%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT292+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:47:01 AM UTC 2026
% Result : Theorem 117.60s 33.15s
% Output : Refutation 124.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1401
% Syntax : Number of formulae : 3460 ( 504 unt; 0 typ; 30 def)
% Number of atoms : 18063 (2619 equ; 0 cnn)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 62154 (3229 ~; 956 |;6769 &;44740 @)
% ( 227 <=>;6233 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 250 ( 247 usr; 32 con; 0-6 aty)
% Number of variables : 8332 ( 5 ^;7969 !; 328 ?;8332 :)
% ( 0 !>; 0 ?*; 0 @-; 30 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_decl,type,
v10_lattices: $i > $o ).
thf(v17_lattices_decl,type,
v17_lattices: $i > $o ).
thf(v3_realset2_decl,type,
v3_realset2: $i > $o ).
thf(l3_lattices_decl,type,
l3_lattices: $i > $o ).
thf(v2_pre_topc_decl,type,
v2_pre_topc: $i > $o ).
thf(l1_pre_topc_decl,type,
l1_pre_topc: $i > $o ).
thf(r1_filter_1_decl,type,
r1_filter_1: $i > $i > $o ).
thf(k6_lopclset_decl,type,
k6_lopclset: $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(k5_finsub_1_decl,type,
k5_finsub_1: $i > $i ).
thf(k2_lattice2_decl,type,
k2_lattice2: $i > $i > $i > $i > $i ).
thf(k5_setwiseo_decl,type,
k5_setwiseo: $i > $i > $i > $i ).
thf(k2_setwiseo_decl,type,
k2_setwiseo: $i > $i > $i ).
thf(k5_lattice4_decl,type,
k5_lattice4: $i > $i ).
thf(k3_lattices_decl,type,
k3_lattices: $i > $i > $i > $i ).
thf(k7_lattices_decl,type,
k7_lattices: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k3_lattice2_decl,type,
k3_lattice2: $i > $i > $i > $i > $i ).
thf(k4_lattices_decl,type,
k4_lattices: $i > $i > $i > $i ).
thf(k2_lattice4_decl,type,
k2_lattice4: $i > $i > $i ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k10_setwiseo_decl,type,
k10_setwiseo: $i > $i > $i > $i > $i ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(v13_lattices_decl,type,
v13_lattices: $i > $o ).
thf(k1_lattice4_decl,type,
k1_lattice4: $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(v14_lattices_decl,type,
v14_lattices: $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(k5_subset_1_decl,type,
k5_subset_1: $i > $i > $i > $i ).
thf(k4_subset_1_decl,type,
k4_subset_1: $i > $i > $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v3_pre_topc_decl,type,
v3_pre_topc: $i > $i > $o ).
thf(v4_pre_topc_decl,type,
v4_pre_topc: $i > $i > $o ).
thf(m2_connsp_2_decl,type,
m2_connsp_2: $i > $i > $i > $o ).
thf(m1_connsp_2_decl,type,
m1_connsp_2: $i > $i > $i > $o ).
thf(k10_borsuk_1_decl,type,
k10_borsuk_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_borsuk_1_decl,type,
k6_borsuk_1: $i > $i > $i ).
thf(k7_borsuk_1_decl,type,
k7_borsuk_1: $i > $i > $i > $i > $i ).
thf(k1_struct_0_decl,type,
k1_struct_0: $i > $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k2_binop_1_decl,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(l2_lattices_decl,type,
l2_lattices: $i > $o ).
thf(r1_lattices_decl,type,
r1_lattices: $i > $i > $i > $o ).
thf(k1_lattices_decl,type,
k1_lattices: $i > $i > $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(m2_subset_1_decl,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k1_lopclset_decl,type,
k1_lopclset: $i > $i ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(k2_pre_topc_decl,type,
k2_pre_topc: $i > $i ).
thf(k3_relat_1_decl,type,
k3_relat_1: $i > $i ).
thf(k6_setfam_1_decl,type,
k6_setfam_1: $i > $i > $i ).
thf(k7_subset_1_decl,type,
k7_subset_1: $i > $i > $i > $i ).
thf(v3_tops_1_decl,type,
v3_tops_1: $i > $i > $o ).
thf(v1_tops_1_decl,type,
v1_tops_1: $i > $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(k3_funct_3_decl,type,
k3_funct_3: $i > $i ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(k10_relat_1_decl,type,
k10_relat_1: $i > $i > $i ).
thf(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(v3_lattices_decl,type,
v3_lattices: $i > $o ).
thf(k8_setfam_1_decl,type,
k8_setfam_1: $i > $i > $i ).
thf(m1_filter_1_decl,type,
m1_filter_1: $i > $i > $i > $o ).
thf(v1_borsuk_1_decl,type,
v1_borsuk_1: $i > $i > $o ).
thf(m1_pre_topc_decl,type,
m1_pre_topc: $i > $i > $o ).
thf(v2_borsuk_1_decl,type,
v2_borsuk_1: $i > $i > $o ).
thf(m1_borsuk_1_decl,type,
m1_borsuk_1: $i > $i > $o ).
thf(v1_pre_topc_decl,type,
v1_pre_topc: $i > $o ).
thf(k21_borsuk_1_decl,type,
k21_borsuk_1: $i > $i > $i > $i ).
thf(k16_borsuk_1_decl,type,
k16_borsuk_1: $i > $i > $i ).
thf(k20_borsuk_1_decl,type,
k20_borsuk_1: $i > $i > $i > $i ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(k1_tops_1_decl,type,
k1_tops_1: $i > $i > $i ).
thf(k2_lopclset_decl,type,
k2_lopclset: $i > $i > $i > $i ).
thf(k1_lattice2_decl,type,
k1_lattice2: $i > $i ).
thf(v2_tops_1_decl,type,
v2_tops_1: $i > $i > $o ).
thf(k2_tops_1_decl,type,
k2_tops_1: $i > $i > $i ).
thf(v5_tops_1_decl,type,
v5_tops_1: $i > $i > $o ).
thf(m1_eqrel_1_decl,type,
m1_eqrel_1: $i > $i > $o ).
thf(k17_borsuk_1_decl,type,
k17_borsuk_1: $i > $i > $i ).
thf(v5_pre_topc_decl,type,
v5_pre_topc: $i > $i > $i > $o ).
thf(k1_funct_3_decl,type,
k1_funct_3: $i > $i ).
thf(k6_pre_topc_decl,type,
k6_pre_topc: $i > $i > $i ).
thf(k2_borsuk_1_decl,type,
k2_borsuk_1: $i > $i > $i ).
thf(k3_borsuk_1_decl,type,
k3_borsuk_1: $i > $i > $i > $i ).
thf(v4_tops_1_decl,type,
v4_tops_1: $i > $i > $o ).
thf(r2_borsuk_1_decl,type,
r2_borsuk_1: $i > $i > $o ).
thf(k1_pre_topc_decl,type,
k1_pre_topc: $i > $i ).
thf(k1_subset_1_decl,type,
k1_subset_1: $i > $i ).
thf(v3_filter_0_decl,type,
v3_filter_0: $i > $o ).
thf(k2_lattices_decl,type,
k2_lattices: $i > $i > $i > $i ).
thf(k5_setfam_1_decl,type,
k5_setfam_1: $i > $i > $i ).
thf(k12_mcart_1_decl,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(r3_lattices_decl,type,
r3_lattices: $i > $i > $i > $o ).
thf(k2_filter_0_decl,type,
k2_filter_0: $i > $i > $i ).
thf(k1_setwiseo_decl,type,
k1_setwiseo: $i > $i ).
thf(l1_lattices_decl,type,
l1_lattices: $i > $o ).
thf(k18_borsuk_1_decl,type,
k18_borsuk_1: $i > $i > $i > $i ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(k4_filter_0_decl,type,
k4_filter_0: $i > $i > $i > $i ).
thf(v1_lattice2_decl,type,
v1_lattice2: $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(v6_group_1_decl,type,
v6_group_1: $i > $o ).
thf(m1_filter_0_decl,type,
m1_filter_0: $i > $i > $o ).
thf(k5_filter_1_decl,type,
k5_filter_1: $i > $i > $i ).
thf(k6_filter_1_decl,type,
k6_filter_1: $i > $i > $i > $i ).
thf(k2_funct_4_decl,type,
k2_funct_4: $i > $i ).
thf(k4_lopclset_decl,type,
k4_lopclset: $i > $i ).
thf(k9_filter_0_decl,type,
k9_filter_0: $i > $i > $i > $i ).
thf(m1_lattice4_decl,type,
m1_lattice4: $i > $i > $i > $o ).
thf(r1_lattice4_decl,type,
r1_lattice4: $i > $i > $i > $o ).
thf(m2_lattice4_decl,type,
m2_lattice4: $i > $i > $o ).
thf(k5_lattices_decl,type,
k5_lattices: $i > $i ).
thf(k6_lattices_decl,type,
k6_lattices: $i > $i ).
thf(k4_lattice4_decl,type,
k4_lattice4: $i > $i > $i ).
thf(k11_borsuk_1_decl,type,
k11_borsuk_1: $i > $i > $i > $i ).
thf(v11_lattices_decl,type,
v11_lattices: $i > $o ).
thf(v2_lattice4_decl,type,
v2_lattice4: $i > $i > $i > $o ).
thf(v15_lattices_decl,type,
v15_lattices: $i > $o ).
thf(v16_lattices_decl,type,
v16_lattices: $i > $o ).
thf(v1_lattice4_decl,type,
v1_lattice4: $i > $i > $i > $o ).
thf(k1_domain_1_decl,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(r2_lattices_decl,type,
r2_lattices: $i > $i > $i > $o ).
thf(k8_filter_1_decl,type,
k8_filter_1: $i > $i > $i ).
thf(k10_filter_1_decl,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(k15_borsuk_1_decl,type,
k15_borsuk_1: $i > $i ).
thf(r1_pre_topc_decl,type,
r1_pre_topc: $i > $i > $o ).
thf(k9_filter_1_decl,type,
k9_filter_1: $i > $i ).
thf(k8_lopclset_decl,type,
k8_lopclset: $i > $i ).
thf(g1_pre_topc_decl,type,
g1_pre_topc: $i > $i > $i ).
thf(v12_lattices_decl,type,
v12_lattices: $i > $o ).
thf(v6_compts_1_decl,type,
v6_compts_1: $i > $i > $o ).
thf(k3_filter_0_decl,type,
k3_filter_0: $i > $i > $i ).
thf(k1_finsub_1_decl,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(k8_borsuk_1_decl,type,
k8_borsuk_1: $i > $i > $i > $i > $i ).
thf(k5_lopclset_decl,type,
k5_lopclset: $i > $i ).
thf(k3_lopclset_decl,type,
k3_lopclset: $i > $i > $i > $i ).
thf(k19_borsuk_1_decl,type,
k19_borsuk_1: $i > $i > $i > $i ).
thf(k2_filter_1_decl,type,
k2_filter_1: $i > $i > $i > $i ).
thf(k11_filter_0_decl,type,
k11_filter_0: $i > $i > $i ).
thf(a_2_3_borsuk_1_decl,type,
a_2_3_borsuk_1: $i > $i > $i ).
thf(u1_pre_topc_decl,type,
u1_pre_topc: $i > $i ).
thf(a_2_2_borsuk_1_decl,type,
a_2_2_borsuk_1: $i > $i > $i ).
thf(a_2_1_lattice4_decl,type,
a_2_1_lattice4: $i > $i > $i ).
thf(l2_struct_0_decl,type,
l2_struct_0: $i > $o ).
thf(a_2_0_borsuk_1_decl,type,
a_2_0_borsuk_1: $i > $i > $i ).
thf(a_2_0_filter_0_decl,type,
a_2_0_filter_0: $i > $i > $i ).
thf(k22_borsuk_1_decl,type,
k22_borsuk_1: $i ).
thf(k23_borsuk_1_decl,type,
k23_borsuk_1: $i ).
thf(k24_borsuk_1_decl,type,
k24_borsuk_1: $i ).
thf(k12_filter_0_decl,type,
k12_filter_0: $i > $i > $i ).
thf(v3_borsuk_1_decl,type,
v3_borsuk_1: $i > $i > $i > $o ).
thf(a_3_1_filter_0_decl,type,
a_3_1_filter_0: $i > $i > $i > $i ).
thf(a_3_1_borsuk_1_decl,type,
a_3_1_borsuk_1: $i > $i > $i > $i ).
thf(r1_filter_0_decl,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(k10_filter_0_decl,type,
k10_filter_0: $i > $i > $i ).
thf(k5_filter_0_decl,type,
k5_filter_0: $i > $i > $i > $i ).
thf(v1_filter_0_decl,type,
v1_filter_0: $i > $i > $o ).
thf(r2_lattice4_decl,type,
r2_lattice4: $i > $i > $i > $o ).
thf(a_3_0_filter_0_decl,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(r8_relat_2_decl,type,
r8_relat_2: $i > $i > $o ).
thf(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(k3_lattice4_decl,type,
k3_lattice4: $i > $i > $i ).
thf(a_2_0_lopclset_decl,type,
a_2_0_lopclset: $i > $i > $i ).
thf(k8_filter_0_decl,type,
k8_filter_0: $i > $i > $i ).
thf(k3_pre_topc_decl,type,
k3_pre_topc: $i > $i > $i ).
thf(k7_lopclset_decl,type,
k7_lopclset: $i > $i ).
thf(k9_lopclset_decl,type,
k9_lopclset: $i > $i ).
thf(m3_lattice4_decl,type,
m3_lattice4: $i > $i > $o ).
thf(k10_lopclset_decl,type,
k10_lopclset: $i > $i ).
thf(a_1_0_filter_1_decl,type,
a_1_0_filter_1: $i > $i ).
thf(a_3_0_borsuk_1_decl,type,
a_3_0_borsuk_1: $i > $i > $i > $i ).
thf(r3_lattice4_decl,type,
r3_lattice4: $i > $i > $i > $o ).
thf(a_2_0_lattice4_decl,type,
a_2_0_lattice4: $i > $i > $i ).
thf(k6_filter_0_decl,type,
k6_filter_0: $i > $i > $i > $i ).
thf(a_1_0_lopclset_decl,type,
a_1_0_lopclset: $i > $i ).
thf(r4_lattice4_decl,type,
r4_lattice4: $i > $i > $i > $o ).
thf(a_2_1_borsuk_1_decl,type,
a_2_1_borsuk_1: $i > $i > $i ).
thf(v3_lattice4_decl,type,
v3_lattice4: $i > $i > $i > $o ).
thf(k7_filter_0_decl,type,
k7_filter_0: $i > $i > $i > $i ).
thf(r1_relat_2_decl,type,
r1_relat_2: $i > $i > $o ).
thf(k1_filter_0_decl,type,
k1_filter_0: $i > $i ).
thf(v1_tops_2_decl,type,
v1_tops_2: $i > $i > $o ).
thf(v2_filter_0_decl,type,
v2_filter_0: $i > $i > $o ).
thf(r3_relat_2_decl,type,
r3_relat_2: $i > $i > $o ).
thf(u2_struct_0_decl,type,
u2_struct_0: $i > $i ).
thf(k11_lopclset_decl,type,
k11_lopclset: $i > $i ).
thf(r1_compts_1_decl,type,
r1_compts_1: $i > $i > $i > $o ).
thf(r4_wellord1_decl,type,
r4_wellord1: $i > $i > $o ).
thf(k13_lopclset_decl,type,
k13_lopclset: $i > $i ).
thf(k12_lopclset_decl,type,
k12_lopclset: $i > $i ).
thf(k1_filter_1_decl,type,
k1_filter_1: $i > $i > $i > $i ).
thf(a_1_1_lopclset_decl,type,
a_1_1_lopclset: $i > $i ).
thf(a_1_2_lopclset_decl,type,
a_1_2_lopclset: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk104_decl,type,
sk104: $i > $i ).
thf(sk105_decl,type,
sk105: $i ).
thf(sk129_decl,type,
sk129: $i ).
thf(sk150_decl,type,
sk150: $i > $i > $i ).
thf(sk152_decl,type,
sk152: $i ).
thf(sk153_decl,type,
sk153: $i ).
thf(sk161_decl,type,
sk161: $i ).
thf(sk184_decl,type,
sk184: $i > $i ).
thf(sk198_decl,type,
sk198: $i ).
