,plain,
! [B: $i,A: $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 )
| ( m1_subset_1 @ ( sk12 @ B @ A ) @ A )
| ( v3_binop_1 @ B @ A ) ),
inference(cnf,[status(esa)],[1173]) ).
thf(2592,plain,
v7_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(6099,plain,
( ( v1_xboole_0 @ sk218 )
!= ( v1_xboole_0 @ sk71 ) ),
inference(paramod_ordered,[status(thm)],[1884,3123]) ).
thf(6100,plain,
sk218 != sk71,
inference(simp,[status(thm)],[6099]) ).
thf(738,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(4954,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(921,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/sandbox2/benchmark/theBenchmark.p',t15_lattice4) ).
thf(5667,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)],[921]) ).
thf(851,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_lattice4) ).
thf(5403,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)],[851]) ).
thf(2984,plain,
v7_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[2980]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( k2_partfun1 @ A @ B @ D @ C )
= ( k2_partfun1 @ A @ B @ E @ C ) )
<=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice2) ).
thf(3490,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)],[439]) ).
thf(8275,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk296 ) ),
inference(paramod_ordered,[status(thm)],[4082,3790]) ).
thf(8280,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk296 ),
inference(simp,[status(thm)],[8275]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',t25_binop_1) ).
thf(3480,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)],[437]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k1_tarski @ B ) )
<=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(2418,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) )
=> ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k3_lattice2 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice2) ).
thf(4832,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)],[711]) ).
thf(939,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattice2) ).
thf(5742,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)],[939]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(2962,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(2212,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)],[214]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(2171,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)],[209]) ).
thf(5094,plain,
! [A: $i] : ( m1_subset_1 @ ( sk389 @ A ) @ A ),
inference(cnf,[status(esa)],[5093]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(2550,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)],[274]) ).
thf(804,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/sandbox2/benchmark/theBenchmark.p',t13_filter_2) ).
thf(5218,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)],[804]) ).
thf(96,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
thf(1528,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(6940,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1057,6857]) ).
thf(6944,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( B != sk71 )
| ( ( k1_relat_1 @ B )
!= sk1 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[6940]) ).
thf(6950,plain,
( ~ ( v1_relat_1 @ sk71 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(simp,[status(thm)],[6944]) ).
thf(7023,plain,
( ~ $true
| ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[6950,1887]) ).
thf(7024,plain,
( ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(simp,[status(thm)],[7023]) ).
thf(11670,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,7024]) ).
thf(11675,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11670]) ).
thf(11701,plain,
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 )
| ( ( k2_relat_1 @ sk71 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[11675]) ).
thf(14297,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,7850]) ).
thf(14379,plain,
! [B: $i,A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( sk207 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14297]) ).
thf(14412,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( sk207 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14379]) ).
thf(25644,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v4_lattices @ k1_xboole_0 )
| ( A != k13_nat_lat ) ),
inference(paramod_ordered,[status(thm)],[1266,2341]) ).
thf(25645,plain,
( ( v1_relat_1 @ ( sk19 @ k13_nat_lat ) )
| ( v4_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25644:[bind(A,$thf( k13_nat_lat ))]]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',d3_binop_1) ).
thf(1643,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)],[113]) ).
thf(8070,plain,
( ( v1_xboole_0 @ sk364 )
!= ( v1_xboole_0 @ sk216 ) ),
inference(paramod_ordered,[status(thm)],[3113,4871]) ).
thf(8084,plain,
sk364 != sk216,
inference(simp,[status(thm)],[8070]) ).
thf(915,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k5_lattices @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattices) ).
thf(5646,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)],[915]) ).
thf(561,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_filter_0) ).
thf(4085,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)],[561]) ).
thf(477,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ 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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_2) ).
thf(3674,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( r2_filter_2 @ A @ 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 ) ) ) ) )
& ( ( ( 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 ) ) ) )
=> ( r2_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(709,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/sandbox2/benchmark/theBenchmark.p',t32_lattice4) ).
thf(4827,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)],[709]) ).
thf(2288,plain,
v4_lattices @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(1112,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = B ) ),
inference(cnf,[status(esa)],[1111]) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1112]) ).
thf(352,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_group_1 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattice2) ).
thf(3016,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v6_group_1 @ A )
& ( v10_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(730,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ ( k20_filter_2 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k20_filter_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_2) ).
thf(4918,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ ( k20_filter_2 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k20_filter_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(27047,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1266,7546]) ).
thf(27048,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[27047:[bind(A,$thf( k1_tarski @ C )),bind(B,$thf( C ))]]) ).
thf(28354,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[27048]) ).
thf(2101,plain,
v4_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
thf(4304,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(831,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r1_lattice4 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice4) ).
thf(5326,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)],[831]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k9_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(5139,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)],[785]) ).
thf(522,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(3908,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(4965,plain,
( ( m1_subset_1 @ sk376 @ f1_s3_funct_2 )
| sk375 ),
inference(cnf,[status(esa)],[4963]) ).
thf(857,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_filter_2) ).
thf(5424,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( r2_filter_2 @ A @ B )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) )
=> ( r2_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(4394,plain,
v9_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(972,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_0) ).
thf(5881,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)],[972]) ).
thf(476,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(3672,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(16441,plain,
! [A: $i] :
( ( m1_subset_1 @ ( sk251 @ A ) @ ( k1_tarski @ k1_xboole_0 ) )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1868,3556]) ).
thf(16442,plain,
m1_subset_1 @ ( sk251 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[16441:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(2878,plain,
~ ( v3_struct_0 @ sk196 ),
inference(cnf,[status(esa)],[2872]) ).
thf(951,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/sandbox2/benchmark/theBenchmark.p',t14_lattice4) ).
thf(5812,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)],[951]) ).
thf(1076,plain,
! [C: $i,B: $i,A: $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_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( m1_subset_1 @ ( sk8 @ C @ B @ A ) @ A )
| ( r6_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1075]) ).
thf(918,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_filter_0) ).
thf(5661,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)],[918]) ).
thf(10642,plain,
! [A: $i] :
( ( ( k1_tarski @ k1_xboole_0 )
!= sk296 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1868,8280]) ).
thf(10643,plain,
( ( k1_tarski @ k1_xboole_0 )
!= sk296 ),
inference(pattern_uni,[status(thm)],[10642:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(11122,plain,
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,6691]) ).
thf(11161,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk71 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11122]) ).
thf(445,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 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( ( ( k3_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) )
= ( k19_filter_2 @ A @ B ) )
& ( ( k3_filter_2 @ A @ B )
= ( k19_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) ) )
& ( ( k3_filter_2 @ A @ ( k8_filter_2 @ A @ C ) )
= ( k19_filter_2 @ ( k1_lattice2 @ A ) @ C ) )
& ( ( k3_filter_2 @ ( k1_lattice2 @ A ) @ C )
= ( k19_filter_2 @ A @ ( k8_filter_2 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_2) ).
thf(3522,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 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( ( ( k3_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) )
= ( k19_filter_2 @ A @ B ) )
& ( ( k3_filter_2 @ A @ B )
= ( k19_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) ) )
& ( ( k3_filter_2 @ A @ ( k8_filter_2 @ A @ C ) )
= ( k19_filter_2 @ ( k1_lattice2 @ A ) @ C ) )
& ( ( k3_filter_2 @ ( k1_lattice2 @ A ) @ C )
= ( k19_filter_2 @ A @ ( k8_filter_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(7542,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2933,4367]) ).
thf(7547,plain,
! [B: $i,A: $i] :
( ( k2_tarski @ A @ B )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[7542]) ).
thf(23750,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1952,7547]) ).
thf(23751,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[23750:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(23766,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[23751]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).
thf(2054,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)],[191]) ).
thf(636,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_lattice4 @ C @ A @ B )
<=> ( v2_funct_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice4) ).
thf(4426,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)],[636]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(1948,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)],[167]) ).
thf(1034,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( sk3 @ C @ A @ B )
| ( v1_funct_2 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[1031]) ).
thf(887,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_0) ).
thf(5538,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)],[887]) ).
thf(900,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice4) ).
thf(5587,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)],[900]) ).
thf(149,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( v4_lattices @ ( k1_lattice2 @ A ) )
& ( v5_lattices @ ( k1_lattice2 @ A ) )
& ( v6_lattices @ ( k1_lattice2 @ A ) )
& ( v7_lattices @ ( k1_lattice2 @ A ) )
& ( v8_lattices @ ( k1_lattice2 @ A ) )
& ( v9_lattices @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
thf(1873,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( v4_lattices @ ( k1_lattice2 @ A ) )
& ( v5_lattices @ ( k1_lattice2 @ A ) )
& ( v6_lattices @ ( k1_lattice2 @ A ) )
& ( v7_lattices @ ( k1_lattice2 @ A ) )
& ( v8_lattices @ ( k1_lattice2 @ A ) )
& ( v9_lattices @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(3193,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(2107,plain,
v8_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(1081,plain,
! [C: $i,B: $i,A: $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_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( m1_subset_1 @ ( sk7 @ C @ B @ A ) @ A )
| ( r6_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1075]) ).
thf(6055,plain,
( ( v1_xboole_0 @ sk71 )
!= ( v1_xboole_0 @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[1884,1196]) ).
thf(6056,plain,
sk71 != sk14,
inference(simp,[status(thm)],[6055]) ).
thf(539,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ ( k1_lattice2 @ B ) ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ ( k1_lattice2 @ B ) ) ) )
=> ( ( D = E )
=> ( ( ( k2_lattice2 @ A @ B @ C @ D )
= ( k3_lattice2 @ A @ ( k1_lattice2 @ B ) @ C @ E ) )
& ( ( k3_lattice2 @ A @ B @ C @ D )
= ( k2_lattice2 @ A @ ( k1_lattice2 @ B ) @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattice2) ).
thf(3975,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)],[539]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(3048,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)],[357]) ).
thf(7084,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1059,6875]) ).
thf(7098,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( B != sk138 )
| ( A != sk1 )
| ( ( k2_relat_1 @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7084]) ).
thf(7120,plain,
( ~ ( v1_relat_1 @ sk138 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7098]) ).
thf(8643,plain,
( ~ $true
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7120,2405]) ).
thf(8644,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[8643]) ).
thf(11668,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,8644]) ).
thf(11680,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[11668]) ).
thf(11689,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[11680]) ).
thf(4688,plain,
l3_lattices @ sk347,
inference(cnf,[status(esa)],[4686]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(2333,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
| ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ),
inference(cnf,[status(esa)],[1144]) ).
thf(984,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_0) ).
thf(5916,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)],[984]) ).
thf(944,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice2) ).
thf(5763,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)],[944]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',d16_nat_lat) ).
thf(3292,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)],[403]) ).
thf(2899,plain,
v3_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(840,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/sandbox2/benchmark/theBenchmark.p',t24_filter_2) ).
thf(5358,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)],[840]) ).
thf(783,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_0) ).
thf(5133,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)],[783]) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_realset1 @ C @ A @ B )
| ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ),
inference(cnf,[status(esa)],[1179]) ).
thf(747,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/sandbox2/benchmark/theBenchmark.p',dt_k12_filter_2) ).
thf(4986,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)],[747]) ).
thf(999,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ A @ B @ C @ D )
<=> ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_0) ).
thf(5991,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)],[999]) ).
thf(2582,plain,
l3_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(897,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v12_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ B @ D )
=> ( ( k1_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_lattices) ).
thf(5570,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v12_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ B @ D )
=> ( ( k1_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ B @ D )
=> ( ( k1_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) ) )
=> ( v12_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(467,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ F @ D )
& ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) )
=> ( r3_lattices @ A @ ( k3_lattice2 @ C @ A @ D @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_lattice2) ).
thf(3640,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)],[467]) ).
thf(906,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) )
<=> ( r3_lattices @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_0) ).
thf(5607,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)],[906]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(3214,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(97,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(1531,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(2882,plain,
v8_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(8075,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk216 ) ),
inference(paramod_ordered,[status(thm)],[3113,3790]) ).
thf(8083,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk216 ),
inference(simp,[status(thm)],[8075]) ).
thf(10652,plain,
! [A: $i] :
( ( ( k1_tarski @ k1_xboole_0 )
!= sk216 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= ( k1_zfmisc_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1868,8083]) ).
thf(10653,plain,
( ( k1_tarski @ k1_xboole_0 )
!= sk216 ),
inference(pattern_uni,[status(thm)],[10652:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(4658,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)],[679]) ).