thf(sk217_decl,type,
sk217: $i ).
thf(sk257_decl,type,
sk257: $i ).
thf(sk267_decl,type,
sk267: $i > $i ).
thf(sk300_decl,type,
sk300: $i ).
thf(sk302_decl,type,
sk302: $i ).
thf(sk304_decl,type,
sk304: $i ).
thf(sk311_decl,type,
sk311: $i ).
thf(sk342_decl,type,
sk342: $i ).
thf(sk362_decl,type,
sk362: $i ).
thf(sk363_decl,type,
sk363: $i ).
thf(sk365_decl,type,
sk365: $i ).
thf(sk372_decl,type,
sk372: $i ).
thf(sk376_decl,type,
sk376: $i ).
thf(sk379_decl,type,
sk379: $i ).
thf(sk386_decl,type,
sk386: $i ).
thf(sk389_decl,type,
sk389: $i ).
thf(sk391_decl,type,
sk391: $i ).
thf(sk393_decl,type,
sk393: $i ).
thf(sk395_decl,type,
sk395: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ k6_lopclset @ ( A @ r1_filter_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk104_def,definition,
( sk104
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk105_def,definition,
( sk105
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk129_def,definition,
( sk129
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk150_def,definition,
( sk150
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A
= ( C @ k1_relat_1 ) ) ) ) ) ) ).
thf(sk152_def,definition,
( sk152
= ( @+[A: $i] :
( ( A @ v3_realset2 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk153_def,definition,
( sk153
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk161_def,definition,
( sk161
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk184_def,definition,
( sk184
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk198_def,definition,
( sk198
= ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).
thf(sk217_def,definition,
( sk217
= ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).
thf(sk257_def,definition,
( sk257
= ( @+[A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk267_def,definition,
( sk267
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk300_def,definition,
( sk300
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk302_def,definition,
( sk302
= ( @+[A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk304_def,definition,
( sk304
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk311_def,definition,
( sk311
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk342_def,definition,
( sk342
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk362_def,definition,
( sk362
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk363_def,definition,
( sk363
= ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).
thf(sk365_def,definition,
( sk365
= ( @+[A: $i] :
( ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk372_def,definition,
( sk372
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk376_def,definition,
( sk376
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk379_def,definition,
( sk379
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk386_def,definition,
( sk386
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk389_def,definition,
( sk389
= ( @+[A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(sk391_def,definition,
( sk391
= ( @+[A: $i] : ( A @ l1_pre_topc ) ) ) ).
thf(sk393_def,definition,
( sk393
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk395_def,definition,
( sk395
= ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).
thf(301,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ k3_tarski ) )
=> ( ( D @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ k3_subset_1 ) @ k3_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_borsuk_1) ).
thf(2630,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ k3_tarski ) )
=> ( ( D @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ k3_subset_1 ) @ k3_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_setwiseo ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_setwiseo) ).
thf(1398,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_setwiseo ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1399,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_setwiseo ) )
= ( B @ k1_tarski ) )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1398]) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 )
| ( ( B @ ( A @ k2_setwiseo ) )
= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[1399]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ k6_lopclset @ ( A @ r1_filter_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lopclset) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ k6_lopclset @ ( A @ r1_filter_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1373,plain,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ k6_lopclset @ ( A @ r1_filter_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1374,plain,
! [A: $i] :
( ( ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) )
& ( sk1 @ l3_lattices )
& ~ ( sk1 @ v3_realset2 )
& ( sk1 @ v17_lattices )
& ( sk1 @ v10_lattices )
& ~ ( sk1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1373]) ).
thf(1379,plain,
sk1 @ v10_lattices,
inference(cnfConj,[status(thm)],[1374]) ).
thf(6,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattice4) ).
thf(1389,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1390,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1389]) ).
thf(1391,plain,
! [B: $i,A: $i] :
( ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B ) ),
inference(lifteq,[status(thm)],[1390]) ).
thf(7560,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ $true
| ( A @ v3_struct_0 )
| ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1379,1391]) ).
thf(7561,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 )
| ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B ) ),
inference(simp,[status(thm)],[7560]) ).
thf(7562,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(pattern_uni,[status(thm)],[7561:[bind(A,$thf( sk1 ))]]) ).
thf(7570,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[7562]) ).
thf(1376,plain,
sk1 @ l3_lattices,
inference(cnfConj,[status(thm)],[1374]) ).
thf(1380,plain,
~ ( sk1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[1374]) ).
thf(7587,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ $true
| $false
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(rewrite,[status(thm)],[7570,1376,1380]) ).
thf(7588,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[7587]) ).
thf(7739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_setwiseo ) )
!= ( C @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) ) )
| ~ ( sk1 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( ( B @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
= C )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1400,7588]) ).
thf(7740,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( ( A @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
= A )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7739:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(7766,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
= A )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7740]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tops_1) ).
thf(1633,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(805,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k17_borsuk_1 ) @ k2_relat_1 )
= ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_borsuk_1) ).
thf(4899,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k17_borsuk_1 ) @ k2_relat_1 )
= ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(764,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k5_lattices ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).
thf(4729,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
=> ( B
= ( A @ k5_lattices ) ) )
& ( ( B
= ( A @ k5_lattices ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(371,axiom,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(2921,plain,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(2427,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1163,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v12_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v16_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_filter_0) ).
thf(6566,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v12_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v16_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_relat_1) ).
thf(2199,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(923,axiom,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(5435,plain,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(5436,plain,
( ( sk257 @ v1_xboole_0 )
& ( sk257 @ v2_funct_1 )
& ( sk257 @ v1_funct_1 )
& ( sk257 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[5435]) ).
thf(5437,plain,
sk257 @ v1_relat_1,
inference(cnfConj,[status(thm)],[5436]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(1665,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(1586,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(638,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(4201,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(2452,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1209,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(6836,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(1410,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1411,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
| ~ ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[1410]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_4) ).
thf(3883,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(850,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) )
= ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattices) ).
thf(5116,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) )
= ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(976,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(5650,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(5651,plain,
! [A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk267 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[5650]) ).
thf(5653,plain,
! [A: $i] : ( A @ sk267 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[5651]) ).
thf(628,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(4159,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(4160,plain,
( ( sk161 @ v1_finset_1 )
& ( sk161 @ v1_funct_1 )
& ( sk161 @ v1_relat_1 )
& ~ ( sk161 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[4159]) ).
thf(4161,plain,
~ ( sk161 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[4160]) ).
thf(10402,plain,
! [A: $i] :
( ( ( A @ sk267 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5653,4161]) ).
thf(10403,plain,
! [A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10402]) ).
thf(10410,plain,
! [A: $i] :
( ( A @ sk267 )
!= sk161 ),
inference(simp,[status(thm)],[10403]) ).
thf(955,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_filter_0 ) )
=> ! [H: $i] :
( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
=> ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
=> ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
& ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
=> ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_filter_0) ).
thf(5561,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_filter_0 ) )
=> ! [H: $i] :
( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
=> ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
=> ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
& ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
=> ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1242,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(6979,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(611,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice2) ).
thf(4094,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(1469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(4835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1110,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_filter_0) ).
thf(6355,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(362,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2889,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(730,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(4571,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(707,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_tops_1) ).
thf(4464,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) )
= ( B @ ( C @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(2336,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(173,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tops_1) ).
thf(2109,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(1453,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
| ~ ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[1453]) ).
thf(1369,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).
thf(7445,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(1767,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(1438,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[1438]) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1439]) ).
thf(1075,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(6172,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(6173,plain,
( ( sk311 @ v1_relat_1 )
& ( sk311 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[6172]) ).
thf(6174,plain,
sk311 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[6173]) ).
thf(530,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(3668,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(3669,plain,
( ( sk129 @ v1_finset_1 )
& ~ ( sk129 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3668]) ).
thf(3670,plain,
~ ( sk129 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3669]) ).
thf(7701,plain,
( ( ( sk311 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6174,3670]) ).
thf(7702,plain,
( ( sk311 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7701]) ).
thf(7708,plain,
sk311 != sk129,
inference(simp,[status(thm)],[7702]) ).
thf(14944,plain,
! [B: $i,A: $i] :
( ( A != sk311 )
| ( B != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7708]) ).
thf(14945,plain,
! [A: $i] :
( ( A != sk129 )
| ( A @ k1_tarski @ ( sk311 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14944:[bind(A,$thf( sk311 ))]]) ).
thf(15303,plain,
sk129 @ k1_tarski @ ( sk311 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14945]) ).
thf(1034,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v16_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_1) ).
thf(5950,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v16_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( B @ l3_lattices )
& ( B @ v16_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v16_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(2412,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(359,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tops_1) ).
thf(2876,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(897,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( B @ ( C @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tops_1) ).
thf(5320,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( B @ ( C @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1095,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_0) ).
thf(6285,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(6980,plain,
( ( sk376 @ v1_funct_1 )
& ( sk376 @ v1_xboole_0 )
& ( sk376 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[6979]) ).
thf(6982,plain,
sk376 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[6980]) ).
thf(129,axiom,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(1895,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1896,plain,
( ( k1_xboole_0 @ k1_tarski )
= ( k1_xboole_0 @ k5_finsub_1 ) ),
inference(lifteq,[status(thm)],[1895]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(2177,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(2178,plain,
( ! [A: $i] : ( A @ k1_tarski @ v1_finset_1 )
& ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[2177]) ).
thf(2179,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2178]) ).
thf(2180,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[2179]) ).
thf(8266,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ~ ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1896,2180]) ).
thf(8267,plain,
~ ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[8266:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(8274,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6982,8267]) ).
thf(8275,plain,
( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8274]) ).
thf(8283,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
!= sk376 ),
inference(simp,[status(thm)],[8275]) ).
thf(1214,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(6855,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(793,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
& ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_1) ).
thf(4852,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
& ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).
thf(3830,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(338,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2787,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(977,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ! [E: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( ( C @ ( B @ ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ k1_lattices ) ) )
= ( E @ ( D @ ( A @ k2_lopclset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lopclset) ).
thf(5654,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ! [E: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( ( C @ ( B @ ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ k1_lattices ) ) )
= ( E @ ( D @ ( A @ k2_lopclset ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1099,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ ( A @ k9_lopclset @ m2_relset_1 ) ) )
& ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ ( A @ k9_lopclset @ v1_funct_2 ) ) )
& ( A @ k9_lopclset @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_lopclset) ).
thf(6317,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ ( A @ k9_lopclset @ m2_relset_1 ) ) )
& ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ ( A @ k9_lopclset @ v1_funct_2 ) ) )
& ( A @ k9_lopclset @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(2499,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(2559,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k2_funct_4 @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_4) ).
thf(4015,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k2_funct_4 @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(1054,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(6070,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(6071,plain,
( ( sk300 @ v2_funct_1 )
& ( sk300 @ v1_funct_1 )
& ( sk300 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[6070]) ).
thf(6074,plain,
sk300 @ v2_funct_1,
inference(cnfConj,[status(thm)],[6071]) ).
thf(473,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setwiseo) ).
thf(3403,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(3404,plain,
! [A: $i] :
( ( A @ sk104 @ v1_finset_1 )
& ( A @ sk104 @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( A @ sk104 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[3403]) ).
thf(3406,plain,
! [A: $i] : ( A @ sk104 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3404]) ).
thf(10351,plain,
! [B: $i,A: $i] :
( ( ( A @ sk104 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,2180]) ).
thf(10352,plain,
! [B: $i,A: $i] :
( ( A @ sk104 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10351]) ).
thf(10363,plain,
! [B: $i,A: $i] :
( ( A @ sk104 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[10352]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(2331,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(4682,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1328,axiom,
k22_borsuk_1 @ l1_pre_topc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k22_borsuk_1) ).
thf(7285,plain,
k22_borsuk_1 @ l1_pre_topc,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(1355,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k8_lopclset @ v1_funct_1 )
& ( A @ k8_lopclset @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_lopclset) ).
thf(7396,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k8_lopclset @ v1_funct_1 )
& ( A @ k8_lopclset @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_funct_1) ).
thf(4992,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(1115,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_borsuk_1) ).
thf(6374,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(1237,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(6950,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(6951,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[6950]) ).
thf(6952,plain,
~ ( sk372 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[6951]) ).
thf(7895,plain,
( ( ( sk376 @ v1_xboole_0 )
!= ( sk372 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6982,6952]) ).
thf(7896,plain,
( ( sk376 @ v1_xboole_0 )
!= ( sk372 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7895]) ).
thf(7903,plain,
sk376 != sk372,
inference(simp,[status(thm)],[7896]) ).
thf(533,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(3680,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(926,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(5454,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(11,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice4) ).
thf(1404,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1405,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1404]) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B ) ),
inference(lifteq,[status(thm)],[1405]) ).
thf(1359,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(7409,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(344,axiom,
! [A: $i] :
( ( A @ k1_setwiseo )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setwiseo) ).
thf(2808,plain,
! [A: $i] :
( ( A @ k1_setwiseo )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k2_tops_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tops_1) ).
thf(5625,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k2_tops_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(758,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(4711,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= A ) )
& ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(1692,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= A ) )
& ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1304,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k7_lopclset @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lopclset) ).
thf(7208,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k7_lopclset @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
thf(1434,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) )
& ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ) ),
inference(cnf,[status(esa)],[1434]) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[1435]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_4) ).
thf(4479,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(3990,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1226,axiom,
? [A: $i] :
( ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pre_topc) ).
thf(6896,plain,
? [A: $i] :
( ( A @ v1_pre_topc )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(6897,plain,
( ( sk365 @ v1_pre_topc )
& ( sk365 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[6896]) ).
thf(6898,plain,
sk365 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[6897]) ).
thf(1378,plain,
! [A: $i] :
( ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[1374]) ).
thf(7886,plain,
! [A: $i] :
( ( ( sk365 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[6898,1378]) ).
thf(7887,plain,
! [A: $i] :
( ( ( sk365 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[7886]) ).
thf(7888,plain,
( ~ ( sk365 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( sk365 @ v2_pre_topc )
| ( sk365 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[7887:[bind(A,$thf( sk365 ))]]) ).
thf(759,axiom,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funct_5) ).
thf(4713,plain,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(4714,plain,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[4713]) ).
thf(377,axiom,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(2972,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(2973,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[2972]) ).
thf(2974,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[2973]) ).
thf(2976,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2974]) ).
thf(134,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(1924,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_setwiseo) ).
thf(1384,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1385,plain,
! [B: $i,A: $i] :
( ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1384]) ).
thf(7593,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
| ~ $true
| ( ( C @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= C )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1385,7588]) ).
thf(7594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
| ( ( C @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= C )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7593]) ).
thf(7595,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( B @ ( A @ k2_setwiseo ) )
!= C )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( ( C @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= C )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7594]) ).
thf(7596,plain,
! [B: $i,A: $i] :
( ( ( A @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( ( B @ ( A @ k2_setwiseo ) @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= ( B @ ( A @ k2_setwiseo ) ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7595]) ).
thf(1350,axiom,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_pre_topc) ).
thf(7380,plain,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(7381,plain,
( ( sk389 @ v2_pre_topc )
& ( sk389 @ v1_pre_topc )
& ~ ( sk389 @ v3_struct_0 )
& ( sk389 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[7380]) ).
thf(7382,plain,
sk389 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[7381]) ).
thf(8007,plain,
! [A: $i] :
( ( ( sk389 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7382,1378]) ).
thf(8008,plain,
! [A: $i] :
( ( ( sk389 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[8007]) ).
thf(8009,plain,
( ~ ( sk389 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( sk389 @ v2_pre_topc )
| ( sk389 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[8008:[bind(A,$thf( sk389 ))]]) ).
thf(7383,plain,
~ ( sk389 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[7381]) ).
thf(7385,plain,
sk389 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[7381]) ).
thf(8043,plain,
( ~ ( sk389 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[8009,7383,7385]) ).
thf(8044,plain,
~ ( sk389 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) ),
inference(simp,[status(thm)],[8043]) ).
thf(740,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(4630,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(4631,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[4630]) ).
thf(4632,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_xboole_0 )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[4631]) ).
thf(4634,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[4632]) ).
thf(4636,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[4634]) ).
thf(4637,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[4636]) ).
thf(1245,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(6994,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(6995,plain,
( ( sk379 @ v1_relat_1 )
& ~ ( sk379 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[6994]) ).
thf(6996,plain,
~ ( sk379 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[6995]) ).
thf(7515,plain,
( ( ( sk379 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4637,6996]) ).
thf(7516,plain,
( ( sk379 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7515]) ).
thf(7517,plain,
sk379 != k1_xboole_0,
inference(simp,[status(thm)],[7516]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finset_1) ).
thf(2495,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(5292,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1064,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6114,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(6115,plain,
sk304 @ v1_xboole_0,
inference(cnf,[status(esa)],[6114]) ).
thf(7686,plain,
( ( ( sk304 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6115,3670]) ).
thf(7687,plain,
( ( sk304 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7686]) ).
thf(7694,plain,
sk304 != sk129,
inference(simp,[status(thm)],[7687]) ).
thf(14980,plain,
! [B: $i,A: $i] :
( ( A != sk304 )
| ( B != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7694]) ).
thf(14981,plain,
! [A: $i] :
( ( A != sk129 )
| ( A @ k1_tarski @ ( sk304 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14980:[bind(A,$thf( sk304 ))]]) ).
thf(15314,plain,
sk129 @ k1_tarski @ ( sk304 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14981]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_connsp_2 ) ) )
& ( C @ ( A @ ( E @ m2_connsp_2 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( D @ ( B @ k1_struct_0 ) @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_borsuk_1 ) ) ) ) ) @ m2_connsp_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_borsuk_1) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_connsp_2 ) ) )
& ( C @ ( A @ ( E @ m2_connsp_2 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( D @ ( B @ k1_struct_0 ) @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_borsuk_1 ) ) ) ) ) @ m2_connsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( C @ k1_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_3) ).
thf(3417,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( C @ k1_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1061,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(6095,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(6096,plain,
( ( sk302 @ v1_finset_1 )
& ( sk302 @ v2_funct_1 )
& ( sk302 @ v1_funct_1 )
& ( sk302 @ v1_relat_1 )
& ( sk302 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[6095]) ).
thf(6101,plain,
sk302 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[6096]) ).
thf(7671,plain,
( ( ( sk302 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6101,3670]) ).
thf(7672,plain,
( ( sk302 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7671]) ).
thf(7679,plain,
sk302 != sk129,
inference(simp,[status(thm)],[7672]) ).
thf(14500,plain,
! [B: $i,A: $i] :
( ( A != sk302 )
| ( B != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7679]) ).
thf(14501,plain,
! [A: $i] :
( ( A != sk129 )
| ( A @ k1_tarski @ ( sk302 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14500:[bind(A,$thf( sk302 ))]]) ).
thf(15143,plain,
sk129 @ k1_tarski @ ( sk302 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14501]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(1618,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1133,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(6458,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(889,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
& ( A @ ( B @ v3_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v3_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_tops_1) ).
thf(5297,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_tops_1 ) )
& ( A @ ( B @ v3_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v3_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( E @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_setwiseo) ).
thf(1401,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( E @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(1420,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1421,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A )
| ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1420]) ).
thf(1422,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
| ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(lifteq,[status(thm)],[1421]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(6900,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(1939,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_tarski ) ) )
& ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(2248,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(2676,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice2) ).
thf(2014,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1002,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(5793,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1346,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k15_borsuk_1 @ m1_borsuk_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_borsuk_1) ).
thf(7368,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k15_borsuk_1 @ m1_borsuk_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(1201,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_4) ).
thf(6776,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) )
= ( A @ ( C @ k10_relat_1 ) @ ( B @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t181_relat_1) ).
thf(3108,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) )
= ( A @ ( C @ k10_relat_1 ) @ ( B @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(175,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) )
= C )
=> ( ( A @ k2_pre_topc )
= ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_pre_topc) ).
thf(2114,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) )
= C )
=> ( ( A @ k2_pre_topc )
= ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(5405,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(494,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_1) ).
thf(3498,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).
thf(4215,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(237,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
<=> ( C @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tops_1) ).
thf(2380,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1298,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k12_lopclset @ l3_lattices )
& ( A @ k12_lopclset @ v10_lattices )
& ~ ( A @ k12_lopclset @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_lopclset) ).
thf(7182,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k12_lopclset @ l3_lattices )
& ( A @ k12_lopclset @ v10_lattices )
& ~ ( A @ k12_lopclset @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(1971,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(354,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(2854,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_subset_1) ).
thf(1426,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_funct_3 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k1_funct_3 @ k1_funct_1 ) )
= ( A @ ( B @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_3) ).
thf(4403,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_funct_3 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k1_funct_3 @ k1_funct_1 ) )
= ( A @ ( B @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(7688,plain,
( ( ( sk372 @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6115,6952]) ).
thf(7689,plain,
( ( sk372 @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7688]) ).
thf(7695,plain,
sk372 != sk304,
inference(simp,[status(thm)],[7689]) ).
thf(592,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v2_tops_1 ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(4011,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v2_tops_1 ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(5288,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(3338,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(664,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( C @ ( E @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( B @ ( D @ ( A @ k2_filter_0 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice4) ).
thf(4279,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( C @ ( E @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( B @ ( D @ ( A @ k2_filter_0 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1213,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(6851,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(260,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(2459,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1225,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(6894,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(824,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattices) ).
thf(4980,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_binop_1) ).
thf(1458,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1356,axiom,
? [A: $i] : ( A @ l1_pre_topc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(7400,plain,
? [A: $i] : ( A @ l1_pre_topc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(3848,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m2_subset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(950,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_borsuk_1) ).
thf(5550,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(5814,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(647,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(4234,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(1007,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(5809,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(5810,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5809]) ).
thf(5811,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5810]) ).
thf(8753,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6982,5811]) ).
thf(8754,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8753]) ).
thf(8765,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk376 ),
inference(simp,[status(thm)],[8754]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ ( B @ k9_relat_1 ) @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(4090,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ ( B @ k9_relat_1 ) @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(5361,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1149,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(6505,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).
thf(5565,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(317,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ k1_funct_4 ) )
= B )
& ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_4) ).
thf(2686,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ k1_funct_4 ) )
= B )
& ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1234,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ! [F: $i] :
~ ( ( D @ ( F @ r1_xboole_0 ) )
& ( E @ ( F @ r2_hidden ) ) )
& ( D @ ( E @ ( A @ r1_compts_1 ) ) )
& ( C @ ( E @ r1_tarski ) ) ) )
& ( D @ ( C @ ( A @ r1_compts_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_borsuk_1) ).
thf(6939,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ! [F: $i] :
~ ( ( D @ ( F @ r1_xboole_0 ) )
& ( E @ ( F @ r2_hidden ) ) )
& ( D @ ( E @ ( A @ r1_compts_1 ) ) )
& ( C @ ( E @ r1_tarski ) ) ) )
& ( D @ ( C @ ( A @ r1_compts_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(788,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tops_1) ).
thf(4839,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(467,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_relat_1) ).
thf(3367,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k8_borsuk_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_borsuk_1) ).
thf(6359,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k8_borsuk_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(370,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(2918,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ~ ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(2141,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ~ ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ~ ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(7509,plain,
( ( ( sk161 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4637,4161]) ).
thf(7510,plain,
( ( sk161 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7509]) ).
thf(7514,plain,
sk161 != k1_xboole_0,
inference(simp,[status(thm)],[7510]) ).
thf(14384,plain,
! [B: $i,A: $i] :
( ( A != sk161 )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7514]) ).
thf(14385,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk161 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14384:[bind(A,$thf( sk161 ))]]) ).
thf(15098,plain,
k1_xboole_0 @ k1_tarski @ ( sk161 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14385]) ).
thf(15916,plain,
k1_xboole_0 @ k5_finsub_1 @ ( sk161 @ k1_tarski @ r1_xboole_0 ),
inference(rewrite,[status(thm)],[15098,1896]) ).
thf(741,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(4638,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1341,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k6_filter_0 ) ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(7345,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k6_filter_0 ) ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(1123,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(6416,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(745,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k10_relat_1 ) )
= ( A @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_relat_1) ).
thf(4650,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k10_relat_1 ) )
= ( A @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(987,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(5713,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1286,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k10_lopclset @ k3_tarski )
= ( A @ k7_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lopclset) ).
thf(7147,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k10_lopclset @ k3_tarski )
= ( A @ k7_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(1761,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(411,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tops_1) ).
thf(3121,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_3_borsuk_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ~ ( C @ u1_struct_0 @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k1_struct_0 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_borsuk_1) ).
thf(6551,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pre_topc ) )
& ~ ( C @ v3_struct_0 )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ~ ( C @ u1_struct_0 @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k1_struct_0 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_3_borsuk_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_3_borsuk_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ~ ( C @ u1_struct_0 @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k1_struct_0 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ l1_pre_topc )
& ( D @ v2_pre_topc )
& ( D @ v1_pre_topc )
& ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( D @ ( C @ ( B @ a_3_0_borsuk_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( B @ a_2_1_borsuk_1 ) @ ( E @ r1_tarski ) )
& ( A
= ( E @ ( D @ u1_struct_0 @ k5_setfam_1 ) ) )
& ( D @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_borsuk_1) ).
thf(6680,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ l1_pre_topc )
& ( D @ v2_pre_topc )
& ( D @ v1_pre_topc )
& ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( ? [E: $i] :
( ( C @ ( B @ a_2_1_borsuk_1 ) @ ( E @ r1_tarski ) )
& ( A
= ( E @ ( D @ u1_struct_0 @ k5_setfam_1 ) ) )
& ( D @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_borsuk_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_borsuk_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( B @ a_2_1_borsuk_1 ) @ ( E @ r1_tarski ) )
& ( A
= ( E @ ( D @ u1_struct_0 @ k5_setfam_1 ) ) )
& ( D @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(2901,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1371,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(7452,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(453,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).
thf(3313,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1000,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k5_filter_1 ) @ k6_lattices )
= ( A @ k6_lattices @ ( B @ ( A @ k6_filter_1 ) ) ) )
& ( B @ ( A @ k5_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v14_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k5_filter_1 ) @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_1) ).
thf(5782,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k5_filter_1 ) @ k6_lattices )
= ( A @ k6_lattices @ ( B @ ( A @ k6_filter_1 ) ) ) )
& ( B @ ( A @ k5_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v14_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k5_filter_1 ) @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_lattice4) ).
thf(3370,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).
thf(4792,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(682,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(4343,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1037,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k11_filter_0 ) )
= ( B @ ( A @ k10_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).
thf(5977,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k11_filter_0 ) )
= ( B @ ( A @ k10_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(622,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice4) ).
thf(4137,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1106,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(6342,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(1062,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) @ ( A @ k2_tops_1 ) @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ k2_tops_1 ) @ ( A @ k2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_tops_1) ).
thf(6102,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) @ ( A @ k2_tops_1 ) @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ k2_tops_1 ) @ ( A @ k2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(458,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ ( C @ v3_pre_topc ) )
=> ( C
= ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_borsuk_1) ).
thf(3335,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ ( C @ v3_pre_topc ) )
=> ( C
= ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(583,axiom,
? [A: $i] :
( ( A @ v3_realset2 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_realset2) ).
thf(3974,plain,
? [A: $i] :
( ( A @ v3_realset2 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(3975,plain,
( ( sk152 @ v3_realset2 )
& ( sk152 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[3974]) ).
thf(3977,plain,
sk152 @ v3_realset2,
inference(cnfConj,[status(thm)],[3975]) ).
thf(1377,plain,
~ ( sk1 @ v3_realset2 ),
inference(cnfConj,[status(thm)],[1374]) ).
thf(7474,plain,
( ( ( sk152 @ v3_realset2 )
!= ( sk1 @ v3_realset2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3977,1377]) ).
thf(7475,plain,
( ( sk152 @ v3_realset2 )
!= ( sk1 @ v3_realset2 ) ),
inference(simp,[status(thm)],[7474]) ).
thf(7476,plain,
sk152 != sk1,
inference(simp,[status(thm)],[7475]) ).
thf(14078,plain,
! [B: $i,A: $i] :
( ( B != sk152 )
| ( A != sk1 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7476]) ).
thf(14079,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk152 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14078:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).
thf(15814,plain,
sk152 @ k1_tarski @ ( sk1 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14079]) ).
thf(16356,plain,
( ( ( sk1 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( sk152 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1896,15814]) ).
thf(16387,plain,
( ( sk1 != k1_xboole_0 )
| ( sk152 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[16356]) ).
thf(463,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) @ ( C @ r2_hidden ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) )
=> ( ~ ( D @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ r1_xboole_0 ) )
& ~ ( D @ ( B @ r1_xboole_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_tops_1) ).
thf(3350,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) )
=> ( ~ ( D @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ r1_xboole_0 ) )
& ~ ( D @ ( B @ r1_xboole_0 ) ) ) ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k2_tops_1 ) @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) )
=> ( ~ ( D @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ r1_xboole_0 ) )
& ~ ( D @ ( B @ r1_xboole_0 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1137,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ k3_tarski @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_borsuk_1) ).
thf(6466,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ k3_tarski @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(2491,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k4_xboole_0 ) @ k2_xboole_0 ) )
= ( A @ ( B @ ( C @ k2_xboole_0 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(1782,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_xboole_0 ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ k3_tarski @ ( C @ r1_tarski ) ) )
=> ( A @ k3_tarski @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1269,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(7079,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(689,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_relat_1) ).
thf(4371,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(607,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(4079,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(23,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1441,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(2020,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1283,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k12_lopclset @ ( A @ r1_filter_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lopclset) ).
thf(7136,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k12_lopclset @ ( A @ r1_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(7936,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ $true
| ( A @ v3_struct_0 )
| ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1379,1406]) ).
thf(7937,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ( A @ v3_struct_0 )
| ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B ) ),
inference(simp,[status(thm)],[7936]) ).
thf(7938,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(pattern_uni,[status(thm)],[7937:[bind(A,$thf( sk1 ))]]) ).
thf(7952,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[7938]) ).
thf(8115,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ $true
| $false
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(rewrite,[status(thm)],[7952,1376,1380]) ).
thf(8116,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8115]) ).
thf(8125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_setwiseo ) )
!= ( C @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) ) )
| ~ ( sk1 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( ( B @ k1_tarski @ ( sk1 @ k1_lattice4 ) )
= C )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1400,8116]) ).
thf(8126,plain,
! [A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( ( A @ k1_tarski @ ( sk1 @ k1_lattice4 ) )
= A )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[8125:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(8133,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ ( sk1 @ k1_lattice4 ) )
= A )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8126]) ).
thf(1314,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k9_filter_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(7235,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k9_filter_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k7_lattices ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(5476,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k7_lattices ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(1613,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1013,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
thf(5825,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(989,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_lopclset @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lopclset) ).
thf(5723,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_lopclset @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) )
= ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_lattice2) ).
thf(1645,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) )
= ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(2886,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(1442,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[1441]) ).
thf(8255,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k5_finsub_1 ) ),
inference(rewrite,[status(thm)],[1442,1896]) ).
thf(393,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(3050,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(3051,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[3050]) ).
thf(11675,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[8255,3051]) ).
thf(11676,plain,
k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[11675:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(12188,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ~ $true
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[11676,8116]) ).
thf(12189,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[12188]) ).
thf(12212,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( k1_xboole_0 != A )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[12189]) ).
thf(12257,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( k1_xboole_0 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= k1_xboole_0 ) ),
inference(simp,[status(thm)],[12212]) ).
thf(5,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice4) ).
thf(1386,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(487,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tops_1) ).
thf(3466,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(891,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(5301,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(637,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k2_pre_topc )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(4198,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k2_pre_topc )
= ( A @ u1_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(568,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r3_lattices ) ) )
<=> ( ( F @ ( E @ ( B @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_1) ).
thf(3898,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( ( F @ ( E @ ( B @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ r3_lattices ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r3_lattices ) ) ) )
& ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r3_lattices ) ) )
=> ( ( F @ ( E @ ( B @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
thf(4963,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(2067,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1143,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).
thf(6483,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(678,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_1) ).
thf(4322,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( C @ k2_funct_4 @ k1_relat_1 )
= ( A @ ( B @ k2_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_4) ).
thf(4156,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( C @ k2_funct_4 @ k1_relat_1 )
= ( A @ ( B @ k2_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(180,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(2136,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(1518,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(733,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(4608,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(4609,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[4608]) ).
thf(4610,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[4609]) ).
thf(1077,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_1) ).