thf(861,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattices) ).
thf(5446,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)],[861]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(1845,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',d19_binop_1) ).
thf(2298,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)],[230]) ).
thf(488,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v15_lattices @ A )
<=> ( ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattices) ).
thf(3737,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)],[488]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k4_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(1770,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)],[131]) ).
thf(824,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_filter_2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_filter_2) ).
thf(5294,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)],[824]) ).
thf(988,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/sandbox2/benchmark/theBenchmark.p',t18_filter_2) ).
thf(5927,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)],[988]) ).
thf(623,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
<=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_2) ).
thf(4360,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
=> ! [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)],[623]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_lattice2) ).
thf(2397,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(720,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k6_lattices @ A ) )
= ( k5_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice4) ).
thf(4864,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)],[720]) ).
thf(524,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/sandbox2/benchmark/theBenchmark.p',t52_domain_1) ).
thf(3913,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)],[524]) ).
thf(10318,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= ( k2_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1098,8997]) ).
thf(10328,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[10318]) ).
thf(14050,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= ( k1_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1099,10328]) ).
thf(14081,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14050]) ).
thf(14088,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14081]) ).
thf(14100,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[14088,1977]) ).
thf(14101,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14100]) ).
thf(510,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/sandbox2/benchmark/theBenchmark.p',t74_lattice2) ).
thf(3842,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)],[510]) ).
thf(734,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).
thf(4937,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)],[734]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(2977,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( r2_hidden @ ( sk10 @ B @ A ) @ ( k1_relat_1 @ A ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1148]) ).
thf(1156,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( r2_hidden @ ( sk10 @ B @ A ) @ ( k1_relat_1 @ A ) ) ),
inference(lifteq,[status(thm)],[1153]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
thf(2060,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)],[194]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',t17_binop_1) ).
thf(1743,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)],[126]) ).
thf(870,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( m1_subset_1 @ ( k6_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(5478,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)],[870]) ).
thf(2588,plain,
v8_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(493,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_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 @ 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 = D ) )
=> ( ( ( k3_filter_2 @ A @ C )
= ( k3_filter_2 @ B @ D ) )
& ( ( k19_filter_2 @ A @ C )
= ( k19_filter_2 @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l48_filter_2) ).
thf(3754,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_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 @ 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 = D ) )
=> ( ( ( k3_filter_2 @ A @ C )
= ( k3_filter_2 @ B @ D ) )
& ( ( k19_filter_2 @ A @ C )
= ( k19_filter_2 @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(659,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_relat_1 @ ( k10_filter_0 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_filter_0) ).
thf(4534,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)],[659]) ).
thf(473,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(3659,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)],[473]) ).
thf(607,axiom,
! [A: $i] :
( ( k2_tarski @ A @ A )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(4287,plain,
! [A: $i] :
( ( k2_tarski @ A @ A )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(4754,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)],[696]) ).
thf(742,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ F ) ) ) )
=> ( r3_lattices @ C @ ( k2_lattice2 @ A @ C @ B @ D ) @ ( k2_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_lattice2) ).
thf(4971,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)],[742]) ).
thf(629,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_filter_0 @ A @ D ) @ B ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ E @ B )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ E ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice4) ).
thf(4377,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)],[629]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
& ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(2160,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)],[206]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k2_lattice2 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice2) ).
thf(4593,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)],[667]) ).
thf(2888,plain,
l3_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(640,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).
thf(4437,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)],[640]) ).
thf(468,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(3642,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(4398,plain,
v6_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(83,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( B
= ( k1_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(1432,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( B
= ( k1_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
& ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ( ( k1_relat_1 @ C )
!= A )
| ~ ( r2_hidden @ ( k1_funct_1 @ C @ ( sk4 @ C @ B @ A ) ) @ B )
| ( sk3 @ C @ A @ B ) ),
inference(cnf,[status(esa)],[1031]) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ C )
!= A )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r2_hidden @ ( k1_funct_1 @ C @ ( sk4 @ C @ B @ A ) ) @ B )
| ( sk3 @ C @ A @ B ) ),
inference(lifteq,[status(thm)],[1036]) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( r2_hidden @ ( k1_funct_1 @ B @ ( sk4 @ B @ A @ ( k1_relat_1 @ B ) ) ) @ A )
| ( sk3 @ B @ ( k1_relat_1 @ B ) @ A ) ),
inference(simp,[status(thm)],[1037]) ).
thf(991,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_2 @ A )
= ( k1_filter_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).
thf(5948,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)],[991]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k12_filter_0 @ A @ B )
= ( k10_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_filter_0) ).
thf(4875,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)],[724]) ).
thf(363,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/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(3080,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)],[363]) ).
thf(298,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(2747,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ D )
| ~ ( v1_funct_2 @ D @ A @ B )
| ~ ( m2_relset_1 @ D @ A @ B )
| ~ ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
| ( r2_hidden @ ( sk5 @ E @ D @ C @ B @ A ) @ C ) ),
inference(cnf,[status(esa)],[1051]) ).
thf(95,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k2_funct_1 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(1499,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k2_funct_1 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_1) ).
thf(1987,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1011,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( k17_filter_2 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_filter_2) ).
thf(6036,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)],[1011]) ).
thf(255,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(2454,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(84,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).
thf(1452,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(501,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
thf(3791,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(484,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/sandbox2/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).
thf(3722,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)],[484]) ).
thf(548,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/sandbox2/benchmark/theBenchmark.p',t72_lattice2) ).
thf(4020,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)],[548]) ).
thf(10301,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk71 )
!= ( k2_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1098,8686]) ).
thf(10325,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ sk71 ) @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[10301]) ).
thf(12640,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= ( k1_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1099,10325]) ).
thf(12662,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[12640]) ).
thf(12675,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[12662]) ).
thf(13088,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[12675,1977]) ).
thf(13089,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[13088]) ).
thf(7561,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_funct_1 @ k1_xboole_0 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2968,6539]) ).
thf(7562,plain,
( ~ ( m2_relset_1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7561:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(7657,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
!= ( m2_relset_1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1059,7562]) ).
thf(7684,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( B != k1_xboole_0 )
| ( A != sk1 )
| ( ( k2_relat_1 @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7657]) ).
thf(7686,plain,
( ~ ( v1_relat_1 @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ k1_xboole_0 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7684]) ).
thf(2975,plain,
v1_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[2974]) ).
thf(10161,plain,
( ~ $true
| ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ k1_xboole_0 )
!= k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7686,2975]) ).
thf(10162,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ k1_xboole_0 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[10161]) ).
thf(10294,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[10162,1098]) ).
thf(10295,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[10294]) ).
thf(10573,plain,
( ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[10295,1099]) ).
thf(11649,plain,
( ~ $true
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[10573,1977]) ).
thf(11650,plain,
( ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[11649]) ).
thf(892,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ B @ D ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ B @ D ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattices) ).
thf(5555,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)],[892]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',t9_realset1) ).
thf(1869,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)],[148]) ).
thf(6914,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1057,6582]) ).
thf(6945,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( B != sk71 )
| ( ( k1_relat_1 @ B )
!= sk1 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[6914]) ).
thf(6952,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ sk71 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(simp,[status(thm)],[6945]) ).
thf(7148,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[6952,1887]) ).
thf(7149,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(simp,[status(thm)],[7148]) ).
thf(2337,plain,
v8_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[2335]) ).
thf(757,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/sandbox2/benchmark/theBenchmark.p',t24_binop_1) ).
thf(5030,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)],[757]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(1980,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)],[174]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(2128,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)],[202]) ).
thf(65,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
thf(1317,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(1763,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)],[130]) ).
thf(156,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( l2_lattices @ A ) )
=> ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattice2) ).
thf(1901,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( l2_lattices @ A ) )
=> ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(6172,plain,
( ( v1_xboole_0 @ sk218 )
!= ( v1_xboole_0 @ sk152 ) ),
inference(paramod_ordered,[status(thm)],[2510,3123]) ).
thf(6174,plain,
sk218 != sk152,
inference(simp,[status(thm)],[6172]) ).
thf(508,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/sandbox2/benchmark/theBenchmark.p',d3_filter_2) ).
thf(3828,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)],[508]) ).
thf(4132,plain,
l1_struct_0 @ sk300,
inference(cnf,[status(esa)],[4131]) ).
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 ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ D ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_0) ).
thf(5152,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)],[788]) ).
thf(596,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( r2_filter_2 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_2) ).
thf(4241,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( r2_filter_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(326,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(2903,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)],[326]) ).
thf(745,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/sandbox2/benchmark/theBenchmark.p',dt_k16_filter_2) ).
thf(4982,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)],[745]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(3412,plain,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',t81_lattice2) ).
thf(3359,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)],[418]) ).
thf(189,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 ) )
=> ( ( ! [E: $i] :
( B
!= ( k1_tarski @ E ) )
& ( ( k5_partfun1 @ A @ B @ C )
= ( k5_partfun1 @ A @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_funct_2) ).
thf(2044,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 ) )
=> ( ( ! [E: $i] :
( B
!= ( k1_tarski @ E ) )
& ( ( k5_partfun1 @ A @ B @ C )
= ( k5_partfun1 @ A @ B @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(568,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/sandbox2/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(4117,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)],[568]) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(1738,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)],[124]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(3041,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)],[356]) ).
thf(438,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/sandbox2/benchmark/theBenchmark.p',dt_k13_filter_2) ).
thf(3488,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)],[438]) ).
thf(924,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r1_filter_0 @ A @ D @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_filter_0) ).
thf(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 ) )
=> ! [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)],[924]) ).
thf(908,axiom,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_nat_lat) ).
thf(5613,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)],[908]) ).
thf(92,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
& ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(1485,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
& ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(2579,plain,
v14_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(638,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/sandbox2/benchmark/theBenchmark.p',t6_filter_2) ).
thf(4431,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)],[638]) ).
thf(4695,plain,
( ( m1_subset_1 @ sk349 @ f1_s13_funct_2 )
| sk348 ),
inference(cnf,[status(esa)],[4689]) ).
thf(592,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ F @ C )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ D @ F ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( C = k1_xboole_0 )
| ( r3_lattices @ A @ ( k2_lattice2 @ B @ A @ C @ D ) @ ( k2_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice2) ).
thf(4225,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)],[592]) ).
thf(361,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( l2_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u2_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 ) )
& ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattice2) ).
thf(3071,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v5_lattices @ A )
& ( l2_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u2_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 ) )
& ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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)],[361]) ).
thf(2892,plain,
v7_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(2584,plain,
v4_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(961,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v17_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_filter_0) ).
thf(5841,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)],[961]) ).
thf(4392,plain,
v11_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(18980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ ( k9_relat_1 @ sk152 @ A ) @ ( k2_relat_1 @ sk152 ) )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18965,1074]) ).
thf(18981,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk152 @ B ) @ A ) @ ( k2_relat_1 @ sk152 ) ),
inference(pattern_uni,[status(thm)],[18980:[bind(A,$thf( F )),bind(B,$thf( k9_relat_1 @ sk152 @ F )),bind(C,$thf( k2_relat_1 @ sk152 )),bind(D,$thf( D ))]]) ).
thf(19046,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk152 @ B ) @ A ) @ ( k2_relat_1 @ sk152 ) ),
inference(simp,[status(thm)],[18981]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(4057,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)],[555]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',t15_binop_1) ).
thf(1898,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)],[155]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(1849,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( ( k2_partfun1 @ A @ B @ C @ E )
= ( k2_partfun1 @ A @ B @ D @ E ) )
=> ( ( k2_funct_2 @ A @ B @ C @ E )
= ( k2_funct_2 @ A @ B @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice2) ).
thf(2838,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)],[316]) ).
thf(277,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).
thf(2558,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(425,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ D @ C )
= ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ E @ C ) )
=> ( ( C = k1_xboole_0 )
| ( ( k3_lattice2 @ B @ A @ C @ D )
= ( k3_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_lattice2) ).
thf(3415,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)],[425]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
<=> ( B
= ( k1_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(3124,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
=> ( B
= ( k1_subset_1 @ A ) ) )
& ( ( B
= ( k1_subset_1 @ A ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(573,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] :
( ( m2_filter_2 @ C @ A )
=> ( ( C
= ( k19_filter_2 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_2) ).
thf(4133,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] :
( ( m2_filter_2 @ C @ A )
=> ( ( ( C
= ( k19_filter_2 @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) )
=> ( C
= ( k19_filter_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(1802,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1335,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_relat_1 @ ( sk25 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1333]) ).
thf(1352,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_relat_1 @ ( sk25 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[1335]) ).
thf(1353,plain,
! [A: $i] : ( v1_relat_1 @ ( sk25 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[1352]) ).
thf(5504,plain,
l2_struct_0 @ sk421,
inference(cnf,[status(esa)],[5502]) ).
thf(950,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= B ) )
& ( ( k2_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_0) ).
thf(5809,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)],[950]) ).
thf(553,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m3_lattice4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattice4) ).
thf(4046,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)],[553]) ).
thf(660,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(4538,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)],[660]) ).
thf(594,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( 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/sandbox2/benchmark/theBenchmark.p',t50_lattice2) ).
thf(4235,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)],[594]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 )
<=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(1585,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 )
=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) )
& ( ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) )
=> ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(2511,plain,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(805,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m3_lattice4 @ ( k3_lattice4 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(5226,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)],[805]) ).
thf(18,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(1093,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1094,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(cnf,[status(esa)],[1093]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(1240,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(2885,plain,
v10_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(80,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(1412,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(2209,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)],[213]) ).
thf(6185,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) )
| ( ( v1_relat_1 @ sk138 )
!= ( v1_relat_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2405,1045]) ).
thf(6186,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk138 @ A ) @ ( k9_relat_1 @ sk138 @ ( k1_relat_1 @ sk138 ) ) ),
inference(pattern_uni,[status(thm)],[6185:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).
thf(16925,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ sk138 @ A ) @ ( k2_relat_1 @ sk138 ) ),
inference(rewrite,[status(thm)],[6186,13749]) ).
thf(2792,plain,
~ ( v3_struct_0 @ sk188 ),
inference(cnf,[status(esa)],[2784]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
& ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(2865,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
& ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
= ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(2875,plain,
v4_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(4639,plain,
( ( m1_subset_1 @ sk341 @ f1_s12_funct_2 )
| sk340 ),
inference(cnf,[status(esa)],[4636]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(3284,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)],[400]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',d10_binop_1) ).
thf(1421,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)],[81]) ).
thf(16934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ ( k9_relat_1 @ sk138 @ A ) @ ( k2_relat_1 @ sk138 ) )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16925,1074]) ).
thf(16935,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk138 @ B ) @ A ) @ ( k2_relat_1 @ sk138 ) ),
inference(pattern_uni,[status(thm)],[16934:[bind(A,$thf( F )),bind(B,$thf( k9_relat_1 @ sk138 @ F )),bind(C,$thf( k2_relat_1 @ sk138 )),bind(D,$thf( D ))]]) ).
thf(16998,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk138 @ B ) @ A ) @ ( k2_relat_1 @ sk138 ) ),
inference(simp,[status(thm)],[16935]) ).
thf(14306,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,6582]) ).
thf(14371,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14306]) ).
thf(14403,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( sk71 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14371]) ).
thf(4288,plain,
! [A: $i] :
( ( k2_tarski @ A @ A )
= ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[4287]) ).
thf(4289,plain,
! [A: $i] :
( ( k2_tarski @ A @ A )
= ( k1_tarski @ A ) ),
inference(lifteq,[status(thm)],[4288]) ).
thf(160,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ ( a_2_3_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_domain_1) ).
thf(1918,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ ( a_2_3_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(635,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 @ ( k18_filter_2 @ A @ B ) @ ( k19_filter_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_2) ).
thf(4424,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 @ ( k18_filter_2 @ A @ B ) @ ( k19_filter_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1080,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $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_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 )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( m1_subset_1 @ E @ A )
| ~ ( 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 ) ) ) ),
inference(cnf,[status(esa)],[1075]) ).
thf(1084,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( 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 ) ) )
| ~ ( 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_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 )
| ~ ( m1_subset_1 @ D @ A )
| ~ ( m1_subset_1 @ E @ A )
| ~ ( m1_subset_1 @ F @ A ) ),
inference(lifteq,[status(thm)],[1080]) ).
thf(23723,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk216 )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1952,8085]) ).
thf(23724,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk216 ),
inference(pattern_uni,[status(thm)],[23723:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).
thf(23774,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= sk216 ),
inference(simp,[status(thm)],[23724]) ).
thf(670,axiom,
m2_nat_lat @ k13_nat_lat @ k6_nat_lat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_nat_lat) ).
thf(4606,plain,
m2_nat_lat @ k13_nat_lat @ k6_nat_lat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(454,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/sandbox2/benchmark/theBenchmark.p',t63_filter_0) ).
thf(3565,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)],[454]) ).
thf(423,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( v13_lattices @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).
thf(3401,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( ( v13_lattices @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) )
=> ( v13_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(689,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ E ) ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice4) ).
thf(4727,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)],[689]) ).
thf(460,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/sandbox2/benchmark/theBenchmark.p',t29_lattice4) ).
thf(3589,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)],[460]) ).
thf(940,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_0) ).
thf(5749,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)],[940]) ).
thf(6981,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk152 ) ),
inference(paramod_ordered,[status(thm)],[2510,4936]) ).
thf(6985,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk152 ),
inference(simp,[status(thm)],[6981]) ).
thf(365,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/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(3092,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)],[365]) ).
thf(3062,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[3060]) ).
thf(3066,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3062]) ).
thf(3067,plain,
! [A: $i] :
( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3066]) ).
thf(1180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m2_realset1 @ C @ A @ B )
| ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ),
inference(cnf,[status(esa)],[1179]) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A )
| ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( k1_funct_1 @ A @ ( sk10 @ B @ A ) )
= ( sk11 @ B @ A ) )
| ( ( k1_funct_1 @ B @ ( sk11 @ B @ A ) )
= ( sk10 @ B @ A ) )
| ( B
= ( k2_funct_1 @ A ) ) ),
inference(cnf,[status(esa)],[1148]) ).
thf(1157,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= ( k2_relat_1 @ B ) )
| ( ( k2_relat_1 @ A )
!= ( k1_relat_1 @ B ) )
| ( ( sk11 @ B @ A )
= ( k1_funct_1 @ A @ ( sk10 @ B @ A ) ) )
| ( ( k1_funct_1 @ B @ ( sk11 @ B @ A ) )
= ( sk10 @ B @ A ) )
| ( B
= ( k2_funct_1 @ A ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v2_funct_1 @ A ) ),
inference(lifteq,[status(thm)],[1150]) ).
thf(736,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(4944,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)],[736]) ).
thf(2310,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(cnf,[status(esa)],[2309]) ).
thf(13988,plain,
! [C: $i,B: $i,A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ ( k2_relat_1 @ sk407 ) @ f2_s11_funct_2 )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13179,1074]) ).
thf(13989,plain,
! [A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ sk407 ) @ A ) @ f2_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[13988:[bind(A,$thf( k2_relat_1 @ sk407 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14037,plain,
! [A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ sk407 ) @ A ) @ f2_s11_funct_2 ) ),
inference(simp,[status(thm)],[13989]) ).
thf(558,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/sandbox2/benchmark/theBenchmark.p',t58_lattice2) ).
thf(4078,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)],[558]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(3725,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(828,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 ) )
<=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v17_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_2) ).
thf(5308,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 ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v17_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v17_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(8268,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk296 ) ),
inference(paramod_ordered,[status(thm)],[4082,2940]) ).
thf(8285,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk296 ),
inference(simp,[status(thm)],[8268]) ).
thf(416,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_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 ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ 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 = E )
& ( D = F ) )
=> ( ( k5_filter_0 @ A @ C @ D )
= ( k5_filter_0 @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l59_filter_2) ).
thf(3346,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_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 ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ 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 = E )
& ( D = F ) )
=> ( ( k5_filter_0 @ A @ C @ D )
= ( k5_filter_0 @ B @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(2110,plain,
v2_struct_0 @ sk95,
inference(cnf,[status(esa)],[2109]) ).
thf(2342,plain,
v3_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[2335]) ).
thf(1866,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(cnf,[status(esa)],[1865]) ).
thf(529,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
thf(3929,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)],[529]) ).
thf(2775,plain,
l3_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(475,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ ( u2_lattices @ A ) @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ ( u2_lattices @ A ) @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( v1_funct_1 @ ( k1_realset1 @ ( u1_lattices @ A ) @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ ( u1_lattices @ A ) @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ ( u1_lattices @ A ) @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_filter_2) ).
thf(3665,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ ( u2_lattices @ A ) @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ ( u2_lattices @ A ) @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( v1_funct_1 @ ( k1_realset1 @ ( u1_lattices @ A ) @ B ) )
& ( v1_funct_2 @ ( k1_realset1 @ ( u1_lattices @ A ) @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
& ( m2_relset_1 @ ( k1_realset1 @ ( u1_lattices @ A ) @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(4574,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)],[663]) ).
thf(13498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ sk315 ) @ A ) @ f2_s4_funct_2 )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13159,1074]) ).
thf(13499,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k4_xboole_0 @ ( k2_relat_1 @ sk315 ) @ B ) @ A ) @ f2_s4_funct_2 ),
inference(pattern_uni,[status(thm)],[13498:[bind(A,$thf( F )),bind(B,$thf( k4_xboole_0 @ ( k2_relat_1 @ sk315 ) @ F )),bind(C,$thf( f2_s4_funct_2 )),bind(D,$thf( D ))]]) ).
thf(13549,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k4_xboole_0 @ ( k2_relat_1 @ sk315 ) @ B ) @ A ) @ f2_s4_funct_2 ),
inference(simp,[status(thm)],[13499]) ).
thf(486,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/sandbox2/benchmark/theBenchmark.p',t11_filter_2) ).
thf(3729,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)],[486]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(1253,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(703,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(4806,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(838,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_lattice4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(5351,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)],[838]) ).
thf(542,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(3991,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1007,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/sandbox2/benchmark/theBenchmark.p',t22_lattice2) ).
thf(6023,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)],[1007]) ).
thf(806,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
& ( B = D )
& ( C = E ) )
=> ( r3_lattices @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_lattice2) ).
thf(5228,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)],[806]) ).
thf(474,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( ( v2_struct_0 @ A )
=> ( A
= ( g2_struct_0 @ ( u1_struct_0 @ A ) @ ( u2_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v2_struct_0) ).
thf(3662,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( ( v2_struct_0 @ A )
=> ( A
= ( g2_struct_0 @ ( u1_struct_0 @ A ) @ ( u2_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',t14_binop_1) ).
thf(2394,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)],[244]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).
thf(1276,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(2591,plain,
v13_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(5055,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(2988,plain,
~ ( v3_struct_0 @ k6_nat_lat ),
inference(cnf,[status(esa)],[2980]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(1385,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(819,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_0) ).
thf(5272,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)],[819]) ).
thf(2290,plain,
v1_lattice2 @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(1903,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)],[157]) ).
thf(750,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k2_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).
thf(5008,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)],[750]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(4683,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)],[682]) ).
thf(848,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k7_lattices @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattices) ).
thf(5394,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)],[848]) ).
thf(751,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/sandbox2/benchmark/theBenchmark.p',dt_k14_filter_2) ).
thf(5010,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)],[751]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(2764,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)],[301]) ).
thf(712,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_lattices @ A @ B @ C )
& ( r1_lattices @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
thf(4834,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_lattices @ A @ B @ C )
& ( r1_lattices @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(443,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/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_2) ).
thf(3516,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)],[443]) ).
thf(4823,plain,
l2_lattices @ sk361,
inference(cnf,[status(esa)],[4822]) ).
thf(880,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_0) ).
thf(5505,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)],[880]) ).
thf(2786,plain,
v3_filter_0 @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(885,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_lattice4 @ A @ ( k1_setwiseo @ ( u1_struct_0 @ A ) ) )
= ( k6_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattice4) ).
thf(5532,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)],[885]) ).