thf(6182,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(4467,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(1335,axiom,
( ( k22_borsuk_1 @ v2_pre_topc )
& ( k22_borsuk_1 @ v1_pre_topc )
& ~ ( k22_borsuk_1 @ v3_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_borsuk_1) ).
thf(7308,plain,
( ( k22_borsuk_1 @ v2_pre_topc )
& ( k22_borsuk_1 @ v1_pre_topc )
& ~ ( k22_borsuk_1 @ v3_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(7309,plain,
( ( k22_borsuk_1 @ v2_pre_topc )
& ( k22_borsuk_1 @ v1_pre_topc )
& ~ ( k22_borsuk_1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[7308]) ).
thf(7311,plain,
k22_borsuk_1 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[7309]) ).
thf(774,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(4775,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(651,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_lattice4 ) @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice4) ).
thf(4249,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_lattice4 ) @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(902,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattices) ).
thf(5342,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
=> ( A @ v14_lattices ) )
& ( ( A @ v14_lattices )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(1887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(12,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) )
= ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice4) ).
thf(1407,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) )
= ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1408,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) )
= ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v14_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1407]) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v14_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ( ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) )
= ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) ) ) ),
inference(lifteq,[status(thm)],[1408]) ).
thf(921,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_0) ).
thf(5429,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(578,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(3938,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1320,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ u1_struct_0 @ ( A @ k2_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_lopclset) ).
thf(7262,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ u1_struct_0 @ ( A @ k2_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(112,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(1822,plain,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1823,plain,
! [A: $i] :
( ( ~ ( A @ k1_tarski @ ( sk20 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk20 @ ( A @ m1_subset_1 ) ) )
& ~ ( sk20 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1822]) ).
thf(1824,plain,
~ ( sk20 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1823]) ).
thf(7684,plain,
( ( ( sk304 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6115,1824]) ).
thf(7685,plain,
( ( sk304 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7684]) ).
thf(7696,plain,
sk304 != sk20,
inference(simp,[status(thm)],[7685]) ).
thf(515,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(3572,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(3573,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3572]) ).
thf(3574,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3573]) ).
thf(552,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(3821,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(3653,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(3043,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1351,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_lopclset )
= ( A @ k8_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_lopclset) ).
thf(7386,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_lopclset )
= ( A @ k8_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(1224,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(6892,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(3976,plain,
sk152 @ l1_struct_0,
inference(cnfConj,[status(thm)],[3975]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(2328,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(103,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_tops_1) ).
thf(1792,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(1429,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1430,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r2_hidden ) )
| ~ ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[1429]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(1660,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1362,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k12_filter_0 ) )
= ( B @ ( A @ k10_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_filter_0) ).
thf(7418,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k12_filter_0 ) )
= ( B @ ( A @ k10_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(1026,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(5883,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_mcart_1) ).
thf(2667,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(7401,plain,
sk391 @ l1_pre_topc,
inference(cnf,[status(esa)],[7400]) ).
thf(626,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(4151,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(995,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_lopclset @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lopclset) ).
thf(5759,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_lopclset @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v3_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(1907,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) )
=> ( B @ k1_tarski @ ( A @ r1_tarski ) ) )
& ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(842,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice4) ).
thf(5064,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) )
=> ( B @ ( A @ ( C @ m1_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(881,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ k1_pre_topc @ ( A @ k1_tops_1 ) )
= ( A @ k1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tops_1) ).
thf(5274,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ k1_pre_topc @ ( A @ k1_tops_1 ) )
= ( A @ k1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(746,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(4653,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(4654,plain,
sk198 @ l1_lattices,
inference(cnf,[status(esa)],[4653]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(3617,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(3125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_funct_3 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k3_funct_3 @ k1_funct_1 ) )
= ( A @ ( B @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funct_3) ).
thf(1826,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_funct_3 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k3_funct_3 @ k1_funct_1 ) )
= ( A @ ( B @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(662,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( C @ v2_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v2_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_tops_1) ).
thf(4275,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( C @ v2_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(4349,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(853,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_4) ).
thf(5130,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(474,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(3408,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(3409,plain,
( ~ ( sk105 @ v3_struct_0 )
& ( sk105 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[3408]) ).
thf(3410,plain,
sk105 @ l1_struct_0,
inference(cnfConj,[status(thm)],[3409]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(1455,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(442,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(3280,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(2562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(2788,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(cnf,[status(esa)],[2787]) ).
thf(712,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(4484,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(4485,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[4484]) ).
thf(4486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk184 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[4485]) ).
thf(4487,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[4486]) ).
thf(4489,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[4487]) ).
thf(4490,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[4489]) ).
thf(10579,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( C @ r2_hidden ) ) )
| ~ $true
| ~ ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1430,4490]) ).
thf(10580,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( C @ r2_hidden ) ) )
| ~ ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[10579]) ).
thf(10581,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( k1_xboole_0 @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[10580:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(16122,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ~ ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1896,10581]) ).
thf(16123,plain,
~ ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[16122:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(16210,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2788,16123]) ).
thf(16211,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[16210]) ).
thf(16232,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[16211]) ).
thf(16240,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16232]) ).
thf(974,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattices) ).
thf(5640,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(3089,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(1182,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(6662,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1103,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k6_lattices @ ( B @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattices) ).
thf(6332,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k6_lattices @ ( B @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(1247,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(7000,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(729,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
thf(4568,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(1044,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_pre_topc) ).
thf(6010,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1171,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_pre_topc @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lopclset) ).
thf(6599,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k1_pre_topc @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) )
= ( A @ k2_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_pre_topc) ).
thf(1572,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) )
= ( A @ k2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(5440,plain,
sk257 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[5436]) ).
thf(7574,plain,
( ( ( sk257 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5440,1824]) ).
thf(7575,plain,
( ( sk257 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7574]) ).
thf(7586,plain,
sk257 != sk20,
inference(simp,[status(thm)],[7575]) ).
thf(14550,plain,
! [B: $i,A: $i] :
( ( B != sk257 )
| ( A != sk20 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7586]) ).
thf(14551,plain,
! [A: $i] :
( ( A != sk20 )
| ( sk257 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14550:[bind(A,$thf( A )),bind(B,$thf( sk257 ))]]) ).
thf(15161,plain,
sk257 @ k1_tarski @ ( sk20 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14551]) ).
thf(223,axiom,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(2323,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(2324,plain,
~ ? [A: $i,B: $i] :
( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[2323]) ).
thf(2325,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2324]) ).
thf(2326,plain,
! [B: $i,A: $i] :
( ~ ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[2325]) ).
thf(2327,plain,
! [A: $i] :
~ ( A @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ),
inference(simp,[status(thm)],[2326]) ).
thf(18991,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ~ ( A @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1896,2327]) ).
thf(18992,plain,
~ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[18991:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(19130,plain,
~ ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ),
inference(rewrite,[status(thm)],[18992,1896]) ).
thf(7578,plain,
( ( ( sk372 @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5440,6952]) ).
thf(7579,plain,
( ( sk372 @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7578]) ).
thf(7585,plain,
sk372 != sk257,
inference(simp,[status(thm)],[7579]) ).
thf(14674,plain,
! [B: $i,A: $i] :
( ( B != sk372 )
| ( A != sk257 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7585]) ).
thf(14675,plain,
! [A: $i] :
( ( A != sk257 )
| ( sk372 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14674:[bind(A,$thf( A )),bind(B,$thf( sk372 ))]]) ).
thf(15199,plain,
sk372 @ k1_tarski @ ( sk257 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14675]) ).
thf(8256,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k5_finsub_1 @ ( sk1 @ k2_lattice4 ) )
= A )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1896,7766]) ).
thf(8257,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ ( sk1 @ k2_lattice4 ) )
= k1_xboole_0 )
| ~ ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[8256:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C
= ( B @ ( A @ k1_funct_4 ) ) )
<=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_4) ).
thf(1545,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) )
=> ( C
= ( B @ ( A @ k1_funct_4 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_4 ) ) )
=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( ~ ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice2) ).
thf(2420,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(320,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_tops_1) ).
thf(2713,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(499,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_pre_topc) ).
thf(3517,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(588,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_0) ).
thf(3998,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_lattice2) ).
thf(1892,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(470,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v11_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( B @ ( A @ k2_lattices ) ) @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_lattices) ).
thf(3385,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( B @ ( A @ k2_lattices ) ) @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) )
=> ( A @ v11_lattices ) )
& ( ( A @ v11_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( B @ ( A @ k2_lattices ) ) @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(7699,plain,
( ( ( sk311 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6174,1824]) ).
thf(7700,plain,
( ( sk311 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7699]) ).
thf(7711,plain,
sk311 != sk20,
inference(simp,[status(thm)],[7700]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ l1_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_borsuk_1) ).
thf(2857,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ l1_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1139,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( B @ ( A @ k5_filter_1 ) @ v3_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_1) ).
thf(6470,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( B @ ( A @ k5_filter_1 ) @ v3_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(736,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ k11_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( E @ r2_hidden ) )
& ( D @ ( B @ ( A @ k11_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( B @ ( A @ k11_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( E @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( D @ ( B @ ( A @ k11_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( E @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_1) ).
thf(4617,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ k11_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( E @ r2_hidden ) )
& ( D @ ( B @ ( A @ k11_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( B @ ( A @ k11_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( E @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( D @ ( B @ ( A @ k11_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( E @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(1176,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice2) ).
thf(6611,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(636,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
<=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_0) ).
thf(4194,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r3_lattices ) ) )
=> ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(4358,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1147,axiom,
k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k23_borsuk_1) ).
thf(6502,plain,
k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(5604,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(4664,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1203,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(6781,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(3084,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1229,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r2_lattice4 ) ) )
<=> ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lattice4) ).
thf(6923,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) )
=> ( C @ ( B @ ( A @ r2_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_lattice4 ) ) )
=> ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1366,axiom,
? [A: $i] : ( A @ l3_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(7436,plain,
? [A: $i] : ( A @ l3_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(1262,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_realset2 )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ k10_lopclset @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( ( C @ ( B @ k9_lopclset @ ( B @ k7_lopclset @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= A )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lopclset) ).
thf(7047,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_realset2 )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( ( C @ ( B @ k9_lopclset @ ( B @ k7_lopclset @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= A )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
=> ( B @ k10_lopclset @ ( A @ r2_hidden ) ) )
& ( ( B @ k10_lopclset @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( ( C @ ( B @ k9_lopclset @ ( B @ k7_lopclset @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) )
= A )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(542,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(3734,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice4) ).
thf(5829,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(688,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( ( A @ k2_pre_topc )
= ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_pre_topc) ).
thf(4368,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( ( A @ k2_pre_topc )
= ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(624,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_tops_1) ).
thf(4141,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(7897,plain,
( ( ( sk376 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6982,4161]) ).
thf(7898,plain,
( ( sk376 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7897]) ).
thf(7901,plain,
sk376 != sk161,
inference(simp,[status(thm)],[7898]) ).
thf(14418,plain,
! [B: $i,A: $i] :
( ( B != sk376 )
| ( A != sk161 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7901]) ).
thf(14419,plain,
! [A: $i] :
( ( A != sk161 )
| ( sk376 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14418:[bind(A,$thf( A )),bind(B,$thf( sk376 ))]]) ).
thf(15110,plain,
sk376 @ k1_tarski @ ( sk161 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14419]) ).
thf(6098,plain,
sk302 @ v2_funct_1,
inference(cnfConj,[status(thm)],[6096]) ).
thf(991,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices )
= ( A @ k1_lattice2 @ k5_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_lattice2) ).
thf(5727,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices )
= ( A @ k1_lattice2 @ k5_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(693,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(4390,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(709,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattice2) ).
thf(4471,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(716,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ v1_funct_2 ) ) )
& ( A @ k1_funct_3 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_3) ).
thf(4507,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ v1_funct_2 ) ) )
& ( A @ k1_funct_3 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(833,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ v6_compts_1 ) )
=> ! [E: $i] :
( ( C @ ( A @ k1_struct_0 ) @ ( D @ ( A @ ( B @ k7_borsuk_1 ) ) ) @ ( A @ ( B @ k6_borsuk_1 ) @ ( E @ m2_connsp_2 ) ) )
=> ? [F: $i] :
( ? [G: $i] :
( ( E @ ( G @ ( F @ ( C @ ( D @ ( A @ ( B @ k10_borsuk_1 ) ) ) ) ) @ r1_tarski ) )
& ( C @ ( A @ ( G @ m1_connsp_2 ) ) ) )
& ( D @ ( B @ ( F @ m2_connsp_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_borsuk_1) ).
thf(5020,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ v6_compts_1 ) )
=> ! [E: $i] :
( ( C @ ( A @ k1_struct_0 ) @ ( D @ ( A @ ( B @ k7_borsuk_1 ) ) ) @ ( A @ ( B @ k6_borsuk_1 ) @ ( E @ m2_connsp_2 ) ) )
=> ? [F: $i] :
( ? [G: $i] :
( ( E @ ( G @ ( F @ ( C @ ( D @ ( A @ ( B @ k10_borsuk_1 ) ) ) ) ) @ r1_tarski ) )
& ( C @ ( A @ ( G @ m1_connsp_2 ) ) ) )
& ( D @ ( B @ ( F @ m2_connsp_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1194,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_borsuk_1) ).
thf(6734,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(353,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_tops_1) ).
thf(2852,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v2_tops_1 ) ) )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(844,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
<=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_tops_1) ).
thf(5077,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(718,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
<=> ( ( B @ ( A @ k1_tops_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_tops_1) ).
thf(4514,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k1_tops_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ v2_tops_1 ) ) )
& ( ( A @ ( B @ v2_tops_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(2533,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1117,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_0) ).
thf(6382,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(1169,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_0) ).
thf(6594,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( ( D @ k1_tarski @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_setwiseo) ).
thf(1847,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( ( D @ k1_tarski @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(770,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_4) ).
thf(4756,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1310,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ u1_struct_0 @ ( A @ k1_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lopclset) ).
thf(7226,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ u1_struct_0 @ ( A @ k1_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_lopclset ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lopclset) ).
thf(5974,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_lopclset ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(2222,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(835,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_filter_0) ).
thf(5027,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(7959,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7285,1378]) ).
thf(7960,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[7959]) ).
thf(7961,plain,
( ~ ( k22_borsuk_1 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( k22_borsuk_1 @ v2_pre_topc )
| ( k22_borsuk_1 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[7960:[bind(A,$thf( k22_borsuk_1 ))]]) ).
thf(7312,plain,
k22_borsuk_1 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[7309]) ).
thf(7310,plain,
~ ( k22_borsuk_1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[7309]) ).
thf(7968,plain,
( ~ ( k22_borsuk_1 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[7961,7312,7310]) ).
thf(7969,plain,
~ ( k22_borsuk_1 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) ),
inference(simp,[status(thm)],[7968]) ).
thf(1076,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
<=> ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattices) ).
thf(6176,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) )
& ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
=> ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(7673,plain,
( ( ( sk372 @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6101,6952]) ).
thf(7674,plain,
( ( sk372 @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7673]) ).
thf(7677,plain,
sk372 != sk302,
inference(simp,[status(thm)],[7674]) ).
thf(335,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tops_1) ).
thf(2777,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(13532,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ~ ( A @ v3_realset2 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,1377]) ).
thf(13533,plain,
! [A: $i] :
( ~ ( A @ v3_realset2 )
| ( sk1 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[13532:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(2017,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(6983,plain,
sk376 @ v1_funct_1,
inference(cnfConj,[status(thm)],[6980]) ).
thf(1318,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_filter_1 ) )
=> ( A @ ( B @ r1_filter_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_filter_1) ).
thf(7258,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_filter_1 ) )
=> ( A @ ( B @ r1_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(4696,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(827,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k2_tops_1 ) @ v3_tops_1 ) )
& ( A @ ( B @ ( A @ k2_tops_1 ) @ v2_tops_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_tops_1) ).
thf(4988,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k2_tops_1 ) @ v3_tops_1 ) )
& ( A @ ( B @ ( A @ k2_tops_1 ) @ v2_tops_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_subset_1) ).
thf(1412,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( B @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
& ( ( C @ ( B @ r1_tarski ) )
| ~ ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[1412]) ).
thf(1415,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( B @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1413]) ).
thf(922,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(5433,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(296,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_4) ).
thf(2616,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1322,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k12_lopclset @ ( A @ ( A @ k13_lopclset @ m1_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_lopclset) ).