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 ) )
=> ( v13_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_0) ).
thf(5692,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)],[930]) ).
thf(1005,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k4_lattice4 @ A @ B )
= ( a_2_0_lattice4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice4) ).
thf(6018,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)],[1005]) ).
thf(4387,plain,
v13_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(932,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattices) ).
thf(5699,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)],[932]) ).
thf(543,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/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
thf(3993,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)],[543]) ).
thf(26198,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( m1_subset_1 @ k1_xboole_0 @ ( u1_struct_0 @ sk1 ) )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[1266,1020]) ).
thf(26199,plain,
( ( v1_relat_1 @ ( sk19 @ sk2 ) )
| ( m1_subset_1 @ k1_xboole_0 @ ( u1_struct_0 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26198:[bind(A,$thf( sk2 ))]]) ).
thf(802,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ( l3_lattices @ A ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_lattice2) ).
thf(5196,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)],[802]) ).
thf(801,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_lattice4) ).
thf(5194,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)],[801]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(2009,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)],[181]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_finset_1 @ A )
=> ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(4182,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_finset_1 @ A )
=> ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(956,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattice4 @ A @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice4) ).
thf(5828,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)],[956]) ).
thf(1026,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ E )
| ( E
!= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
| ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) ) ),
inference(cnf,[status(esa)],[1024]) ).
thf(1029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
!= ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
| ( ( k1_relat_1 @ E )
= ( k2_tarski @ A @ C ) )
| ~ ( v1_relat_1 @ E ) ),
inference(lifteq,[status(thm)],[1026]) ).
thf(1030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
= ( k2_tarski @ A @ C ) )
| ~ ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ) ),
inference(simp,[status(thm)],[1029]) ).
thf(997,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v3_filter_0 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k2_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ ( k2_lattices @ A @ B @ E ) @ C )
=> ( r1_lattices @ A @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_0) ).
thf(5963,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v3_filter_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k2_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ ( k2_lattices @ A @ B @ E ) @ C )
=> ( r1_lattices @ A @ E @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k2_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ ( k2_lattices @ A @ B @ E ) @ C )
=> ( r1_lattices @ A @ E @ D ) ) ) ) ) )
=> ( v3_filter_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(583,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/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(4197,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)],[583]) ).
thf(678,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(4649,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)],[678]) ).
thf(305,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(2796,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(792,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k5_lattices @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattices) ).
thf(5164,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)],[792]) ).
thf(791,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_0) ).
thf(5162,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)],[791]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',redefinition_k21_filter_2) ).
thf(3267,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)],[397]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( r3_lattices @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(4299,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( v8_lattices @ A )
& ( v9_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( r3_lattices @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
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 ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattice4) ).
thf(5837,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)],[959]) ).
thf(376,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u1_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 ) )
& ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice2) ).
thf(3149,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A ) )
=> ( ( v1_relat_1 @ ( u1_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 ) )
& ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
& ( v1_partfun1 @ ( 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)],[376]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).
thf(1308,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(518,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v2_lattice4 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice4) ).
thf(3896,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)],[518]) ).
thf(1077,plain,
! [C: $i,B: $i,A: $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_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ~ ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
| ( m1_subset_1 @ ( sk9 @ C @ B @ A ) @ A )
| ( r6_binop_1 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1075]) ).
thf(890,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 @ ( k18_filter_2 @ A @ B ) )
& ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k18_filter_2 @ A @ B ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k18_filter_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_2) ).
thf(5549,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 @ ( k18_filter_2 @ A @ B ) )
& ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k18_filter_2 @ A @ B ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k18_filter_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(896,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k21_filter_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_2) ).
thf(5568,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k21_filter_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(2230,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)],[217]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(1893,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(2294,plain,
l3_lattices @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(494,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/sandbox2/benchmark/theBenchmark.p',t16_filter_2) ).
thf(3761,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)],[494]) ).
thf(2779,plain,
v7_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(11150,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,6596]) ).
thf(11208,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk138 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11150]) ).
thf(967,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/sandbox2/benchmark/theBenchmark.p',dt_k20_filter_2) ).
thf(5864,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)],[967]) ).
thf(821,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/sandbox2/benchmark/theBenchmark.p',redefinition_k9_filter_2) ).
thf(5287,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)],[821]) ).
thf(25018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_tarski @ A )
!= ( sk251 @ B ) )
| ( ( k2_tarski @ A @ A )
!= ( k2_tarski @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4289,11718]) ).
thf(25019,plain,
! [B: $i,A: $i] :
( ( k1_tarski @ A )
!= ( sk251 @ B ) ),
inference(pattern_uni,[status(thm)],[25018:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(2287,plain,
v10_lattices @ sk118,
inference(cnf,[status(esa)],[2285]) ).
thf(11660,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,7410]) ).
thf(11681,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11660]) ).
thf(11690,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 )
| ( ( k2_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[11681]) ).
thf(2983,plain,
v6_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[2980]) ).
thf(818,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
<=> ? [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
& ( v3_lattice4 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattice4) ).
thf(5268,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)],[818]) ).
thf(517,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 ) )
=> ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
& ! [E: $i] :
( B
!= ( k1_tarski @ E ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_funct_2) ).
thf(3892,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 ) )
=> ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
& ! [E: $i] :
( B
!= ( k1_tarski @ E ) ) )
=> ( r1_tarski @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(21491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ B @ D ) @ C )
| ( ( r1_tarski @ ( k9_relat_1 @ sk218 @ A ) @ ( k2_relat_1 @ sk218 ) )
!= ( r1_tarski @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21476,1074]) ).
thf(21492,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk218 @ B ) @ A ) @ ( k2_relat_1 @ sk218 ) ),
inference(pattern_uni,[status(thm)],[21491:[bind(A,$thf( F )),bind(B,$thf( k9_relat_1 @ sk218 @ F )),bind(C,$thf( k2_relat_1 @ sk218 )),bind(D,$thf( D ))]]) ).
thf(21566,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ sk218 @ B ) @ A ) @ ( k2_relat_1 @ sk218 ) ),
inference(simp,[status(thm)],[21492]) ).
thf(11717,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk251 @ A ) )
!= ( v1_xboole_0 @ ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3555,4936]) ).
thf(11722,plain,
! [B: $i,A: $i] :
( ( sk251 @ A )
!= ( k1_tarski @ B ) ),
inference(simp,[status(thm)],[11717]) ).
thf(765,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/sandbox2/benchmark/theBenchmark.p',dt_k22_filter_2) ).
thf(5078,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)],[765]) ).
thf(715,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/sandbox2/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(4843,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)],[715]) ).
thf(4597,plain,
( ( m1_subset_1 @ sk333 @ f1_s14_funct_2 )
| sk332 ),
inference(cnf,[status(esa)],[4595]) ).
thf(1115,plain,
! [C: $i,B: $i,A: $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(cnf,[status(esa)],[1114]) ).
thf(1116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 )
| ~ ( v1_funct_1 @ C )
| ~ ( v1_funct_2 @ C @ k1_xboole_0 @ A )
| ~ ( m2_relset_1 @ C @ k1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[1115]) ).
thf(11112,plain,
( ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk207 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,7850]) ).
thf(11167,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk207 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk207 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11112]) ).
thf(26384,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v10_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1266,1021]) ).
thf(26385,plain,
( ( v1_relat_1 @ ( sk19 @ sk1 ) )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26384:[bind(A,$thf( sk1 ))]]) ).
thf(2102,plain,
v3_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(5677,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)],[925]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(2517,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)],[265]) ).
thf(699,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/sandbox2/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(4794,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)],[699]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(1578,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(782,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_0) ).
thf(5129,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)],[782]) ).
thf(4399,plain,
v17_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(4687,plain,
v3_lattices @ sk347,
inference(cnf,[status(esa)],[4686]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_subset_1) ).
thf(3785,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
= ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(3733,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(704,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( B
= ( k1_filter_0 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_0) ).
thf(4811,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)],[704]) ).
thf(2587,plain,
v5_lattices @ sk157,
inference(cnf,[status(esa)],[2578]) ).
thf(993,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/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_2) ).
thf(5954,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)],[993]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(5232,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)],[807]) ).
thf(434,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ ( k3_filter_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_0) ).
thf(3464,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)],[434]) ).
thf(73,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(1380,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(310,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/sandbox2/benchmark/theBenchmark.p',d13_binop_1) ).
thf(2815,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)],[310]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(4787,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)],[698]) ).
thf(882,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k18_filter_2 @ A @ B )
= ( a_2_0_filter_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
thf(5522,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k18_filter_2 @ A @ B )
= ( a_2_0_filter_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(3337,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(869,axiom,
m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1) ).
thf(5477,plain,
m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(14322,plain,
! [B: $i,A: $i] :
( ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ k1_xboole_0 @ A @ B )
!= ( m2_relset_1 @ sk315 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[2156,8307]) ).
thf(14378,plain,
! [B: $i,A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( sk315 != k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14322]) ).
thf(14411,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk315 @ sk1 @ k1_xboole_0 )
| ( sk315 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14378]) ).
thf(650,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(4491,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)],[650]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(4663,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)],[681]) ).
thf(622,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/sandbox2/benchmark/theBenchmark.p',t7_filter_2) ).
thf(4357,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)],[622]) ).
thf(726,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ( ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ D @ B )
= ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ E @ B ) )
=> ( ( k2_lattice2 @ A @ C @ B @ D )
= ( k2_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_lattice2) ).
thf(4885,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)],[726]) ).
thf(753,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(5014,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)],[753]) ).
thf(480,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k10_filter_0 @ A @ B ) )
<=> ( ( r1_tarski @ ( k3_relat_1 @ C ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C )
<=> ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_filter_0) ).
thf(3690,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)],[480]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_partfun1) ).
thf(1480,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(3196,plain,
( ! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
=> ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ~ ( ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) )
& ( A
!= ( k1_tarski @ C ) )
& ( A
!= ( k2_tarski @ B @ C ) ) )
=> ( r1_tarski @ A @ ( k2_tarski @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[3195]) ).
thf(3199,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( r1_tarski @ A @ ( k2_tarski @ B @ C ) ) ),
inference(cnf,[status(esa)],[3196]) ).
thf(3202,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( r1_tarski @ A @ ( k2_tarski @ B @ C ) ) ),
inference(lifteq,[status(thm)],[3199]) ).
thf(3203,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
inference(simp,[status(thm)],[3202]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(4455,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)],[642]) ).
thf(26584,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A
!= ( sk352 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1266,15065]) ).
thf(26585,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( sk352 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26584:[bind(A,$thf( sk352 @ C )),bind(B,$thf( C ))]]) ).
thf(28693,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( sk352 @ A ) ) ),
inference(simp,[status(thm)],[26585]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(4146,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(411,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
= ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_binop_1) ).
thf(3328,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)],[411]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ C )
<=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).
thf(1989,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)],[177]) ).
thf(64,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 ) )
=> ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_2) ).
thf(1314,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 ) )
=> ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(560,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_struct_0) ).
thf(4083,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(512,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice4) ).
thf(3850,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)],[512]) ).
thf(1171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ! [D: $i] : ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(miniscope,[status(thm)],[1170]) ).
thf(1172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( m1_relset_1 @ C @ A @ B )
| ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[1171]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice2) ).
thf(1197,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(1891,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)],[152]) ).
thf(1063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ A )
| ~ ( 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 )
| ~ ( m1_subset_1 @ D @ A )
| ( ( k1_binop_1 @ C @ B @ D )
= D ) ),
inference(cnf,[status(esa)],[1060]) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_binop_1 @ C @ B @ D )
= D )
| ~ ( m1_subset_1 @ B @ A )
| ~ ( 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 )
| ~ ( m1_subset_1 @ D @ A ) ),
inference(lifteq,[status(thm)],[1063]) ).
thf(11141,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,6875]) ).
thf(11204,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk315 != sk138 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11141]) ).
thf(5276,plain,
( ( f3_s11_funct_2 = f4_s11_funct_2 )
| ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ sk407 @ f4_s11_funct_2 )
= f6_s11_funct_2 ) ),
inference(cnf,[status(esa)],[5274]) ).
thf(5283,plain,
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ sk407 @ f4_s11_funct_2 )
= f6_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5276]) ).
thf(777,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/sandbox2/benchmark/theBenchmark.p',t67_lattice2) ).
thf(5110,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)],[777]) ).
thf(540,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_lattice4 @ C @ B @ A )
& ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ F ) ) )
=> ( r3_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice4) ).
thf(3982,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)],[540]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(3822,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)],[506]) ).
thf(285,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v10_lattices @ A )
<=> ( ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v8_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v9_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattices) ).
thf(2636,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v10_lattices @ A )
=> ( ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v8_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v9_lattices @ A ) ) )
& ( ( ( v4_lattices @ A )
& ( v5_lattices @ A )
& ( v8_lattices @ A )
& ( v6_lattices @ A )
& ( v7_lattices @ A )
& ( v9_lattices @ A ) )
=> ( v10_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(790,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_0) ).
thf(5159,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)],[790]) ).
thf(11127,plain,
( ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ sk315 @ f1_s4_funct_2 @ f2_s4_funct_2 )
!= ( m2_relset_1 @ sk216 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[4353,7948]) ).
thf(11199,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk216 @ sk1 @ k1_xboole_0 )
| ( sk315 != sk216 )
| ( sk1 != f1_s4_funct_2 )
| ( f2_s4_funct_2 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[11127]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(1657,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k7_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(3560,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)],[452]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(4895,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v6_lattices @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattices @ A @ B @ C )
= ( k1_lattices @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
thf(4281,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v4_lattices @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattices @ A @ B @ C )
= ( k1_lattices @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(587,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_domain_1) ).
thf(4210,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)],[587]) ).
thf(822,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/sandbox2/benchmark/theBenchmark.p',dt_k21_filter_2) ).
thf(5290,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)],[822]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(4631,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)],[675]) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',t17_lattice2) ).
thf(3804,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)],[503]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(4007,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)],[547]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k7_filter_0 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(5105,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)],[775]) ).
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 ) )
=> ( ( v14_lattices @ A )
=> ( ( k6_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_filter_0) ).
thf(5441,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)],[859]) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(2366,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)],[241]) ).
thf(5339,plain,
v13_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[5337]) ).
thf(409,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v17_lattices @ A )
& ( r4_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice4) ).
thf(3323,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)],[409]) ).
thf(354,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/sandbox2/benchmark/theBenchmark.p',d8_binop_1) ).
thf(3030,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)],[354]) ).
thf(844,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_filter_0) ).
thf(5378,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)],[844]) ).
thf(2795,plain,
v4_lattices @ sk188,
inference(cnf,[status(esa)],[2784]) ).
thf(803,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
thf(5215,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)],[803]) ).
thf(2340,plain,
v9_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[2335]) ).
thf(1165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_funct_1 @ C )
| ~ ( m2_relset_1 @ C @ A @ B )
| ~ ( v2_funct_1 @ C )
| ( v1_funct_1 @ ( k2_funct_1 @ C ) ) ),
inference(cnf,[status(esa)],[1163]) ).
thf(7610,plain,
! [B: $i,A: $i] :
( ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) )
| ( ( v1_relat_1 @ k1_xboole_0 )
!= ( v1_relat_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2975,1045]) ).
thf(7611,plain,
! [A: $i] : ( r1_tarski @ ( k9_relat_1 @ k1_xboole_0 @ A ) @ ( k9_relat_1 @ k1_xboole_0 @ ( k1_relat_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[7610:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(19105,plain,
r1_tarski @ k1_xboole_0 @ k1_xboole_0,
inference(rewrite,[status(thm)],[7611,2937]) ).
thf(2783,plain,
v8_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(830,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m3_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(5324,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)],[830]) ).
thf(419,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(3362,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)],[419]) ).
thf(2583,plain,
~ ( v3_struct_0 @ sk157 ),
inference(cnf,[status(esa)],[2578]) ).
thf(649,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( ( k3_filter_0 @ A @ B )
= ( k1_filter_0 @ A ) )
& ( ( k3_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_0) ).
thf(4484,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)],[649]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
<=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(3886,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
=> ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( r2_hidden @ A @ C )
& ( r2_hidden @ B @ C ) )
=> ( r1_tarski @ ( k2_tarski @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(1885,plain,
v2_funct_1 @ sk71,
inference(cnf,[status(esa)],[1883]) ).
thf(2241,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk110 @ B @ A ) ),
inference(cnf,[status(esa)],[2239]) ).
thf(878,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k9_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_0) ).
thf(5500,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)],[878]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(4129,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $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 )
| ~ ( m1_realset1 @ C @ A @ B )
| ( v1_funct_1 @ ( k1_realset1 @ B @ C ) ) ),
inference(cnf,[status(esa)],[1126]) ).
thf(25608,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( v10_lattices @ k1_xboole_0 )
| ( A != sk197 ) ),
inference(paramod_ordered,[status(thm)],[1266,2889]) ).
thf(25609,plain,
( ( v1_relat_1 @ ( sk19 @ sk197 ) )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25608:[bind(A,$thf( sk197 ))]]) ).
thf(14458,plain,
! [C: $i,B: $i,A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B )
| ( ( r1_tarski @ ( k1_relat_1 @ sk407 ) @ f1_s11_funct_2 )
!= ( r1_tarski @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13187,1074]) ).
thf(14459,plain,
! [A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ sk407 ) @ A ) @ f1_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[14458:[bind(A,$thf( k1_relat_1 @ sk407 )),bind(B,$thf( f1_s11_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14514,plain,
! [A: $i] :
( ( f4_s11_funct_2 = f3_s11_funct_2 )
| ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ sk407 ) @ A ) @ f1_s11_funct_2 ) ),
inference(simp,[status(thm)],[14459]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(3057,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)],[358]) ).
thf(701,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_0) ).
thf(4799,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)],[701]) ).
thf(2898,plain,
v8_lattices @ sk197,
inference(cnf,[status(esa)],[2887]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(2485,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)],[260]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(1582,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( ( v1_funct_1 @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(2265,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)],[223]) ).
thf(1019,plain,
~ ( r1_filter_2 @ ( u1_struct_0 @ sk1 ) @ ( k22_filter_2 @ sk1 @ sk2 @ sk2 ) @ ( k6_domain_1 @ ( u1_struct_0 @ sk1 ) @ sk2 ) ),
inference(cnf,[status(esa)],[1018]) ).
thf(998,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( D
= ( k4_filter_0 @ A @ B @ C ) )
<=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_0) ).
thf(5975,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)],[998]) ).
thf(536,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).
thf(3965,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)],[536]) ).
thf(926,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_filter_0) ).
thf(5681,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)],[926]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) )
<=> ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).
thf(5060,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ C ) ) )
=> ( ( ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) )
=> ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) ) )
& ( ? [F: $i,G: $i] :
( ( m1_subset_1 @ F @ B )
& ( m1_subset_1 @ G @ C )
& ( A
= ( k1_domain_1 @ B @ C @ F @ G ) )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ G @ E ) )
=> ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(995,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) )
= ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattices) ).
thf(5958,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)],[995]) ).
thf(945,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k18_filter_2 @ A @ B )
= ( k2_filter_2 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) ) )
& ( ( k18_filter_2 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k2_filter_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_2) ).
thf(5768,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k18_filter_2 @ A @ B )
= ( k2_filter_2 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) ) )
& ( ( k18_filter_2 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k2_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(953,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) )
= ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattices) ).
thf(5821,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)],[953]) ).
thf(4395,plain,
v5_lattices @ sk317,
inference(cnf,[status(esa)],[4383]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(1713,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(976,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_filter_0 @ A @ B )
= ( a_2_0_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_0) ).
thf(5891,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)],[976]) ).
thf(616,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
<=> ( v14_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).
thf(4330,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)],[616]) ).
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] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k18_filter_2 @ A @ C ) )
<=> ( r3_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_2) ).
thf(5468,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 @ ( k18_filter_2 @ A @ C ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ A @ B @ C )
=> ( r2_hidden @ B @ ( k18_filter_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(4271,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)],[602]) ).
thf(109,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(1621,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(4088,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(624,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/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(4363,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)],[624]) ).
thf(7388,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ sk71 ) ),
inference(paramod_ordered,[status(thm)],[1884,2940]) ).
thf(7392,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= sk71 ),
inference(simp,[status(thm)],[7388]) ).
thf(25008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
!= ( sk251 @ B ) )
| ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
!= ( k2_tarski @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1952,11718]) ).
thf(25009,plain,
! [B: $i,A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ B ) )
!= ( sk251 @ A ) ),
inference(pattern_uni,[status(thm)],[25008:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 )),bind(D,$thf( k1_tarski @ E ))]]) ).
thf(25026,plain,
! [B: $i,A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ B ) )
!= ( sk251 @ A ) ),
inference(simp,[status(thm)],[25009]) ).
thf(235,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(2321,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(10315,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( k2_relat_1 @ sk138 )
!= ( k2_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1098,8644]) ).
thf(10327,plain,
( ~ ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[10315]) ).
thf(12910,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( r1_tarski @ k1_xboole_0 @ A )
!= ( r1_tarski @ ( k1_relat_1 @ sk138 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1977,10327]) ).
thf(12917,plain,
! [A: $i] :
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[12910]) ).
thf(12927,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[12917]) ).
thf(12934,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= ( k1_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1099,12927]) ).
thf(12955,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[12934]) ).
thf(12965,plain,
( ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk138 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[12955]) ).
thf(2881,plain,
v13_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(916,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_2 @ ( k1_filter_2 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_2) ).
thf(5649,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)],[916]) ).
thf(6918,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A )
!= ( m2_relset_1 @ sk71 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1057,6691]) ).
thf(6941,plain,
! [B: $i,A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( B != sk71 )
| ( ( k1_relat_1 @ B )
!= sk1 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[6918]) ).
thf(6965,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ sk71 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(simp,[status(thm)],[6941]) ).
thf(7309,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[6965,1887]) ).
thf(7310,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk71 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk71 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk71 )
!= sk1 ) ),
inference(simp,[status(thm)],[7309]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(2832,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)],[313]) ).
thf(429,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/sandbox2/benchmark/theBenchmark.p',redefinition_k12_filter_2) ).
thf(3443,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)],[429]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
<=> ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(1468,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) )
=> ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) ) )
& ( ( ~ ( r2_hidden @ A @ C )
& ( ( r2_hidden @ B @ C )
| ( A = B ) ) )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(7557,plain,
! [A: $i] :
( ~ ( m2_relset_1 @ A @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ A @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( v1_funct_1 @ k1_xboole_0 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2968,6496]) ).
thf(7558,plain,
( ~ ( m2_relset_1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7557:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(7625,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( v10_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) )
!= ( m2_relset_1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1059,7558]) ).
thf(7647,plain,
! [B: $i,A: $i] :
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( B != k1_xboole_0 )
| ( A != sk1 )
| ( ( k2_relat_1 @ B )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7625]) ).
thf(7656,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ k1_xboole_0 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7647]) ).
thf(9546,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ k1_xboole_0 )
!= k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[7656,2975]) ).
thf(9547,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( ( k2_relat_1 @ k1_xboole_0 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[9546]) ).
thf(10296,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[9547,1098]) ).
thf(10297,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k1_relat_1 @ k1_xboole_0 ) @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[10296]) ).
thf(10574,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ k1_xboole_0 @ sk1 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[10297,1099]) ).
thf(11647,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[10574,1977]) ).
thf(11648,plain,
( ( v10_lattices @ k1_xboole_0 )
| ~ ( v1_partfun1 @ k1_xboole_0 @ sk1 @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[11647]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(2655,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)],[287]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(4335,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(795,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v6_group_1 @ A )
<=> ( v6_group_1 @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_lattice2) ).
thf(5172,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)],[795]) ).
thf(2879,plain,
v3_lattices @ sk196,
inference(cnf,[status(esa)],[2872]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( ( k2_tarski @ A @ B )
= ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(3461,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( ( k2_tarski @ A @ B )
= ( k1_tarski @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',t28_binop_1) ).
thf(1320,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)],[66]) ).
thf(902,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k4_lattice4 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(5591,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)],[902]) ).
thf(983,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_filter_0) ).
thf(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 ) )
=> ! [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)],[983]) ).
thf(6171,plain,
( ( v1_xboole_0 @ sk152 )
!= ( v1_xboole_0 @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[2510,1196]) ).
thf(6173,plain,
sk152 != sk14,
inference(simp,[status(thm)],[6171]) ).
thf(603,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_struct_0) ).
thf(4274,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m1_struct_0 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(195,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 ) )
& ( v3_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v4_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v5_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v6_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v7_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v8_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v9_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_filter_0) ).
thf(2074,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 ) )
& ( v3_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v4_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v5_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v6_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v7_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v8_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v9_lattices @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(26492,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk19 @ A ) )
| ( A
!= ( sk80 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1266,13612]) ).
thf(26493,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( sk80 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26492:[bind(A,$thf( sk80 @ C )),bind(B,$thf( C ))]]) ).