thf(7268,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k12_lopclset @ ( A @ ( A @ k13_lopclset @ m1_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(8278,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6174,8267]) ).
thf(8279,plain,
( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8278]) ).
thf(8284,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
!= sk311 ),
inference(simp,[status(thm)],[8279]) ).
thf(1324,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v3_filter_0 )
& ( A @ v3_filter_0 ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v3_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_1) ).
thf(7273,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v3_filter_0 )
=> ( ( B @ v3_filter_0 )
& ( A @ v3_filter_0 ) ) )
& ( ( ( B @ v3_filter_0 )
& ( A @ v3_filter_0 ) )
=> ( B @ ( A @ k8_filter_1 ) @ v3_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(2794,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(1285,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k13_lopclset )
= ( A @ k8_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k13_lopclset) ).
thf(7144,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k13_lopclset )
= ( A @ k8_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(4329,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_relat_1) ).
thf(1811,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(1445,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1446,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C = F )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( B = E )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( A = D )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1445]) ).
thf(1447,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1446]) ).
thf(1450,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( A = D )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) ) ),
inference(lifteq,[status(thm)],[1447]) ).
thf(1332,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_filter_1 )
= ( A @ a_1_0_filter_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_1) ).
thf(7300,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k9_filter_1 )
= ( A @ a_1_0_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).
thf(3724,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(364,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) )
= ( D @ ( C @ ( A @ k4_filter_0 ) ) @ ( B @ ( A @ k4_filter_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_filter_1) ).
thf(2893,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) )
= ( D @ ( C @ ( A @ k4_filter_0 ) ) @ ( B @ ( A @ k4_filter_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(263,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
thf(2469,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(589,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(4001,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
& ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(5333,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(783,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) )
= ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ( A @ v11_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattices) ).
thf(4820,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) )
= ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ( A @ v11_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(1416,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( C @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( B @ r1_xboole_0 ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1417,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
& ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
| ~ ( C @ ( B @ r1_xboole_0 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[1416]) ).
thf(1418,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
| ~ ( C @ ( B @ r1_xboole_0 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1417]) ).
thf(205,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(2236,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(6745,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(1156,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k5_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v10_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v3_lattices )
& ~ ( B @ ( A @ k5_filter_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_1) ).
thf(6534,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k5_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v10_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v3_lattices )
& ~ ( B @ ( A @ k5_filter_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(1348,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( A @ ( B @ k8_filter_1 ) @ ( B @ ( A @ k8_filter_1 ) @ r1_filter_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_1) ).
thf(7376,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( A @ ( B @ k8_filter_1 ) @ ( B @ ( A @ k8_filter_1 ) @ r1_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(791,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_3 @ k1_funct_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_3) ).
thf(4847,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_3 @ k1_funct_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(954,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_0) ).
thf(5558,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1033,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r3_lattice4 ) ) )
& ( A @ v13_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice4) ).
thf(5946,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r3_lattice4 ) ) )
& ( A @ v13_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(121,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(1864,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice4) ).
thf(1381,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1381]) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ),
inference(lifteq,[status(thm)],[1382]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(4134,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1252,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( B @ ( A @ k3_lopclset ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_lopclset) ).
thf(7015,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( B @ ( A @ k3_lopclset ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(210,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_lattice4 ) @ ( A @ k7_lattices ) )
= ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice4) ).
thf(2254,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_lattice4 ) @ ( A @ k7_lattices ) )
= ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(3569,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(8016,plain,
! [A: $i] :
( ( ( sk391 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7401,1378]) ).
thf(8017,plain,
! [A: $i] :
( ( ( sk391 @ l1_pre_topc )
!= ( A @ l1_pre_topc ) )
| ~ ( A @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(simp,[status(thm)],[8016]) ).
thf(8018,plain,
( ~ ( sk391 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ ( sk391 @ v2_pre_topc )
| ( sk391 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[8017:[bind(A,$thf( sk391 ))]]) ).
thf(1005,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(5805,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(2034,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(8288,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
= A )
| ~ $true
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6502,7766]) ).
thf(8289,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
= A )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8288]) ).
thf(8400,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( k23_borsuk_1 != A )
| ( ( A @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
= A )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8289]) ).
thf(8433,plain,
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( ( k23_borsuk_1 @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
= k23_borsuk_1 )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8400]) ).
thf(12703,plain,
( ( sk1 != k22_borsuk_1 )
| ( ( k23_borsuk_1 @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
= k23_borsuk_1 )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8433]) ).
thf(855,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_lattice2) ).
thf(5135,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(450,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(3300,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(3093,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(4115,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(996,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(5761,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relat_1) ).
thf(1581,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k3_relat_1 )
= ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1127,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ v4_pre_topc ) )
<=> ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_pre_topc) ).
thf(6438,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ v4_pre_topc ) ) )
& ( ( B @ ( C @ v4_pre_topc ) )
=> ? [D: $i] :
( ( ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) )
= C )
& ( A @ ( D @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(4162,plain,
sk161 @ v1_relat_1,
inference(cnfConj,[status(thm)],[4160]) ).
thf(7889,plain,
( ( ( sk379 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6982,6996]) ).
thf(7890,plain,
( ( sk379 @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7889]) ).
thf(7899,plain,
sk379 != sk376,
inference(simp,[status(thm)],[7890]) ).
thf(10398,plain,
! [A: $i] :
( ( ( A @ sk267 @ v1_xboole_0 )
!= ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5653,8267]) ).
thf(10399,plain,
! [A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
!= ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10398]) ).
thf(10404,plain,
! [A: $i] :
( ( A @ sk267 )
!= ( k1_xboole_0 @ k5_finsub_1 ) ),
inference(simp,[status(thm)],[10399]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(2367,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(536,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(3712,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1144,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_connsp_2 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ ( D @ m2_connsp_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_borsuk_1) ).
thf(6491,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_connsp_2 ) ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ ( D @ m2_connsp_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_1) ).
thf(2371,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(864,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v3_borsuk_1 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_borsuk_1) ).
thf(5169,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) )
=> ( B @ ( A @ ( C @ v3_borsuk_1 ) ) ) )
& ( ( B @ ( A @ ( C @ v3_borsuk_1 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(600,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ r1_pre_topc ) )
<=> ( ( A @ k2_pre_topc )
= ( B @ ( A @ u1_struct_0 @ k5_setfam_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
thf(4040,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( A @ k2_pre_topc )
= ( B @ ( A @ u1_struct_0 @ k5_setfam_1 ) ) )
=> ( B @ ( A @ r1_pre_topc ) ) )
& ( ( B @ ( A @ r1_pre_topc ) )
=> ( ( A @ k2_pre_topc )
= ( B @ ( A @ u1_struct_0 @ k5_setfam_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice2) ).
thf(2982,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) ) )
& ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(1358,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(7404,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(7405,plain,
( ( sk393 @ v3_lattices )
& ~ ( sk393 @ v3_struct_0 )
& ( sk393 @ l3_lattices ) ),
inference(cnf,[status(esa)],[7404]) ).
thf(7408,plain,
sk393 @ v3_lattices,
inference(cnfConj,[status(thm)],[7405]) ).
thf(1360,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices @ ( A @ k7_lattices ) )
= ( A @ k5_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice4) ).
thf(7413,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices @ ( A @ k7_lattices ) )
= ( A @ k5_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k3_lopclset ) ) @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lopclset) ).
thf(5572,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k3_lopclset ) ) @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(7697,plain,
( ( ( sk379 @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6174,6996]) ).
thf(7698,plain,
( ( sk379 @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7697]) ).
thf(7707,plain,
sk379 != sk311,
inference(simp,[status(thm)],[7698]) ).
thf(1130,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_1) ).
thf(6451,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1179,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r3_relat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_filter_0) ).
thf(6631,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r3_relat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(398,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( ( A @ v2_funct_1 )
& ( B @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_1) ).
thf(3068,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( ( A @ v2_funct_1 )
& ( B @ v2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(2618,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).
thf(2833,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r1_realset1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(913,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(5401,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(909,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k1_funct_3 ) )
<=> ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k9_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_3) ).
thf(5379,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k9_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_zfmisc_1 ) ) )
=> ( B
= ( A @ k1_funct_3 ) ) )
& ( ( B
= ( A @ k1_funct_3 ) )
=> ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k9_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_zfmisc_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(789,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r1_tarski ) )
=> ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_setwiseo) ).
thf(4842,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r1_tarski ) )
=> ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(8310,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ~ $true
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[6502,7588]) ).
thf(8311,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8310]) ).
thf(8404,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( k23_borsuk_1 != A )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8311]) ).
thf(8437,plain,
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( ( k23_borsuk_1 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= k23_borsuk_1 ) ),
inference(simp,[status(thm)],[8404]) ).
thf(8454,plain,
( ( sk1 != k22_borsuk_1 )
| ( ( k23_borsuk_1 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= k23_borsuk_1 ) ),
inference(simp,[status(thm)],[8437]) ).
thf(975,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) @ ( B @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( B @ r2_hidden ) )
& ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tops_1) ).
thf(5643,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i,C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ r2_hidden ) )
& ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k1_tops_1 ) @ ( B @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( B @ r2_hidden ) )
& ( C @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(1197,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k3_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
thf(6740,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k3_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(1338,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lattice4) ).
thf(7336,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k10_relat_1 ) @ ( B @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( A @ ( B @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_setwiseo) ).
thf(4504,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k10_relat_1 ) @ ( B @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( A @ ( B @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(999,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( C @ v1_pre_topc ) )
=> ( ( C
= ( B @ ( A @ k6_borsuk_1 ) ) )
<=> ( ( ( C @ u1_pre_topc )
= ( C @ ( B @ ( A @ a_3_0_borsuk_1 ) ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_borsuk_1) ).
thf(5772,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( C @ v1_pre_topc ) )
=> ( ( ( ( ( C @ u1_pre_topc )
= ( C @ ( B @ ( A @ a_3_0_borsuk_1 ) ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) ) ) )
=> ( C
= ( B @ ( A @ k6_borsuk_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k6_borsuk_1 ) ) )
=> ( ( ( C @ u1_pre_topc )
= ( C @ ( B @ ( A @ a_3_0_borsuk_1 ) ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(273,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) )
= ( C @ ( A @ u1_struct_0 @ k3_subset_1 ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tops_1) ).
thf(2523,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) )
= ( C @ ( A @ u1_struct_0 @ k3_subset_1 ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(275,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(2530,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setwiseo) ).
thf(1392,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1392]) ).
thf(1394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( A @ v1_xboole_0 )
| ( ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( D @ ( A @ k2_setwiseo ) @ ( B @ ( A @ k10_setwiseo ) ) ) ) ) ),
inference(lifteq,[status(thm)],[1393]) ).
thf(10386,plain,
! [A: $i] :
( ( ( A @ sk267 @ v1_xboole_0 )
!= ( sk379 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5653,6996]) ).
thf(10387,plain,
! [A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
!= ( sk379 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10386]) ).
thf(10405,plain,
! [A: $i] :
( ( A @ sk267 )
!= sk379 ),
inference(simp,[status(thm)],[10387]) ).
thf(333,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k6_lopclset @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k6_lopclset @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_lopclset @ k3_lattices ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_lopclset) ).
thf(2772,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k6_lopclset @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k6_lopclset @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_lopclset @ k3_lattices ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(420,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(3157,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(876,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relat_1) ).
thf(5246,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(1526,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ~ ( B @ ( D @ r2_hidden ) ) )
& ( ~ ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(2181,plain,
! [A: $i] : ( A @ k1_tarski @ v1_finset_1 ),
inference(cnfConj,[status(thm)],[2179]) ).
thf(2182,plain,
! [A: $i] : ( A @ k1_tarski @ v1_finset_1 ),
inference(simp,[status(thm)],[2181]) ).
thf(10056,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( k1_xboole_0 @ k5_finsub_1 @ v1_finset_1 ) ),
inference(paramod_ordered,[status(thm)],[1896,2182]) ).
thf(10057,plain,
k1_xboole_0 @ k5_finsub_1 @ v1_finset_1,
inference(pattern_uni,[status(thm)],[10056:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1200,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice4) ).
thf(6772,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1217,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(6863,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(1306,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( B @ ( A @ k3_filter_0 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_0) ).
thf(7213,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( B @ ( A @ k3_filter_0 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(8164,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6982,2180]) ).
thf(8165,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk376 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8164]) ).
thf(8173,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk376 ),
inference(simp,[status(thm)],[8165]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(1431,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ k1_funct_1 ) )
= B )
| ~ ( A @ ( C @ r2_hidden ) )
| ~ ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1431]) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ r2_hidden ) )
| ~ ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( ( C @ ( D @ k1_funct_1 ) )
= B ) ),
inference(lifteq,[status(thm)],[1432]) ).
thf(937,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r8_relat_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_filter_0) ).
thf(5489,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r8_relat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(520,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(3588,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k10_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( D @ k1_funct_1 ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice2) ).
thf(4379,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( D @ k1_funct_1 ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1011,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_filter_0) ).
thf(5819,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(7893,plain,
( ( ( sk376 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6982,3670]) ).
thf(7894,plain,
( ( sk376 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7893]) ).
thf(7900,plain,
sk376 != sk129,
inference(simp,[status(thm)],[7894]) ).
thf(14994,plain,
! [B: $i,A: $i] :
( ( B != sk376 )
| ( A != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7900]) ).
thf(14995,plain,
! [A: $i] :
( ( A != sk129 )
| ( sk376 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14994:[bind(A,$thf( A )),bind(B,$thf( sk376 ))]]) ).
thf(15321,plain,
sk376 @ k1_tarski @ ( sk129 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14995]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k10_relat_1 ) @ v1_finset_1 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finset_1) ).
thf(3906,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k10_relat_1 ) @ v1_finset_1 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(1521,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1334,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k7_lopclset )
= ( A @ a_1_1_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lopclset) ).
thf(7305,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k7_lopclset )
= ( A @ a_1_1_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(1312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k1_filter_1 ) ) )
= ( B @ ( C @ ( A @ k1_filter_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k1_filter_1) ).
thf(7230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k1_filter_1 ) ) )
= ( B @ ( C @ ( A @ k1_filter_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(1302,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_filter_1) ).
thf(7197,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(6856,plain,
sk363 @ l2_struct_0,
inference(cnf,[status(esa)],[6855]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(6731,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(2364,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(5545,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(4557,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(455,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v3_realset2 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_realset2) ).
thf(3318,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B = C ) ) )
=> ( A @ v3_realset2 ) )
& ( ( A @ v3_realset2 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_filter_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_1) ).
thf(1708,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(943,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( B @ ( A @ k8_lopclset @ k1_funct_1 ) @ ( C @ r2_hidden ) )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( A @ ( C @ v1_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lopclset) ).
thf(5519,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( ( ( C @ ( B @ r2_hidden ) )
& ( A @ ( C @ v1_filter_0 ) ) )
=> ( B @ ( A @ k8_lopclset @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k8_lopclset @ k1_funct_1 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ r2_hidden ) )
& ( A @ ( C @ v1_filter_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(1094,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k6_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_0) ).
thf(6282,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k6_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_1) ).
thf(1651,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1161,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ u1_pre_topc @ ( C @ k3_tarski @ r2_hidden ) )
<=> ( B @ ( A @ k16_borsuk_1 ) @ u1_pre_topc @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_borsuk_1) ).
thf(6560,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k16_borsuk_1 ) @ u1_pre_topc @ ( C @ r2_hidden ) )
=> ( A @ u1_pre_topc @ ( C @ k3_tarski @ r2_hidden ) ) )
& ( ( A @ u1_pre_topc @ ( C @ k3_tarski @ r2_hidden ) )
=> ( B @ ( A @ k16_borsuk_1 ) @ u1_pre_topc @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(2910,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(2204,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(451,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice2) ).
thf(3303,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(14386,plain,
! [B: $i,A: $i] :
( ( B != sk161 )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7514]) ).
thf(14387,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk161 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14386:[bind(A,$thf( A )),bind(B,$thf( sk161 ))]]) ).
thf(15099,plain,
sk161 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14387]) ).
thf(15967,plain,
sk161 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ),
inference(rewrite,[status(thm)],[15099,1896]) ).
thf(10353,plain,
! [A: $i] :
( ( ( A @ sk104 @ v1_xboole_0 )
!= ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,8267]) ).