thf(28673,plain,
! [A: $i] : ( v1_relat_1 @ ( sk19 @ ( sk80 @ A ) ) ),
inference(simp,[status(thm)],[26493]) ).
thf(6980,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ sk71 ) ),
inference(paramod_ordered,[status(thm)],[1884,4936]) ).
thf(6984,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk71 ),
inference(simp,[status(thm)],[6980]) ).
thf(6925,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( l3_lattices @ k1_xboole_0 )
| ( ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A )
!= ( m2_relset_1 @ sk138 @ sk1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1057,6705]) ).
thf(6949,plain,
! [B: $i,A: $i] :
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ B )
| ~ ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( B != sk138 )
| ( ( k1_relat_1 @ B )
!= sk1 )
| ( A != k1_xboole_0 ) ),
inference(simp,[status(thm)],[6925]) ).
thf(6956,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( v1_relat_1 @ sk138 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(simp,[status(thm)],[6949]) ).
thf(7273,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ $true
| ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[6956,2405]) ).
thf(7274,plain,
( ( l3_lattices @ k1_xboole_0 )
| ~ ( r1_tarski @ ( k2_relat_1 @ sk138 ) @ k1_xboole_0 )
| ~ ( v1_partfun1 @ sk138 @ sk1 @ k1_xboole_0 )
| ( ( k1_relat_1 @ sk138 )
!= sk1 ) ),
inference(simp,[status(thm)],[7273]) ).
thf(7263,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k4_tarski @ A @ B ) )
!= ( v1_xboole_0 @ sk71 ) ),
inference(paramod_ordered,[status(thm)],[1884,2308]) ).
thf(7267,plain,
! [B: $i,A: $i] :
( ( k4_tarski @ A @ B )
!= sk71 ),
inference(simp,[status(thm)],[7263]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',t18_lattice2) ).
thf(3316,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)],[408]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(2834,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)],[314]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(4189,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)],[581]) ).
thf(2106,plain,
v6_lattices @ sk94,
inference(cnf,[status(esa)],[2098]) ).
thf(3933,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[3932]) ).
thf(982,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/sandbox2/benchmark/theBenchmark.p',fc1_filter_2) ).
thf(5911,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)],[982]) ).
thf(457,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/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(3575,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)],[457]) ).
thf(2771,plain,
v10_lattices @ sk187,
inference(cnf,[status(esa)],[2770]) ).
thf(35949,plain,
$false,
inference(e,[status(thm)],[2163,1665,5365,5561,4262,1105,3434,8283,1083,3927,5028,6014,1950,5686,2822,4201,8960,4094,1024,5918,5088,2744,2889,1190,2295,2306,4464,2341,2336,5593,1454,4909,2109,4824,5136,1633,2778,4729,4022,2876,20993,2921,4290,3477,1031,3863,2787,2544,5999,1179,6042,5733,2280,7549,1110,1211,14414,1068,1618,4391,5237,1305,1041,1200,5444,4714,1158,2309,7940,6177,2940,5141,2104,2644,4515,8082,5292,2908,3549,2776,1808,2590,1401,13159,2947,2248,1939,4697,5878,3098,5625,2014,3910,4960,3108,4711,4603,3012,1205,2099,2282,2114,5405,1142,7850,5265,4215,6031,5529,5348,11724,5383,4747,14409,1173,4532,18951,3217,13187,5361,12244,5589,1867,4279,2459,3121,1354,3794,1608,18878,4403,3745,26201,1137,5906,1310,3004,2035,4839,3367,4026,1735,1164,2316,3446,2448,2933,2434,2712,6851,12742,1640,2580,2901,3313,5178,5636,26301,2042,1222,3717,6046,3276,2575,1746,1835,2972,3502,4371,3513,1046,13751,3688,4386,4941,14292,1095,3335,1196,11171,25611,3350,5740,2723,1127,5486,2985,5935,2227,13179,1391,16720,1935,3947,2886,5903,1359,1601,3466,3809,4607,29076,2400,4963,2825,2136,4610,2531,4467,2405,1228,1482,4511,11720,5342,1887,5553,3263,5585,2039,21086,2708,2217,1323,1279,3248,4238,1055,1409,3195,4348,11203,1660,5883,2339,5284,2501,5274,11178,11200,5182,3845,3089,1832,2897,1992,4984,1462,1059,1132,5256,1147,11247,34172,25698,4265,2989,8278,5338,4119,12682,3998,2857,4353,5866,2403,3638,1087,4194,5127,4179,5604,2767,1347,5397,5622,5480,5925,1741,4830,4368,2520,4952,2730,28999,3951,13489,4383,1815,4390,5091,5020,3557,4400,5493,4302,2388,1100,5617,3788,4595,2456,2178,3431,21476,2880,2777,1183,3771,2950,4205,13771,4396,7268,8284,5663,10641,2794,5888,3934,5084,4578,2105,3393,5861,1373,2996,1911,2782,1040,2893,4297,5333,4820,3163,5856,3453,2236,5558,14408,2122,1828,11691,1978,2291,1020,5805,4871,3923,3300,5761,4686,2335,2017,5834,11168,2058,5773,5353,4033,5643,3712,25647,5897,3870,2508,5059,1169,5738,33881,14410,1886,7936,3505,3685,1072,3036,2523,1796,1119,11723,1394,5296,2772,5321,4307,8686,5169,2002,6021,2809,2799,2286,2103,2750,2965,5665,1104,1242,3606,3211,5824,3906,4475,2586,2982,2884,4082,4065,1651,5961,3582,3011,5157,5012,27617,8078,5017,5545,7410,21174,2790,1868,5298,1863,1074,25623,2204,3303,7393,4888,5839,3720,3984,7550,3531,3635,2364,5438,3186,2296,4576,5519,10639,2773,5281,5122,3418,4925,1057,1163,1091,2428,2541,4397,27196,11217,2890,5049,2589,2705,2409,18965,3261,5670,1343,3972,1021,3603,1580,6032,2277,4375,4434,1123,4878,5579,1570,4989,11719,5956,5815,2969,4091,4521,3069,3233,25812,2937,8081,3134,5754,4284,6496,2986,6178,4661,2528,4044,3286,6582,1883,14401,7842,4725,13612,1888,4327,5038,4979,2327,2741,2112,1573,3595,4063,3166,2445,5826,5391,2873,23776,1920,4585,8085,24377,7185,4994,3137,3499,3065,3556,3578,1178,2872,4385,7545,11174,3028,2345,1128,4104,2547,2344,4732,29237,3105,2157,2100,2801,3862,4429,2509,14413,5081,3916,1118,4898,3968,2245,28681,3782,5904,1234,1983,4957,5098,3122,2990,24566,1953,5673,5345,6691,2895,4248,2841,6028,8282,34008,1064,1111,5502,4636,15065,7838,2694,4845,3386,2631,2268,4219,5475,5951,1567,28314,25716,5075,1075,4513,23775,2108,4736,3573,2781,4333,3954,1329,1160,2877,1028,4518,1082,3326,5166,1964,1942,5694,3000,5651,2561,5107,1182,5620,4389,4421,3010,5464,4750,5253,5337,5786,11243,2240,5547,4744,5932,4861,4054,1207,6539,4867,7404,4444,5905,3555,4457,4384,3541,3059,3743,5683,4689,15934,4223,5245,4804,3242,2968,2285,1114,5850,3656,7948,3654,1099,7544,5149,6033,2836,4508,1266,2900,1231,5234,1974,25643,2243,5498,1192,1932,2581,1060,1050,4934,2006,5058,1799,3937,1852,2813,3115,5305,1429,2862,2482,2697,5801,8307,1720,4259,3920,3364,11725,4644,3563,4081,4212,8080,2883,5417,1895,6038,4572,2909,21074,10651,3824,5112,3903,4184,2788,25714,1563,5415,2057,3306,8279,3592,1054,6011,1170,1035,2368,1466,1071,2402,1187,25742,2408,2793,3190,5249,2662,1185,2338,5872,6524,1727,2176,2585,5451,1273,2941,5400,5241,3343,4921,15427,1251,5483,3130,5996,6053,4131,5722,11692,4470,1754,2292,11705,4872,13726,2556,4354,4393,3289,28372,3839,5095,5525,3111,2894,4365,5720,4268,1929,4122,5831,3900,5876,4381,5239,5503,1488,5535,4000,3187,3741,4662,2048,2859,2938,5474,1884,5488,1389,2791,3240,2789,3519,1125,2525,4159,2849,2981,4309,5923,1752,2514,2568,4975,4612,5752,4758,6705,4505,1669,25651,3646,1058,2753,5449,2166,4854,5735,1258,34365,2573,6048,26131,3223,1139,5185,26203,3773,2029,4186,5363,2293,5471,4796,2891,2308,4837,3077,5908,5595,3651,5859,4099,29153,5282,1865,2935,4822,5086,3340,12099,1332,3123,5784,1464,2474,2311,5071,4337,3996,3251,3155,4620,2774,2906,2257,5491,5610,2896,11718,4388,2510,11169,1194,7546,28379,25661,23779,2084,5244,3764,5103,2987,3551,1117,1349,5853,3270,1492,2955,2246,1722,4805,1144,13749,5407,1043,5093,2856,4176,5689,1122,5381,4477,4107,3456,5114,2343,5894,1821,14402,1838,2874,5885,2553,2911,2578,3219,5563,7768,3747,4541,13164,5994,2111,5175,1630,4818,5335,2780,33990,3572,3932,1909,1162,5286,4208,28216,7551,2785,2593,4850,3006,6044,2289,5180,1022,3861,2928,32869,1177,2974,8079,5410,8281,1061,32704,24556,1952,4232,2401,1213,11721,3806,1176,2592,6100,4954,5667,5403,2156,2984,3490,8280,3480,2770,2418,4832,5742,2962,2212,2171,5094,1044,2550,5218,1066,1528,11701,14412,25645,1643,8084,5646,4085,3674,4827,2288,1113,3016,4918,28354,2022,2101,4304,5326,5139,3908,4965,5424,4394,5881,7403,2784,3672,16442,2878,5812,1076,5661,10643,11161,3009,3522,23766,2054,4426,1948,1034,2239,5538,5587,1873,3193,1166,2107,1081,6056,3975,3048,11689,4688,2333,1145,5916,1018,4355,5763,3292,2899,5358,5133,1181,4986,5991,2582,6875,1049,5570,3640,5607,3214,13759,1531,2882,10653,4658,5446,1845,1798,2298,3737,1770,5294,5927,4360,2397,4864,3913,14101,3842,3112,4937,2977,1156,2060,1743,5478,2588,3754,4534,3659,4287,4754,4971,4377,8295,6596,2160,4593,1098,2888,4437,3642,4398,1432,1186,1038,3554,5948,4875,3080,2747,1053,1499,1987,6036,2454,1452,3114,3791,3722,4020,13089,11650,5555,1869,7149,2337,5030,1980,2128,1317,1763,4351,1901,6174,3828,4132,1085,5152,4241,2903,8644,4982,3412,3359,2044,1130,4117,1738,3041,2056,3488,5675,5613,1485,2579,4431,4695,4225,3071,2892,2584,5841,4392,19046,5902,4057,1898,1849,2838,2558,3415,3124,4133,1802,1023,1221,2975,1353,5504,5809,4046,4538,4235,1585,2511,5226,1094,1140,1240,8299,6850,2885,1412,2209,16925,2792,2865,2875,4639,3284,1421,16998,14403,4289,1918,4424,1084,23774,4606,3565,3401,4727,7024,3589,5749,6985,3092,3067,1180,1157,4944,2310,14037,7547,1126,4078,3725,5308,8285,3346,2110,2342,1866,3929,2775,1108,3665,4574,13549,3729,1253,4806,2098,5351,3991,6023,5228,3662,2394,1276,2591,5055,2988,1385,5272,2290,1903,5008,2406,12743,4683,5394,5010,2764,4834,3516,4823,8083,5505,2786,5532,7451,5692,6018,4387,5699,3993,26199,5196,5194,2009,4182,5828,1030,5963,4197,4649,2796,5164,5162,8997,3267,4299,5837,3149,13761,1308,3896,1077,5549,5568,2230,1893,2294,4869,3761,2779,2019,11208,1045,5864,5287,1161,25019,5852,2287,11690,2155,2983,5268,3892,21566,13753,11722,5078,4843,4597,4367,1116,11167,26385,1133,2102,5677,2517,4794,1578,5129,4399,4687,4706,3860,3785,3733,4811,2587,5954,5232,3464,1380,2815,4787,3790,5522,3337,1148,5477,14411,4491,4663,4357,4885,5014,3690,1480,3203,4455,28693,4146,3328,1989,1314,4083,3850,1172,1197,1891,1065,11204,5283,5110,3982,3822,2636,5159,11199,1657,3560,4895,4281,4210,5290,4631,3804,4007,5105,1056,5441,2366,5339,2404,3323,3030,5378,2795,5215,2340,1165,19105,2783,5324,1093,3362,2583,4484,3886,3113,1885,1120,2241,5500,4129,1977,1129,25609,14514,3057,4799,2898,2485,1582,2265,1019,1976,5975,3965,5681,5060,5958,3392,5768,5821,4936,4395,1713,5891,4330,5468,4271,1621,4088,4363,5473,7392,25026,2321,12965,2881,5649,7310,2832,6857,3443,1468,1069,11648,2655,4335,5172,7548,2879,3461,1320,5591,5913,6173,4274,2887,2074,28673,5788,6984,7274,7267,3316,2834,4189,1088,2106,3933,5911,2980,3575,13107,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT328+2 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.13 % Command : run_Leo-III %s %d
% 0.13/0.32 % Computer : n007.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Thu May 18 14:10:09 EDT 2023
% 0.13/0.32 % CPUTime :
% 0.89/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.30/1.27 % [INFO] Parsing done (448ms).
% 2.63/1.28 % [INFO] Running in sequential loop mode.
% 2.98/1.50 % [INFO] eprover registered as external prover.
% 2.98/1.51 % [INFO] cvc4 registered as external prover.
% 2.98/1.51 % [INFO] Scanning for conjecture ...
% 4.05/1.74 % [INFO] Found a conjecture and 3000 axioms. Running axiom selection ...
% 5.50/2.27 % [INFO] Axiom selection finished. Selected 1015 axioms (removed 1985 axioms).
% 7.26/2.84 % [INFO] Problem is first-order (TPTP FOF).
% 7.26/2.88 % [INFO] Type checking passed.
% 7.26/2.88 % [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 ...
% 139.87/28.79 % External prover 'e' found a proof!
% 139.87/28.79 % [INFO] Killing All external provers ...
% 139.87/28.79 % Time passed: 28335ms (effective reasoning time: 27507ms)
% 139.87/28.79 % 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)>
% 139.87/28.80 % Axioms used in derivation (1015): t31_lattice2, d14_filter_2, t7_filter_0, dt_k4_filter_2, t1_filter_2, t45_lattice4, t2_filter_0, t21_zfmisc_1, t11_filter_2, t13_relset_1, dt_k7_filter_0, rc1_lattice2, d1_lattices, t119_funct_2, t158_relat_1, t17_lattice4, dt_k9_filter_2, t50_lattice4, redefinition_m2_relset_1, fraenkel_a_1_0_domain_1, t51_partfun1, t24_filter_0, t10_lattice2, d13_filter_0, t38_filter_2, fraenkel_a_3_2_domain_1, cc5_lattice2, t31_filter_0, t37_lattice2, t78_filter_0, t43_lattice2, dt_m1_lattice4, fc1_zfmisc_1, t35_subset_1, t135_zfmisc_1, t25_relset_1, t30_relat_1, d4_funct_1, t20_lattice4, t39_lattices, t76_lattice2, d10_lattices, t20_zfmisc_1, d1_tarski, dt_k2_lattice2, d20_binop_1, t66_funct_2, t62_filter_0, t66_partfun1, dt_k1_filter_2, t80_filter_0, t53_subset_1, t44_filter_2, d6_filter_0, d5_relat_1, t109_xboole_1, redefinition_k16_filter_2, t25_lattice2, d10_binop_1, t10_filter_2, t36_lattice4, t19_filter_2, t34_filter_2, t29_filter_0, fc2_filter_0, t81_filter_0, t24_lattice4, d13_lattices, cc3_lattice2, d14_binop_1, dt_k9_domain_1, d6_lattice2, t7_subset_1, t30_lattice2, t32_funct_2, d11_binop_1, t2_realset1, t3_xboole_1, d4_lattice4, t3_realset1, d3_subset_1, fc1_xboole_0, rc12_lattices, dt_k7_domain_1, t34_xboole_1, t29_lattice2, t59_filter_2, d1_lattice2, t56_partfun1, t63_filter_2, t59_partfun1, s12_funct_2, t43_lattices, s3_funct_2, t28_filter_2, t42_filter_0, cc6_lattices, t57_lattice2, t33_lattice2, t16_funct_2, d16_lattices, t113_zfmisc_1, t67_lattice2, t7_lattice2, t48_domain_1, t111_zfmisc_1, dt_k2_subset_1, t8_subset_1, t80_lattice2, t9_filter_2, existence_l1_lattices, t32_lattice4, d5_tarski, t15_funct_1, dt_k11_domain_1, t26_lattices, fc4_relat_1, t19_lattices, t4_ordinal1, t1_subset, dt_k1_lattice4, t147_relat_1, t10_partfun1, t47_lattice2, d5_xboole_0, t4_lattice4, t9_lattice2, fc4_subset_1, t12_filter_2, t168_funct_2, t10_relset_1, dt_k15_filter_2, fc3_relat_1, d8_funct_1, t69_filter_0, t57_filter_2, t144_relat_1, t57_domain_1, existence_l3_lattices, dt_k6_nat_lat, t39_filter_2, t53_lattices, dt_k3_funct_2, dt_k5_lattices, t7_funct_2, t87_filter_0, fc4_lattice2, t42_zfmisc_1, t21_lattice2, t14_binop_1, dt_k1_subset_1, t19_relat_1, dt_k16_filter_2, t28_binop_1, dt_k13_domain_1, fc1_lattice2, dt_g2_struct_0, t72_lattice2, t117_zfmisc_1, t32_relat_1, dt_k4_subset_1, t83_filter_0, t35_lattice4, t55_filter_2, t23_filter_0, redefinition_k12_filter_2, t16_lattice4, abstractness_v2_struct_0, t46_lattice4, dt_m2_nat_lat, d7_binop_1, existence_m3_lattice4, existence_m1_struct_0, dt_k3_lattice4, t35_zfmisc_1, t18_filter_0, rc2_struct_0, dt_k1_lattice2, t65_partfun1, t44_funct_2, fraenkel_a_2_0_lattice4, t117_funct_1, d10_filter_0, cc4_lattice2, dt_k1_struct_0, t26_lattice4, cc2_lattice2, t85_filter_0, dt_m1_realset1, t110_zfmisc_1, t103_zfmisc_1, dt_k19_filter_2, dt_u2_struct_0, t63_partfun1, t15_relset_1, t14_filter_0, fraenkel_a_2_0_filter_0, rc2_partfun1, t18_relat_1, fc1_filter_0, t48_filter_0, d9_lattice4, t49_funct_2, t41_lattice2, t64_filter_2, t50_funct_2, t70_zfmisc_1, t69_zfmisc_1, cc4_lattices, redefinition_k11_filter_0, fc2_filter_2, rc3_funct_1, fraenkel_a_3_3_domain_1, l70_filter_2, dt_k5_filter_0, dt_k3_filter_0, d1_struct_0, t27_zfmisc_1, t37_xboole_1, t41_zfmisc_1, fc2_lattice2, dt_m2_relset_1, cc1_relat_1, dt_k7_funct_2, dt_k5_filter_2, t59_lattice2, t70_partfun1, fc3_lattice2, t26_filter_0, t56_relat_1, t83_lattice2, t17_funct_1, t21_filter_2, t43_filter_2, redefinition_k2_funct_2, t2_funct_1, t36_subset_1, t29_partfun1, t33_lattice4, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, t32_filter_0, commutativity_k7_domain_1, t46_lattice2, fraenkel_a_2_0_domain_1, d2_tarski, dt_k2_binop_1, involutiveness_k3_subset_1, rc1_funct_1, t53_filter_0, d5_lattices, t17_binop_1, t25_funct_2, t31_relat_1, t15_binop_1, dt_m2_realset1, redefinition_k13_filter_2, redefinition_k6_filter_0, dt_k1_filter_0, dt_k6_filter_2, t115_zfmisc_1, t66_lattice2, t62_funct_1, t65_funct_2, t19_funct_1, dt_m2_lattice4, t41_filter_2, d11_filter_0, t26_filter_2, t31_lattices, s13_funct_2, fraenkel_a_2_2_domain_1, t129_zfmisc_1, d4_subset_1, t2_binop_1, d6_binop_1, dt_m1_filter_2, t27_lattices, t64_funct_2, reflexivity_r3_lattices, t20_filter_2, d1_xboole_0, d9_lattices, t56_filter_0, fraenkel_a_3_0_filter_0, t130_zfmisc_1, t3_filter_2, t175_partfun1, t15_relat_1, t48_funct_2, fraenkel_a_3_7_domain_1, d16_lattice4, t70_filter_0, t72_filter_0, t48_filter_2, t46_filter_0, t40_lattice2, t64_relat_1, t138_zfmisc_1, t25_subset_1, t37_filter_0, rc11_lattices, rc3_lattices, t52_filter_0, t108_zfmisc_1, t165_funct_2, t57_filter_0, dt_l1_lattices, dt_k12_filter_2, dt_k4_lattice4, t45_filter_2, t60_partfun1, existence_m1_realset1, dt_k11_filter_2, t31_partfun1, dt_k7_lattices, t3_funct_2, rc2_subset_1, existence_l2_lattices, l59_filter_2, t27_relset_1, t52_domain_1, t118_zfmisc_1, t55_partfun1, s4_subset_1, t8_funct_2, t118_funct_2, t29_lattice4, t76_nat_lat, t14_relset_1, t39_lattice4, t16_relset_1, t38_lattice4, d13_relat_1, t28_lattice2, t164_funct_2, d15_lattice4, fc2_funct_2, t6_boole, t12_funct_1, dt_k6_subset_1, t10_relat_1, d1_relat_1, t59_filter_0, t1_xboole_1, t26_relset_1, t64_partfun1, t47_lattice4, d5_filter_2, existence_l2_struct_0, t32_lattices, t19_filter_0, t44_lattice4, t49_filter_0, t5_subset, t17_filter_2, redefinition_k12_filter_0, t29_relat_1, d14_lattice4, cc6_lattice2, t50_filter_2, t77_funct_2, t59_domain_1, t34_filter_0, d4_filter_2, t5_lattice4, t54_filter_2, t22_lattices, t32_partfun1, d6_tarski, t4_relat_1, t26_binop_1, t28_subset_1, d12_lattices, d17_lattice4, fc3_subset_1, t128_zfmisc_1, t39_partfun1, t75_zfmisc_1, redefinition_k4_filter_2, t8_lattice4, rc1_filter_0, d2_realset1, t51_filter_2, fc2_subset_1, t45_funct_2, d9_filter_2, t25_zfmisc_1, d4_relat_1, d7_lattices, t6_lattice2, t23_binop_1, t150_relat_1, existence_m1_relset_1, t1_zfmisc_1, dt_m2_filter_2, t47_filter_2, t50_lattices, fc4_filter_2, s8_domain_1, dt_l3_lattices, t48_lattice2, t30_filter_2, d16_nat_lat, t79_zfmisc_1, t12_lattice2, t5_funct_2, dt_k8_funct_2, d12_lattice4, t16_filter_2, t167_funct_2, dt_m1_struct_0, t17_lattices, t11_funct_2, t40_funct_2, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t24_binop_1, t27_lattice4, t75_lattice2, t4_filter_0, t89_filter_0, dt_l2_lattices, redefinition_k7_domain_1, t40_filter_0, d3_filter_2, d12_filter_2, t72_partfun1, t8_funct_1, t2_tarski, t16_funct_1, t28_zfmisc_1, t72_zfmisc_1, t82_funct_2, dt_k4_filter_0, t33_xboole_1, s9_domain_1, t84_lattice2, t47_lattices, d7_filter_2, d20_lattices, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t38_filter_0, d3_lattices, t23_zfmisc_1, t34_lattice4, cc5_lattices, t4_subset, t38_subset_1, d18_lattices, t169_funct_2, t44_lattices, dt_k2_funct_1, cc1_funct_2, t39_subset_1, d8_filter_0, t56_lattice2, t52_subset_1, t60_filter_0, t5_ordinal1, rc13_lattices, t4_boole, t71_lattice2, d2_funct_2, t22_lattice2, t8_filter_2, t70_lattice2, dt_k8_domain_1, dt_k17_filter_2, fc3_filter_2, t15_lattice4, t74_zfmisc_1, t32_xboole_1, t61_filter_2, dt_k8_filter_0, t14_funct_1, t5_filter_2, t9_zfmisc_1, d7_filter_0, existence_m2_realset1, existence_m3_realset1, t56_subset_1, dt_k1_domain_1, t17_funct_2, t85_lattice2, redefinition_k14_filter_2, t75_filter_0, t13_lattice2, fc1_realset1, t25_filter_2, t