thf(10354,plain,
! [A: $i] :
( ( A @ sk104 @ v1_xboole_0 )
!= ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10353]) ).
thf(10362,plain,
! [A: $i] :
( ( A @ sk104 )
!= ( k1_xboole_0 @ k5_finsub_1 ) ),
inference(simp,[status(thm)],[10354]) ).
thf(1046,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k7_lattices ) ) )
<=> ( B @ ( C @ ( A @ r2_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattices) ).
thf(6015,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r2_lattices ) ) )
=> ( C
= ( B @ ( A @ k7_lattices ) ) ) )
& ( ( C
= ( B @ ( A @ k7_lattices ) ) )
=> ( B @ ( C @ ( A @ r2_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(1329,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ r1_filter_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_filter_1) ).
thf(7286,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ r1_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(585,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) @ ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k7_borsuk_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_borsuk_1) ).
thf(3984,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ k1_tops_1 ) )
= ( D @ ( B @ k1_tops_1 ) @ ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k7_borsuk_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(2646,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(13016,plain,
! [B: $i,A: $i] :
( ( A != sk376 )
| ( B != sk372 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7903]) ).
thf(13017,plain,
! [A: $i] :
( ( A != sk372 )
| ( A @ k1_tarski @ ( sk376 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[13016:[bind(A,$thf( sk376 ))]]) ).
thf(15379,plain,
sk372 @ k1_tarski @ ( sk376 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[13017]) ).
thf(1259,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(7037,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ k3_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_3) ).
thf(5017,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ k3_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(5438,plain,
sk257 @ v1_funct_1,
inference(cnfConj,[status(thm)],[5436]) ).
thf(984,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(5697,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(1050,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v14_lattices )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k6_lattices )
= ( A @ k6_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_filter_0) ).
thf(6058,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v14_lattices )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k6_lattices )
= ( A @ k6_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(2118,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(5034,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1253,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_0) ).
thf(7019,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1218,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(6865,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(4076,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1249,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).
thf(7005,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(1098,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_lopclset) ).
thf(6307,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_lopclset @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ v4_pre_topc ) )
& ( B @ ( C @ v3_pre_topc ) )
& ( A = C )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(395,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k5_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice4) ).
thf(3054,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) )
=> ( B
= ( A @ k5_lattice4 ) ) )
& ( ( B
= ( A @ k5_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(946,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_0) ).
thf(5540,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(4031,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(2621,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(674,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k1_pre_topc )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(4312,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k1_pre_topc )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(3550,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1136,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ u1_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(6464,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ u1_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(852,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(5122,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(1280,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_lattice4) ).
thf(7129,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(810,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(4925,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(6092,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(548,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(3795,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(289,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k8_funct_2 ) ) ) )
= C )
& ( A @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_borsuk_1) ).
thf(2589,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k8_funct_2 ) ) ) )
= C )
& ( A @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(2409,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(1748,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1749,plain,
~ ? [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= k1_xboole_0 ),
inference(miniscope,[status(thm)],[1748]) ).
thf(1750,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(cnf,[status(esa)],[1749]) ).
thf(1751,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1750]) ).
thf(18470,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( B @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1896,1751]) ).
thf(18471,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[18470:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(18493,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k5_finsub_1 @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[18471]) ).
thf(993,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k10_filter_0 ) ) )
<=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
<=> ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) )
& ( A @ u1_struct_0 @ ( C @ k3_relat_1 @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_filter_0) ).
thf(5734,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
=> ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) )
& ( A @ u1_struct_0 @ ( C @ k3_relat_1 @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k10_filter_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_filter_0 ) ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
=> ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) )
& ( A @ u1_struct_0 @ ( C @ k3_relat_1 @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) @ k3_tarski )
= ( B @ ( A @ a_2_0_borsuk_1 ) @ k3_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_borsuk_1) ).
thf(4920,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) @ k3_tarski )
= ( B @ ( A @ a_2_0_borsuk_1 ) @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1114,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(6371,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(2133,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(7580,plain,
( ( ( sk257 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5440,4161]) ).
thf(7581,plain,
( ( sk257 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7580]) ).
thf(7583,plain,
sk257 != sk161,
inference(simp,[status(thm)],[7581]) ).
thf(14570,plain,
! [B: $i,A: $i] :
( ( B != sk257 )
| ( A != sk161 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7583]) ).
thf(14571,plain,
! [A: $i] :
( ( A != sk161 )
| ( sk257 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14570:[bind(A,$thf( A )),bind(B,$thf( sk257 ))]]) ).
thf(15169,plain,
sk257 @ k1_tarski @ ( sk161 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14571]) ).
thf(10396,plain,
! [B: $i,A: $i] :
( ( ( A @ sk267 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5653,2180]) ).
thf(10397,plain,
! [B: $i,A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10396]) ).
thf(10409,plain,
! [B: $i,A: $i] :
( ( A @ sk267 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[10397]) ).
thf(941,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
=> ( ( B @ ( A @ a_2_1_lattice4 ) )
= ( B @ ( A @ k3_lattice4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice4) ).
thf(5507,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
=> ( ( B @ ( A @ a_2_1_lattice4 ) )
= ( B @ ( A @ k3_lattice4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(749,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tops_1) ).
thf(4661,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(6079,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(554,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relat_1) ).
thf(3827,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(972,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( F @ ( E @ ( B @ r2_lattices ) ) )
& ( D @ ( C @ ( A @ r2_lattices ) ) ) )
<=> ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r2_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_1) ).
thf(5630,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r2_lattices ) ) )
=> ( ( F @ ( E @ ( B @ r2_lattices ) ) )
& ( D @ ( C @ ( A @ r2_lattices ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ r2_lattices ) ) )
& ( D @ ( C @ ( A @ r2_lattices ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ r2_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(343,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k5_relat_1 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( A @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_relat_1) ).
thf(2805,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k5_relat_1 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( A @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1102,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_0) ).
thf(6328,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(582,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relat_1) ).
thf(3972,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k5_filter_1 ) @ u1_struct_0 @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_1) ).
thf(6605,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k5_filter_1 ) @ u1_struct_0 @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(279,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_qc_lang1) ).
thf(2541,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(3022,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_borsuk_1) ).
thf(4252,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(7703,plain,
( ( ( sk372 @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6174,6952]) ).
thf(7704,plain,
( ( sk372 @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7703]) ).
thf(7710,plain,
sk372 != sk311,
inference(simp,[status(thm)],[7704]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_lattices ) ) )
<=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
thf(1487,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= C )
=> ( C @ ( B @ ( A @ r1_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(4449,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_lattices ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(4493,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_lattices ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(665,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( A @ ( E @ m1_connsp_2 ) ) )
=> ! [F: $i] :
( ( D @ ( B @ ( F @ m1_connsp_2 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k8_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ ( F @ ( E @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ m1_connsp_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_borsuk_1) ).
thf(4284,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( A @ ( E @ m1_connsp_2 ) ) )
=> ! [F: $i] :
( ( D @ ( B @ ( F @ m1_connsp_2 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k8_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ ( F @ ( E @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ m1_connsp_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(7690,plain,
( ( ( sk304 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6115,4161]) ).
thf(7691,plain,
( ( sk304 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7690]) ).
thf(7692,plain,
sk304 != sk161,
inference(simp,[status(thm)],[7691]) ).
thf(18590,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ~ ( A @ v3_realset2 )
| ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1896,13533]) ).
thf(18591,plain,
( ~ ( k1_xboole_0 @ v3_realset2 )
| ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[18590:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(19208,plain,
( ( ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) )
!= ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) )
| ~ $true
| ~ ( k1_xboole_0 @ v3_realset2 ) ),
inference(paramod_ordered,[status(thm)],[18591,19130]) ).
thf(19209,plain,
( ( ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) )
!= ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) )
| ~ ( k1_xboole_0 @ v3_realset2 ) ),
inference(simp,[status(thm)],[19208]) ).
thf(19262,plain,
( ( ( sk1 @ k1_tarski )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ~ ( k1_xboole_0 @ v3_realset2 ) ),
inference(simp,[status(thm)],[19209]) ).
thf(19300,plain,
( ( ( sk1 @ k1_tarski )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ~ ( k1_xboole_0 @ v3_realset2 ) ),
inference(simp,[status(thm)],[19262]) ).
thf(19369,plain,
( ( ( sk1 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ~ ( k1_xboole_0 @ v3_realset2 ) ),
inference(paramod_ordered,[status(thm)],[1896,19300]) ).
thf(19370,plain,
( ( ( sk1 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ~ ( k1_xboole_0 @ v3_realset2 ) ),
inference(simp,[status(thm)],[19369]) ).
thf(19396,plain,
( ( sk1 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_realset2 ) ),
inference(simp,[status(thm)],[19370]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(2396,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1317,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v11_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_lattice2) ).
thf(7244,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v11_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) )
=> ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v11_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(498,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k2_pre_topc )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(3514,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k2_pre_topc )
= ( A @ u1_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(595,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finset_1) ).
thf(4021,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(1349,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice4) ).
thf(7378,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(546,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
thf(3778,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ r2_hidden ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(444,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(3286,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(5843,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_subset_1) ).
thf(2433,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1370,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k1_lattice2 )
= ( B @ k1_lattice2 @ ( A @ k1_lattice2 @ k8_filter_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_1) ).
thf(7449,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k1_lattice2 )
= ( B @ k1_lattice2 @ ( A @ k1_lattice2 @ k8_filter_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(928,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5460,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(1624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
= ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1386]) ).
thf(1388,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ),
inference(lifteq,[status(thm)],[1387]) ).
thf(7522,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ~ $true
| ( A @ v3_struct_0 )
| ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1379,1388]) ).
thf(7523,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ),
inference(simp,[status(thm)],[7522]) ).
thf(7524,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ~ ( sk1 @ v17_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( sk1 @ k5_lattice4 @ ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ ( sk1 @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( A @ ( sk1 @ k7_lattices ) @ ( sk1 @ k5_lattice4 @ ( B @ ( sk1 @ ( sk1 @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( sk1 @ k4_lattices ) ) ) ) ),
inference(pattern_uni,[status(thm)],[7523:[bind(A,$thf( sk1 ))]]) ).
thf(7538,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ~ ( sk1 @ v17_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( sk1 @ k5_lattice4 @ ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ ( sk1 @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( A @ ( sk1 @ k7_lattices ) @ ( sk1 @ k5_lattice4 @ ( B @ ( sk1 @ ( sk1 @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( sk1 @ k4_lattices ) ) ) ) ),
inference(simp,[status(thm)],[7524]) ).
thf(1375,plain,
sk1 @ v17_lattices,
inference(cnfConj,[status(thm)],[1374]) ).
thf(7544,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ $true
| ~ $true
| $false
| ( ( sk1 @ k5_lattice4 @ ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ ( sk1 @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( A @ ( sk1 @ k7_lattices ) @ ( sk1 @ k5_lattice4 @ ( B @ ( sk1 @ ( sk1 @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( sk1 @ k4_lattices ) ) ) ) ),
inference(rewrite,[status(thm)],[7538,1376,1380,1375]) ).
thf(7545,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( ( sk1 @ k5_lattice4 @ ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ ( sk1 @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( A @ ( sk1 @ k7_lattices ) @ ( sk1 @ k5_lattice4 @ ( B @ ( sk1 @ ( sk1 @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( sk1 @ k4_lattices ) ) ) ) ),
inference(simp,[status(thm)],[7544]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) )
= ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice4) ).
thf(1395,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) )
= ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) )
= ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v13_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1395]) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v13_lattices )
| ~ ( A @ v10_lattices )
| ( A @ v3_struct_0 )
| ( ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ),
inference(lifteq,[status(thm)],[1396]) ).
thf(7656,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v13_lattices )
| ~ $true
| ( A @ v3_struct_0 )
| ( ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1379,1397]) ).
thf(7657,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v13_lattices )
| ( A @ v3_struct_0 )
| ( ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ),
inference(simp,[status(thm)],[7656]) ).
thf(7658,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ~ ( sk1 @ v13_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( B @ ( A @ ( sk1 @ k1_lattice4 ) @ ( sk1 @ k3_lattices ) ) )
= ( B @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( A @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ k1_lattice4 ) ) ) ),
inference(pattern_uni,[status(thm)],[7657:[bind(A,$thf( sk1 ))]]) ).
thf(7664,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ~ ( sk1 @ v13_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( B @ ( A @ ( sk1 @ k1_lattice4 ) @ ( sk1 @ k3_lattices ) ) )
= ( B @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( A @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ k1_lattice4 ) ) ) ),
inference(simp,[status(thm)],[7658]) ).
thf(7712,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( A @ m1_subset_1 ) )
| ~ $true
| ~ ( sk1 @ v13_lattices )
| $false
| ( ( B @ ( A @ ( sk1 @ k1_lattice4 ) @ ( sk1 @ k3_lattices ) ) )
= ( B @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( A @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ k1_lattice4 ) ) ) ),
inference(rewrite,[status(thm)],[7664,1376,1380]) ).
thf(7713,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ v13_lattices )
| ( ( B @ ( A @ ( sk1 @ k1_lattice4 ) @ ( sk1 @ k3_lattices ) ) )
= ( B @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( A @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ k1_lattice4 ) ) ) ),
inference(simp,[status(thm)],[7712]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(3282,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(1423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1274,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(7097,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(579,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(3940,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(3941,plain,
~ ? [A: $i,B: $i] :
( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[3940]) ).
thf(3942,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk150 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) )
& ( ( B
= ( A @ ( B @ sk150 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( B @ sk150 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( B @ sk150 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( A @ ( B @ sk150 ) @ k2_relat_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) )
& ( ( B
= ( A @ ( B @ sk150 ) @ k1_relat_1 ) )
| ( A = k1_xboole_0 ) )
& ( ( A @ ( B @ sk150 ) @ v1_funct_1 )
| ( A = k1_xboole_0 ) )
& ( ( A @ ( B @ sk150 ) @ v1_relat_1 )
| ( A = k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3941]) ).
thf(3943,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk150 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3942]) ).
thf(3957,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk150 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3943]) ).
thf(3958,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk150 ) @ v1_funct_1 ),
inference(simp,[status(thm)],[3957]) ).
thf(1315,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k6_borsuk_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_borsuk_1) ).
thf(7237,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k6_borsuk_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(2758,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(910,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finset_1) ).
thf(5391,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1025,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k5_lattices )
= ( B @ k5_lattices @ ( A @ k5_lattices @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_1) ).
thf(5879,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k5_lattices )
= ( B @ k5_lattices @ ( A @ k5_lattices @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(358,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_relat_1) ).
thf(2873,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(5492,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( ( A @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(1837,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(440,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(3269,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(1178,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k2_pre_topc @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lopclset) ).
thf(6629,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k2_pre_topc @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(7576,plain,
( ( ( sk257 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5440,3670]) ).
thf(7577,plain,
( ( sk257 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7576]) ).
thf(7584,plain,
sk257 != sk129,
inference(simp,[status(thm)],[7577]) ).
thf(14928,plain,
! [B: $i,A: $i] :
( ( A != sk257 )
| ( B != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7584]) ).
thf(14929,plain,
! [A: $i] :
( ( A != sk129 )
| ( A @ k1_tarski @ ( sk257 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14928:[bind(A,$thf( sk257 ))]]) ).
thf(15296,plain,
sk129 @ k1_tarski @ ( sk257 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14929]) ).
thf(1125,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattices) ).
thf(6432,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(2628,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k2_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(635,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(4192,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(310,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( B @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
thf(2670,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( B @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(1920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r1_xboole_0 ) )
& ( A @ ( C @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( D @ ( C @ k2_xboole_0 ) ) ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k2_tops_1 ) @ v3_tops_1 ) )
& ( A @ ( B @ ( A @ k2_tops_1 ) @ v2_tops_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_tops_1) ).
thf(4725,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k2_tops_1 ) @ v3_tops_1 ) )
& ( A @ ( B @ ( A @ k2_tops_1 ) @ v2_tops_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(1968,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(430,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(3198,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_relat_1) ).
thf(5177,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(511,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ ( B @ ( C @ v1_lattice4 ) ) ) )
=> ( F @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice4) ).
thf(3556,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ ( B @ ( C @ v1_lattice4 ) ) ) )
=> ( F @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(3578,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(7891,plain,
( ( ( sk376 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6982,1824]) ).
thf(7892,plain,
( ( sk376 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7891]) ).
thf(7902,plain,
sk376 != sk20,
inference(simp,[status(thm)],[7892]) ).
thf(1456,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) )
| ~ ( A @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1455]) ).
thf(1457,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1456]) ).
thf(838,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v4_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tops_1) ).
thf(5038,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v4_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(417,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(3143,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(3144,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(cnf,[status(esa)],[3143]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(5113,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( C @ ( B @ a_2_1_borsuk_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( C @ u1_pre_topc @ ( E @ r2_hidden ) )
& ( B @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k12_mcart_1 ) ) ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_borsuk_1) ).
thf(6392,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( ? [D: $i,E: $i] :
( ( C @ u1_pre_topc @ ( E @ r2_hidden ) )
& ( B @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k12_mcart_1 ) ) ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_borsuk_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_borsuk_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( C @ u1_pre_topc @ ( E @ r2_hidden ) )
& ( B @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ u1_struct_0 @ ( B @ u1_struct_0 @ k12_mcart_1 ) ) ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(1074,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] :
( ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_pre_topc) ).
thf(6168,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] :
( ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(978,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ~ ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ ( B @ v1_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lopclset) ).
thf(5658,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ~ ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ ( B @ v1_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
thf(2211,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1091,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k2_lattice4 ) )
= ( A @ k6_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattice4) ).
thf(6267,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k2_lattice4 ) )
= ( A @ k6_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_3) ).
thf(2313,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(541,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_1) ).
thf(3727,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) )
=> ( B @ ( A @ ( C @ m1_filter_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1183,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(6664,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(6665,plain,
( ( sk342 @ v3_lattices )
& ( sk342 @ l3_lattices ) ),
inference(cnf,[status(esa)],[6664]) ).
thf(6666,plain,
sk342 @ l3_lattices,
inference(cnfConj,[status(thm)],[6665]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(2741,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(8272,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6101,8267]) ).
thf(8273,plain,
( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8272]) ).
thf(8287,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
!= sk302 ),
inference(simp,[status(thm)],[8273]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ k3_tarski )
= ( A @ k3_tarski @ ( B @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_3) ).
thf(4461,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ k3_tarski )
= ( A @ k3_tarski @ ( B @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
thf(2228,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(596,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4027,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(5285,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1192,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattices) ).
thf(6728,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(2300,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(98,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_3) ).
thf(1772,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(2377,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(318,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( D != k1_xboole_0 )
& ( C @ ( D @ r1_tarski ) ) ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( C != k1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_tops_1) ).
thf(2692,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( D != k1_xboole_0 )
& ( C @ ( D @ r1_tarski ) ) ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( C != k1_xboole_0 ) ) )
=> ( A @ ( B @ v2_tops_1 ) ) )
& ( ( A @ ( B @ v2_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( D != k1_xboole_0 )
& ( C @ ( D @ r1_tarski ) ) ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( C != k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(5847,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(93,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_lattice4 ) @ ( A @ k7_lattices ) )
= ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice4) ).
thf(1755,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_lattice4 ) @ ( A @ k7_lattices ) )
= ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(3001,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(6075,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(618,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattices) ).
thf(4123,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funct_3) ).
thf(3615,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
<=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).
thf(1541,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(13361,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A @ v10_lattices )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,1379]) ).
thf(13362,plain,
! [A: $i] :
( ( A @ v10_lattices )
| ( sk1 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[13361:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(817,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relat_1) ).
thf(4957,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(1363,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
= ( A @ k6_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice4) ).
thf(7421,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
= ( A @ k6_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(436,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( D @ ( A @ k2_lattice4 ) ) )
& ( B @ ( A @ k4_lattice4 ) @ ( D @ r1_tarski ) ) ) )
& ( B @ ( A @ k4_lattice4 ) @ ( C @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice4) ).
thf(3254,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( D @ ( A @ k2_lattice4 ) ) )
& ( B @ ( A @ k4_lattice4 ) @ ( D @ r1_tarski ) ) ) )
& ( B @ ( A @ k4_lattice4 ) @ ( C @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(1794,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_2) ).
thf(4512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(1303,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k10_lopclset )
= ( A @ k9_lopclset @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lopclset) ).
thf(7205,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k10_lopclset )
= ( A @ k9_lopclset @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ k2_funct_4 @ k2_funct_4 )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_4) ).
thf(5238,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ k2_funct_4 @ k2_funct_4 )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(920,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= C ) )
=> ( B
= ( A @ k6_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice2) ).
thf(5423,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= C ) )
=> ( B
= ( A @ k6_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1266,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(7065,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(1167,axiom,
k22_borsuk_1 @ u1_struct_0 @ ( k24_borsuk_1 @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k24_borsuk_1) ).
thf(6589,plain,
k22_borsuk_1 @ u1_struct_0 @ ( k24_borsuk_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(8630,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k24_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ~ $true
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[6589,8116]) ).
thf(8631,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k24_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8630]) ).
thf(8662,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( k24_borsuk_1 != A )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8631]) ).
thf(8697,plain,
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( ( k24_borsuk_1 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= k24_borsuk_1 ) ),
inference(simp,[status(thm)],[8662]) ).
thf(10413,plain,
( ( sk1 != k22_borsuk_1 )
| ( ( k24_borsuk_1 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= k24_borsuk_1 ) ),
inference(simp,[status(thm)],[8697]) ).
thf(8270,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4637,8267]) ).
thf(8271,plain,
( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8270]) ).
thf(8282,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8271]) ).
thf(286,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_realset2 )
<=> ? [B: $i] :
( ( A @ u1_struct_0 )
= ( B @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_6) ).
thf(2577,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ? [B: $i] :
( ( A @ u1_struct_0 )
= ( B @ k1_tarski ) )
=> ( A @ v3_realset2 ) )
& ( ( A @ v3_realset2 )
=> ? [B: $i] :
( ( A @ u1_struct_0 )
= ( B @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1352,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset )
= ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lopclset) ).
thf(7389,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset )
= ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(939,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_0) ).
thf(5502,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1003,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
<=> ( ( A @ v14_lattices )
& ( A @ v13_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattices) ).
thf(5798,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v14_lattices )
& ( A @ v13_lattices ) )
=> ( A @ v15_lattices ) )
& ( ( A @ v15_lattices )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(721,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_tops_1) ).
thf(4525,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( C = k1_xboole_0 ) ) )
=> ( A @ ( B @ v2_tops_1 ) ) )
& ( ( A @ ( B @ v2_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( C = k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) )
| ( B = k1_xboole_0 )
| ~ ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1423]) ).
thf(1425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) )
| ~ ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( B = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1424]) ).
thf(755,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(4693,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(5583,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(580,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_tops_1) ).
thf(3963,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(4930,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1032,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k3_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(5919,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k3_tarski ) ) )
& ( ( B
= ( A @ k3_tarski ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1027,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice4) ).
thf(5889,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(7507,plain,
( ( ( sk129 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4637,3670]) ).
thf(7508,plain,
( ( sk129 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7507]) ).
thf(7513,plain,
sk129 != k1_xboole_0,
inference(simp,[status(thm)],[7508]) ).
thf(400,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v3_struct_0 )
<=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
thf(3078,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( ( A @ u1_struct_0 @ v1_xboole_0 )
=> ( A @ v3_struct_0 ) )
& ( ( A @ v3_struct_0 )
=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(801,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(4883,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(614,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] : ( B @ ( B @ ( A @ k9_relat_1 ) @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
thf(4109,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] : ( B @ ( B @ ( A @ k9_relat_1 ) @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(7794,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( sk1 @ k2_lattice4 ) )
!= ( B @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) ) )
| ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ( A = B )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[7766,7588]) ).
thf(7800,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski )
!= ( B @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) ) )
| ( sk1 != sk1 )
| ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( A = B )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7794]) ).
thf(7809,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski )
!= ( B @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) ) )
| ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( A = B )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7800]) ).
thf(425,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k4_lopclset @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k4_lopclset @ v1_funct_2 ) ) )
& ( A @ k4_lopclset @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lopclset) ).
thf(3176,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k4_lopclset @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k4_lopclset @ v1_funct_2 ) ) )
& ( A @ k4_lopclset @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(4817,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(574,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(3922,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(4983,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(701,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(4425,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(537,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k17_borsuk_1 ) @ ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_borsuk_1) ).
thf(3714,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k17_borsuk_1 ) @ ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(8162,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6101,2180]) ).
thf(8163,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8162]) ).
thf(8177,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk302 ),
inference(simp,[status(thm)],[8163]) ).
thf(429,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_0) ).
thf(3194,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(2038,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) )
=> ( ( D @ ( C @ r1_xboole_0 ) )
| ( C = D ) ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(8170,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5440,2180]) ).
thf(8171,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8170]) ).
thf(8176,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk257 ),
inference(simp,[status(thm)],[8171]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
!= C ) )
& ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_partfun1) ).
thf(1493,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
!= C ) )
& ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(677,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_filter_0) ).
thf(4320,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_3) ).
thf(1683,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(545,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) )
= ( C @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k2_tops_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tops_1) ).
thf(3775,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) )
= ( C @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k2_tops_1 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(452,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_3) ).
thf(3311,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(1300,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset )
= ( A @ a_1_0_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lopclset) ).
thf(7189,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset )
= ( A @ a_1_0_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ v1_funct_2 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_4) ).
thf(3326,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ v1_funct_2 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(863,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(5166,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(836,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 @ ( B @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(5031,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 @ ( B @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(6175,plain,
sk311 @ v1_relat_1,
inference(cnfConj,[status(thm)],[6173]) ).
thf(1154,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc ) )
=> ( ( C
= ( B @ ( A @ k3_pre_topc ) ) )
<=> ( ( C @ k2_pre_topc )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_pre_topc) ).
thf(6518,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ m1_pre_topc ) )
& ( C @ v1_pre_topc ) )
=> ( ( ( ( C @ k2_pre_topc )
= B )
=> ( C
= ( B @ ( A @ k3_pre_topc ) ) ) )
& ( ( C
= ( B @ ( A @ k3_pre_topc ) ) )
=> ( ( C @ k2_pre_topc )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(983,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k7_lopclset @ k4_xboole_0 ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lopclset) ).
thf(5694,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k7_lopclset @ k4_xboole_0 ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(14568,plain,
! [B: $i,A: $i] :
( ( A != sk257 )
| ( B != sk161 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7583]) ).
thf(14569,plain,
! [A: $i] :
( ( A != sk161 )
| ( A @ k1_tarski @ ( sk257 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14568:[bind(A,$thf( sk257 ))]]) ).
thf(15168,plain,
sk161 @ k1_tarski @ ( sk257 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14569]) ).
thf(3407,plain,
! [A: $i] : ( A @ sk104 @ v1_finset_1 ),
inference(cnfConj,[status(thm)],[3404]) ).
thf(986,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_0) ).
thf(5705,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1210,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k4_lattices ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattices) ).
thf(6844,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k4_lattices ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(433,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k6_pre_topc ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pre_topc) ).
thf(3210,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k6_pre_topc ) ) ) )
& ( ( C
= ( B @ ( A @ k6_pre_topc ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ~ ( ( E @ ( B @ r1_xboole_0 ) )
& ( E @ ( D @ r2_hidden ) )
& ( A @ ( E @ v3_pre_topc ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(1065,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ v3_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_filter_1) ).
thf(6116,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ v3_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(1279,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v17_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_1) ).
thf(7111,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v17_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v17_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(2830,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(675,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(4315,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(930,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_0) ).
thf(5464,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ r1_tarski ) )
| ~ ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1413]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ ( B @ k2_funct_1 @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k2_funct_1 @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(2240,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ ( B @ k2_funct_1 @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k2_funct_1 @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(697,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ k2_pre_topc @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tops_1) ).
thf(4406,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ k2_pre_topc @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(1584,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(5547,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(137,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(1937,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1088,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_0) ).
thf(6256,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(4861,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(4648,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(602,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(4054,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1264,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).
thf(7059,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(3671,plain,
sk129 @ v1_finset_1,
inference(cnfConj,[status(thm)],[3669]) ).
thf(525,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_1) ).
thf(3643,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1235,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k2_pre_topc @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_pre_topc) ).
thf(6946,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k2_pre_topc @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(1029,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_borsuk_1) ).
thf(5905,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v1_borsuk_1 ) )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(1889,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1336,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v11_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_1) ).
thf(7313,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v11_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) )
=> ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v11_lattices )
& ( B @ ( A @ k8_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_1 ) @ v3_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(378,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v6_group_1 )
<=> ( A @ u1_struct_0 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_group_1) ).
thf(2978,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( ( A @ u1_struct_0 @ v1_finset_1 )
=> ( A @ v6_group_1 ) )
& ( ( A @ v6_group_1 )
=> ( A @ u1_struct_0 @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(4621,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1233,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( B @ ( F @ ( E @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( ( B @ ( F @ ( D @ ( A @ k4_lattices ) ) @ ( E @ ( C @ ( A @ k4_lattices ) ) @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( B @ ( F @ ( D @ ( A @ k3_lattices ) ) @ ( E @ ( C @ ( A @ k3_lattices ) ) @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_1) ).
thf(6935,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( B @ ( F @ ( E @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( ( B @ ( F @ ( D @ ( A @ k4_lattices ) ) @ ( E @ ( C @ ( A @ k4_lattices ) ) @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( B @ ( F @ ( D @ ( A @ k3_lattices ) ) @ ( E @ ( C @ ( A @ k3_lattices ) ) @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(2649,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(4180,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(2317,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(447,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(3294,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_setwiseo ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_setwiseo) ).
thf(1744,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_setwiseo ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(577,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k9_relat_1 ) )
= ( A @ ( B @ k9_relat_1 ) @ ( C @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
thf(3935,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k9_relat_1 ) )
= ( A @ ( B @ k9_relat_1 ) @ ( C @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1052,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v12_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v12_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_filter_0) ).
thf(6065,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v12_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v12_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ r1_xboole_0 ) )
| ~ ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1417]) ).
thf(257,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(2450,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(6097,plain,
sk302 @ v1_finset_1,
inference(cnfConj,[status(thm)],[6096]) ).
thf(315,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(2681,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(351,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ ( A @ k2_tops_1 ) @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_tops_1) ).
thf(2845,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ ( B @ ( A @ k2_tops_1 ) @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(785,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(4829,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_1) ).
thf(4717,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1043,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_pre_topc) ).
thf(6005,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v1_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(655,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_pre_topc) ).
thf(4259,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(3074,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1078,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_borsuk_1 ) )
=> ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_borsuk_1) ).
thf(6186,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_borsuk_1 ) )
=> ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(2756,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_subset_1) ).
thf(1627,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(896,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ k3_tarski @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_3) ).
thf(5317,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ k3_tarski @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1019,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C
= ( B @ ( A @ k3_filter_0 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_filter_0) ).
thf(5850,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k3_filter_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_filter_0 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(1448,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1446]) ).
thf(1451,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( B = E )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) ) ),
inference(lifteq,[status(thm)],[1448]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(5149,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1284,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
<=> ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_lattices) ).
thf(7138,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) )
=> ( A @ v17_lattices ) )
& ( ( A @ v17_lattices )
=> ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(183,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
thf(2153,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(239,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relat_1) ).
thf(2387,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(8759,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5440,5811]) ).
thf(8760,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8759]) ).
thf(8764,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk257 ),
inference(simp,[status(thm)],[8760]) ).
thf(1308,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_lattices ) @ ( A @ k7_lattices ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattices) ).
thf(7221,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_lattices ) @ ( A @ k7_lattices ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(1028,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( A @ ( D @ v1_filter_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
<=> ( ( D @ ( C @ r2_hidden ) )
| ( D @ ( B @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lopclset) ).
thf(5900,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( A @ ( D @ v1_filter_0 ) )
=> ( ( ( ( D @ ( C @ r2_hidden ) )
| ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( D @ ( C @ r2_hidden ) )
| ( D @ ( B @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(148,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattice4) ).
thf(1974,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1082,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(6207,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1294,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v11_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_0) ).
thf(7169,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v11_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(1068,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(6129,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(711,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ k1_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(4482,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ k1_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1221,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(6876,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_3) ).
thf(2465,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(8573,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k24_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ~ $true
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[6589,7588]) ).
thf(8574,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k24_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8573]) ).
thf(8655,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( k24_borsuk_1 != A )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8574]) ).