132_funct_2, t45_lattices, t49_lattice4, t51_funct_2, d12_binop_1, t21_lattices, t12_zfmisc_1, d2_lattice4, t38_lattice2, t139_zfmisc_1, t16_lattice2, cc1_funct_1, t4_funct_2, redefinition_k1_filter_2, d10_lattice4, s11_funct_2, d3_relat_2, s2_domain_1, rc3_struct_0, t3_ordinal1, t9_domain_1, d6_filter_2, t25_lattices, t7_boole, dt_k14_filter_2, dt_k5_lattice4, t11_binop_1, t55_filter_0, t143_relat_1, d2_subset_1, t27_lattice2, commutativity_k4_lattices, redefinition_k9_filter_2, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, rc2_lattice2, commutativity_k2_struct_0, t7_filter_2, t23_filter_2, dt_k6_domain_1, t157_funct_1, t31_lattice4, fc5_lattice2, d17_lattices, dt_k2_partfun1, rc2_funct_1, t158_funct_2, dt_k9_filter_0, t90_filter_0, redefinition_k15_filter_2, t4_subset_1, redefinition_k1_domain_1, rc1_funct_2, l48_filter_2, t26_zfmisc_1, t6_filter_2, t69_partfun1, t7_ordinal1, dt_k10_filter_2, t9_funct_2, t31_funct_2, rc1_subset_1, t48_lattice4, t68_filter_0, fc6_lattice2, t8_lattice2, t18_lattices, cc1_lattices, t5_filter_0, t64_zfmisc_1, fc5_relat_1, dt_k3_lattice2, t30_filter_0, t40_lattice4, t13_filter_2, redefinition_r3_lattices, t40_lattices, t4_filter_2, t113_funct_2, t71_partfun1, d21_lattices, t41_lattices, t159_funct_2, t116_zfmisc_1, d4_lattices, existence_m1_filter_0, t2_lattice2, redefinition_m1_filter_2, dt_k2_struct_0, t49_lattices, t14_funct_2, t27_binop_1, t48_lattices, dt_k2_lattice4, t9_filter_0, t65_funct_1, t40_filter_2, fc1_nat_lat, fraenkel_a_3_1_domain_1, t60_funct_2, t7_lattice4, t36_filter_2, cc2_funct_1, t5_realset1, s4_funct_2, t41_lattice4, rc9_lattices, dt_k7_filter_2, d2_zfmisc_1, cc1_filter_0, t169_partfun1, fraenkel_a_2_1_lattice4, t26_lattice2, dt_k24_filter_2, t17_lattice2, t18_funct_1, d3_lattice2, t4_relset_1, t10_filter_0, t31_subset_1, t3_subset, cc1_relset_1, fc1_filter_2, t25_binop_1, d2_binop_1, d6_lattice4, t30_lattice4, s1_domain_1, t12_filter_0, t124_funct_1, t50_lattice2, t55_subset_1, t79_funct_2, dt_u1_lattices, fraenkel_a_2_1_domain_1, d13_filter_2, existence_m1_subset_1, t22_lattice4, existence_m1_filter_2, commutativity_k2_tarski, t3_relat_1, t22_filter_0, t24_relat_1, t8_relset_1, t106_zfmisc_1, t125_zfmisc_1, t73_filter_0, t11_relset_1, t155_relat_1, t27_filter_2, t15_subset_1, t44_filter_0, t118_funct_1, d9_binop_1, t19_lattice2, t146_relat_1, t35_xboole_1, t49_domain_1, d17_binop_1, dt_k2_filter_0, dt_k2_funct_2, d2_filter_0, rc1_nat_lat, t5_lattice2, free_g2_struct_0, dt_k20_filter_2, t17_relset_1, cc3_lattices, d5_subset_1, t99_partfun1, t107_zfmisc_1, t9_realset1, t121_funct_2, t114_zfmisc_1, dt_k23_filter_2, t58_partfun1, d1_zfmisc_1, t27_filter_0, t15_filter_2, t11_lattice4, rc2_relat_1, t36_lattice2, existence_m2_relset_1, d4_binop_1, t64_filter_0, t38_zfmisc_1, t75_nat_lat, t9_lattice4, t69_enumset1, t82_lattice2, t22_zfmisc_1, t14_filter_2, d1_filter_0, redefinition_k7_filter_0, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, t62_lattice2, t39_filter_0, t74_lattice2, t11_filter_0, t29_filter_2, existence_m2_lattice4, t23_lattice4, d4_lattice2, t116_funct_2, fraenkel_a_3_6_domain_1, t168_partfun1, s14_funct_2, t51_filter_0, t14_lattice4, t37_lattice4, redefinition_k2_binop_1, t74_filter_0, t60_nat_lat, t61_lattice2, t6_funct_2, redefinition_k24_filter_2, t32_filter_2, t58_filter_2, t44_lattice2, t41_subset_1, fc3_nat_lat, d3_lattice4, t157_relat_1, cc3_finsub_1, t56_filter_2, t65_lattice2, t42_filter_2, t51_subset_1, t21_subset_1, existence_m1_lattice4, d5_filter_0, d10_filter_2, t36_zfmisc_1, d4_filter_0, reflexivity_r1_filter_2, t45_lattice2, t8_realset1, dt_m3_lattice4, d3_tarski, cc6_funct_2, redefinition_k1_struct_0, t25_lattice4, d8_realset1, rc1_relat_1, t54_funct_1, t24_filter_2, t40_subset_1, t17_subset_1, t6_relset_1, d1_relset_1, redefinition_k11_filter_2, fc1_struct_0, t52_lattice2, t18_binop_1, redefinition_k3_lattices, t78_lattice2, t37_filter_2, fraenkel_a_3_1_filter_0, t39_zfmisc_1, d1_realset1, d15_lattices, t131_funct_2, dt_k22_filter_2, t119_zfmisc_1, dt_k4_lattices, t60_relat_1, rc1_lattice4, t77_lattice2, fraenkel_a_3_4_domain_1, t24_lattice2, t19_lattice4, reflexivity_r1_tarski, t9_funct_1, t6_zfmisc_1, t18_funct_2, dt_l2_struct_0, t52_lattices, t1_realset1, t2_xboole_1, t35_lattice2, t57_partfun1, t9_mcart_1, t34_funct_2, t67_filter_0, t52_filter_2, symmetry_r1_filter_2, t27_finsub_1, redefinition_m1_struct_0, t18_filter_2, t10_subset_1, t41_filter_0, existence_m2_nat_lat, d12_funct_1, d2_lattices, t9_relset_1, dt_g3_lattices, fc6_relat_1, d15_binop_1, rc6_lattices, free_g3_lattices, t77_filter_0, cc7_lattices, d14_lattices, dt_k10_filter_0, t54_lattice2, t21_lattice4, t36_xboole_1, dt_k8_subset_1, dt_k3_filter_2, t58_filter_0, redefinition_k2_filter_2, d4_xboole_0, t47_filter_0, t39_lattice2, d7_lattice4, d8_filter_2, t20_relat_1, dt_k1_lattices, t73_zfmisc_1, t69_lattice2, dt_k12_domain_1, t53_filter_2, t18_lattice4, d5_binop_1, t54_subset_1, t123_funct_1, t29_lattices, t88_filter_0, d1_relat_2, t82_filter_0, t33_filter_2, redefinition_k2_struct_0, t54_filter_0, t15_filter_0, dt_k2_filter_2, t68_zfmisc_1, t12_funct_2, d16_binop_1, t20_filter_0, t28_finsub_1, t32_lattice2, d8_binop_1, abstractness_v3_lattices, t26_finsub_1, t51_lattice2, t136_zfmisc_1, t8_boole, rc1_xboole_0, t24_partfun1, redefinition_k8_funct_2, t35_filter_2, t34_zfmisc_1, t80_zfmisc_1, t5_relat_1, t24_zfmisc_1, t55_lattice2, t120_funct_2, t59_funct_2, fc7_relat_1, t60_funct_1, t46_filter_2, t23_finsub_1, t30_finsub_1, dt_k21_filter_2, t134_zfmisc_1, fc8_relat_1, t10_realset1, dt_k3_binop_1, rc5_struct_0, t23_relat_1, t10_zfmisc_1, t2_subset, redefinition_k21_filter_2, d9_filter_0, t38_funct_2, t33_partfun1, t34_finsub_1, d3_relat_1, t85_funct_2, t37_zfmisc_1, t49_filter_2, t65_relat_1, t21_relat_1, dt_k6_filter_0, t156_relat_1, t109_zfmisc_1, fraenkel_a_2_3_domain_1, t60_domain_1, t152_relat_1, dt_k6_lattices, t25_partfun1, dt_m1_filter_0, d18_binop_1, redefinition_k10_filter_2, t115_funct_2, d6_lattices, t9_tarski, t51_lattices, commutativity_k3_lattices, t149_relat_1, fc2_realset1, d13_lattice4, t32_finsub_1, t48_subset_1, d1_lattice4, d8_lattices, t28_relat_1, d1_funct_1, d1_filter_2, t81_lattice2, t34_lattices, d12_filter_0, t42_lattice4, t50_subset_1, t65_filter_0, d10_xboole_0, d2_lattice2, d11_filter_2, t34_lattice2, dt_k2_lattices, d19_lattices, t67_partfun1, t3_boole, fc1_lattice4, dt_u2_lattices, d8_relat_2, t25_relat_1, dt_k8_filter_2, t13_binop_1, t53_lattice2, existence_l1_struct_0, t45_filter_0, t49_subset_1, t7_tarski, rc1_partfun1, t71_filter_0, redefinition_r1_filter_2, t28_lattice4, t79_lattice2, d5_funct_1, t6_ordinal1, dt_k18_filter_2, redefinition_k6_subset_1, rc10_lattices, t12_relset_1, cc1_lattice2, cc5_funct_2, t60_lattice2, t50_filter_0, t43_lattice4, t58_lattice2, t22_filter_2, d3_filter_0, d1_binop_1, rc2_xboole_0, fraenkel_a_3_5_domain_1, s7_domain_1, t62_filter_2, dt_m3_realset1, dt_k13_nat_lat, t30_zfmisc_1, rc4_struct_0, dt_k10_domain_1, t49_lattice2, fraenkel_a_0_1_domain_1, t66_filter_0, t16_binop_1, t31_filter_2, t6_filter_0, redefinition_k3_filter_2, d13_binop_1, idempotence_k4_subset_1, t40_zfmisc_1, d11_lattices, t63_filter_0, t63_lattice2, t174_partfun1, t55_funct_2, t18_lattice2, t112_zfmisc_1, t73_lattice2, existence_m2_filter_2, d3_binop_1, t60_filter_2, t6_lattice4, t14_lattice2, dt_k13_filter_2, t13_filter_0, d2_relat_1, dt_k3_lattices, t68_lattice2, d19_binop_1, cc2_lattices, redefinition_k4_lattices, t61_funct_2, fc3_lattices, dt_k3_subset_1, fraenkel_a_0_2_domain_1, fc1_funct_2, cc1_binop_1, t6_relat_1, t172_partfun1, t33_subset_1, t30_partfun1, t65_zfmisc_1, t63_subset_1, t112_partfun1, t38_xboole_1, fraenkel_a_4_1_domain_1, t23_lattices, t3_filter_0, t10_lattice4, antisymmetry_r2_hidden, d5_lattice4, d8_lattice4, t64_lattice2, t22_subset_1, redefinition_k6_domain_1
% 139.87/28.80 % No. of inferences in proof: 3009
% 139.87/28.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 28335 ms resp. 27507 ms w/o parsing
% 141.70/29.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 141.70/29.48 % [INFO] Killing All external provers ...
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