thf(8690,plain,
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( ( k24_borsuk_1 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= k24_borsuk_1 ) ),
inference(simp,[status(thm)],[8655]) ).
thf(813,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) )
= ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_0) ).
thf(4934,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) )
= ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(2497,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(1108,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( A @ k4_lattice4 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(6346,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( A @ k4_lattice4 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(1255,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(7027,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(118,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(1852,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1271,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v14_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_0) ).
thf(7086,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v14_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(356,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( F @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( E @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A @ ( F @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_setwiseo) ).
thf(2862,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( E @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A @ ( F @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( E @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( E @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(8303,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ k1_tarski @ ( sk1 @ k1_lattice4 ) )
= A )
| ~ $true
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6502,8133]) ).
thf(8304,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ k1_tarski @ ( sk1 @ k1_lattice4 ) )
= A )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8303]) ).
thf(8392,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( k23_borsuk_1 != A )
| ( ( A @ k1_tarski @ ( sk1 @ k1_lattice4 ) )
= A )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8304]) ).
thf(8425,plain,
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( ( k23_borsuk_1 @ k1_tarski @ ( sk1 @ k1_lattice4 ) )
= k23_borsuk_1 )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8392]) ).
thf(806,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(4902,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(3162,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1296,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k12_lopclset )
= ( A @ k11_lopclset @ k6_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lopclset) ).
thf(7174,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k12_lopclset )
= ( A @ k11_lopclset @ k6_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t179_relat_1) ).
thf(4223,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(10394,plain,
! [B: $i,A: $i] :
( ( ( A @ sk267 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5653,5811]) ).
thf(10395,plain,
! [B: $i,A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10394]) ).
thf(10406,plain,
! [B: $i,A: $i] :
( ( A @ sk267 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[10395]) ).
thf(8160,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4637,2180]) ).
thf(8161,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8160]) ).
thf(8174,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8161]) ).
thf(10345,plain,
! [A: $i] :
( ( ( A @ sk104 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,1824]) ).
thf(10346,plain,
! [A: $i] :
( ( A @ sk104 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10345]) ).
thf(10366,plain,
! [A: $i] :
( ( A @ sk104 )
!= sk20 ),
inference(simp,[status(thm)],[10346]) ).
thf(7667,plain,
( ( ( sk379 @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6101,6996]) ).
thf(7668,plain,
( ( sk379 @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7667]) ).
thf(7678,plain,
sk379 != sk302,
inference(simp,[status(thm)],[7668]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice2) ).
thf(1814,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(281,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_filter_0 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
=> ( D @ ( E @ ( A @ r1_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_0) ).
thf(2546,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
=> ( D @ ( E @ ( A @ r1_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) )
=> ( A @ v3_filter_0 ) )
& ( ( A @ v3_filter_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
=> ( D @ ( E @ ( A @ r1_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(7407,plain,
~ ( sk393 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[7405]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
<=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
thf(4782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) ) )
& ( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(772,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k6_setfam_1 ) @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_pre_topc) ).
thf(4765,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k6_setfam_1 ) @ v4_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(561,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( A @ ( B @ m1_eqrel_1 ) )
<=> ( B = k1_xboole_0 ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( A @ ( B @ m1_eqrel_1 ) )
<=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(3856,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( ( B = k1_xboole_0 )
=> ( A @ ( B @ m1_eqrel_1 ) ) )
& ( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B = k1_xboole_0 ) ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) )
=> ( A @ ( B @ m1_eqrel_1 ) ) )
& ( ( A @ ( B @ m1_eqrel_1 ) )
=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(1189,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_tops_1) ).
thf(6716,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
<=> ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_setwiseo) ).
thf(2057,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) )
& ( ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
=> ( ( C @ ( A @ r1_tarski ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(1466,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(369,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(2915,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(829,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v4_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tops_1) ).
thf(4995,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v4_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1146,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(6497,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(4163,plain,
sk161 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4160]) ).
thf(483,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
<=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tops_1) ).
thf(3454,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ k6_pre_topc ) @ v2_tops_1 ) )
=> ( A @ ( B @ v3_tops_1 ) ) )
& ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ ( A @ k6_pre_topc ) @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
~ ( ( ( C @ k1_tarski @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).
thf(2634,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
~ ( ( ( C @ k1_tarski @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(328,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_0) ).
thf(2749,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(3903,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(1287,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k7_lopclset @ ( B @ ( A @ a_2_0_lopclset ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lopclset) ).
thf(7150,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k7_lopclset @ ( B @ ( A @ a_2_0_lopclset ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(4184,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(4212,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(802,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(4889,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(427,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_setwiseo) ).
thf(3183,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(424,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_lattice4 ) @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattice4) ).
thf(3173,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_lattice4 ) @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1216,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
=> ( ( C @ ( A @ k3_filter_0 ) )
= ( B @ ( A @ k2_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_0) ).
thf(6859,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
=> ( ( C @ ( A @ k3_filter_0 ) )
= ( B @ ( A @ k2_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(16144,plain,
! [B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( k1_xboole_0 @ ( B @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2788,10581]) ).
thf(16145,plain,
! [B: $i,A: $i] :
( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( k1_xboole_0 @ ( B @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[16144]) ).
thf(16163,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( k1_xboole_0 @ ( B @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[16145]) ).
thf(16169,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k1_tarski @ k2_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16163]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(1515,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(918,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k11_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ a_3_1_borsuk_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_borsuk_1) ).
thf(5417,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k11_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ a_3_1_borsuk_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(2189,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( D @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( B
= ( C @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1049,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ~ ( ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k7_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_subset_1) ).
thf(6038,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k7_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1330,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k11_lopclset @ k1_lopclset @ ( A @ k10_lopclset @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l49_lopclset) ).
thf(7289,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k11_lopclset @ k1_lopclset @ ( A @ k10_lopclset @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1231,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_funct_3) ).
thf(6931,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(54,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finsub_1) ).
thf(1616,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(10355,plain,
! [A: $i] :
( ( ( A @ sk104 @ v1_xboole_0 )
!= ( sk372 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,6952]) ).
thf(10356,plain,
! [A: $i] :
( ( A @ sk104 @ v1_xboole_0 )
!= ( sk372 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10355]) ).
thf(10359,plain,
! [A: $i] :
( ( A @ sk104 )
!= sk372 ),
inference(simp,[status(thm)],[10356]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(3422,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1015,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(5840,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(2338,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ~ ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1023,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_pre_topc) ).
thf(5872,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( B @ v2_pre_topc )
& ( B @ v1_pre_topc )
& ( A @ ( B @ m1_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(944,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
<=> ( A @ k1_lattice2 @ v13_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_lattice2) ).
thf(5524,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k1_lattice2 @ v13_lattices )
=> ( A @ v14_lattices ) )
& ( ( A @ v14_lattices )
=> ( A @ k1_lattice2 @ v13_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(1150,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k7_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_0) ).
thf(6507,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k7_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(214,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v5_tops_1 ) )
=> ( ( A @ ( C @ v4_tops_1 ) )
& ( A @ ( C @ v4_pre_topc ) ) ) )
& ( ( ( B @ ( D @ v4_tops_1 ) )
& ( B @ ( D @ v4_pre_topc ) ) )
=> ( B @ ( D @ v5_tops_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_tops_1) ).
thf(2292,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v5_tops_1 ) )
=> ( ( A @ ( C @ v4_tops_1 ) )
& ( A @ ( C @ v4_pre_topc ) ) ) )
& ( ( ( B @ ( D @ v4_tops_1 ) )
& ( B @ ( D @ v4_pre_topc ) ) )
=> ( B @ ( D @ v5_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(143,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tops_1) ).
thf(1959,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(7505,plain,
( ( ( sk372 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4637,6952]) ).
thf(7506,plain,
( ( sk372 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7505]) ).
thf(7512,plain,
sk372 != k1_xboole_0,
inference(simp,[status(thm)],[7506]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_lopclset ) ) )
= ( B @ ( C @ ( A @ k3_lopclset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lopclset) ).
thf(5451,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_lopclset ) ) )
= ( B @ ( C @ ( A @ k3_lopclset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1289,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice4) ).
thf(7155,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1058,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tops_1) ).
thf(6084,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1041,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( B @ l1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pre_topc) ).
thf(6001,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( B @ l1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(3396,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ v1_funct_1 )
& ( B @ ( A @ k1_funct_4 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_4) ).
thf(3343,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ v1_funct_1 )
& ( B @ ( A @ k1_funct_4 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(1291,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_filter_1 ) ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_1) ).
thf(7160,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k1_filter_1 ) ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(2121,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(2936,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(65,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_lattice4) ).
thf(1648,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(981,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ a_1_0_filter_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A
= ( D @ ( C @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k1_domain_1 ) ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(5666,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A
= ( D @ ( C @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k1_domain_1 ) ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_filter_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_filter_1 @ ( A @ r2_hidden ) )
=> ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A
= ( D @ ( C @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ k1_domain_1 ) ) ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_subset_1) ).
thf(1510,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(1764,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_borsuk_1) ).
thf(3130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(7572,plain,
( ( ( sk379 @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5440,6996]) ).
thf(7573,plain,
( ( sk379 @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7572]) ).
thf(7582,plain,
sk379 != sk257,
inference(simp,[status(thm)],[7573]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(6026,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(3358,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1207,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice4) ).
thf(6824,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(6203,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(565,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_borsuk_1 ) @ k1_tops_1 ) )
= ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_borsuk_1) ).
thf(3890,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_borsuk_1 ) @ k1_tops_1 ) )
= ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1250,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(7010,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(799,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_0) ).
thf(4874,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(699,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k5_lopclset ) )
<=> ! [C: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k3_lopclset ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lopclset) ).
thf(4412,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k3_lopclset ) ) ) ) ) )
=> ( B
= ( A @ k5_lopclset ) ) )
& ( ( B
= ( A @ k5_lopclset ) )
=> ! [C: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k3_lopclset ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(375,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_lattice2) ).
thf(2941,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) )
=> ( ( A @ l3_lattices )
& ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l3_lattices )
& ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1164,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_filter_0) ).
thf(6578,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(1205,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_filter_0) ).
thf(6792,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m1_filter_0 ) ) )
& ( ( A @ ( B @ m1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(8367,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ~ $true
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[6502,8116]) ).
thf(8368,plain,
! [A: $i] :
( ( ( k22_borsuk_1 @ u1_struct_0 @ ( k23_borsuk_1 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8367]) ).
thf(8414,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( k23_borsuk_1 != A )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[8368]) ).
thf(8448,plain,
( ( ( sk1 @ u1_struct_0 )
!= ( k22_borsuk_1 @ u1_struct_0 ) )
| ( ( k23_borsuk_1 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= k23_borsuk_1 ) ),
inference(simp,[status(thm)],[8414]) ).
thf(8771,plain,
( ( sk1 != k22_borsuk_1 )
| ( ( k23_borsuk_1 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k1_lattice4 ) )
= k23_borsuk_1 ) ),
inference(simp,[status(thm)],[8448]) ).
thf(291,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(2602,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ v1_funct_2 ) ) )
& ( C @ k1_funct_3 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_3) ).
thf(3375,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ v1_funct_2 ) ) )
& ( C @ k1_funct_3 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(564,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_setwiseo) ).
thf(3888,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_lopclset ) ) @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lopclset) ).
thf(6454,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_lopclset ) ) @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ m1_borsuk_1 ) )
& ( A @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ v2_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k20_borsuk_1) ).
thf(3839,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ m1_borsuk_1 ) )
& ( A @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ v2_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ~ ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_4) ).
thf(3523,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ~ ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(325,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(2734,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ ( B @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ k2_relat_1 @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_3) ).
thf(3111,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ ( B @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ k2_relat_1 @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(3274,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(659,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(4269,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(594,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_0) ).
thf(4017,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_lattice4 ) @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(5598,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_lattice4 ) @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k19_borsuk_1 ) ) @ m1_borsuk_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_borsuk_1) ).
thf(5241,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k19_borsuk_1 ) ) @ m1_borsuk_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(8010,plain,
( ( ( sk389 @ v2_pre_topc )
!= ( sk365 @ v2_pre_topc ) )
| ~ ( sk365 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| ( sk365 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7385,7888]) ).
thf(8011,plain,
( ( ( sk389 @ v2_pre_topc )
!= ( sk365 @ v2_pre_topc ) )
| ~ ( sk365 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ( sk365 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[8010]) ).
thf(8015,plain,
( ( sk389 != sk365 )
| ~ ( sk365 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ( sk365 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[8011]) ).
thf(1138,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ r1_filter_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_filter_0) ).
thf(6468,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ r1_filter_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1151,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ k1_lattice2 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice2) ).
thf(6510,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ k1_lattice2 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
thf(1701,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(321,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tops_1) ).
thf(2716,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_connsp_2 ) ) )
& ( C @ ( A @ ( E @ m2_connsp_2 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_borsuk_1 ) ) ) ) ) )
= ( F @ ( E @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_borsuk_1) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_connsp_2 ) ) )
& ( C @ ( A @ ( E @ m2_connsp_2 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_borsuk_1 ) ) ) ) ) )
= ( F @ ( E @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(7820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_setwiseo ) )
!= ( D @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) ) )
| ( ( B @ k1_tarski )
!= ( C @ k1_tarski ) )
| ~ ( sk1 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
| ( C = D )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1400,7809]) ).
thf(7821,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski )
!= ( B @ k1_tarski ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ( B = A )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7820:[bind(A,$thf( sk1 @ u1_struct_0 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(7828,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski )
!= ( B @ k1_tarski ) )
| ~ ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ( B = A )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7821]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(2827,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(3536,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1070,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m3_lattice4 ) )
=> ( ( C
= ( B @ ( A @ k3_lattice4 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattice4) ).
thf(6140,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m3_lattice4 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k3_lattice4 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_lattice4 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(7705,plain,
( ( ( sk311 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6174,4161]) ).
thf(7706,plain,
( ( sk311 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7705]) ).
thf(7709,plain,
sk311 != sk161,
inference(simp,[status(thm)],[7706]) ).
thf(1292,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_filter_1 ) )
<=> ? [C: $i] :
( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
& ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattice4) ).
thf(7162,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
& ( B @ ( A @ ( C @ m1_lattice4 ) ) ) )
=> ( B @ ( A @ r1_filter_1 ) ) )
& ( ( B @ ( A @ r1_filter_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
& ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( B @ ( C @ ( A @ k7_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(3547,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( B @ ( C @ ( A @ k7_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(19139,plain,
( ( ( sk152 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) )
!= ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) )
| ~ $true
| ( sk1 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[16387,19130]) ).
thf(19140,plain,
( ( ( sk152 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) )
!= ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[19139]) ).
thf(19263,plain,
( ( ( sk152 @ k1_tarski )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[19140]) ).
thf(19301,plain,
( ( ( sk152 @ k1_tarski )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[19263]) ).
thf(927,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r2_lattice4 ) ) )
& ( A @ v14_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattice4) ).
thf(5456,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r2_lattice4 ) ) )
& ( A @ v14_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1145,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( D @ ( B @ k6_pre_topc ) )
= ( B @ k2_pre_topc @ ( C @ ( A @ k6_pre_topc ) @ k3_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_pre_topc) ).
thf(6493,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( D @ ( B @ k6_pre_topc ) )
= ( B @ k2_pre_topc @ ( C @ ( A @ k6_pre_topc ) @ k3_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(8258,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k5_finsub_1 @ ( sk1 @ k1_lattice4 ) )
= A )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1896,8133]) ).
thf(8259,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ ( sk1 @ k1_lattice4 ) )
= k1_xboole_0 )
| ~ ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[8258:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k17_borsuk_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k16_borsuk_1 ) @ ( A @ ( B @ ( A @ k17_borsuk_1 ) @ v5_pre_topc ) ) )
& ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k17_borsuk_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k17_borsuk_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_borsuk_1) ).
thf(2048,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k17_borsuk_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k16_borsuk_1 ) @ ( A @ ( B @ ( A @ k17_borsuk_1 ) @ v5_pre_topc ) ) )
& ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k17_borsuk_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k17_borsuk_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ v1_funct_2 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_4) ).
thf(3925,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ v1_funct_2 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(8747,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4637,5811]) ).
thf(8748,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8747]) ).
thf(8762,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8748]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(2225,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1239,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k3_filter_0 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_0) ).
thf(6959,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k3_filter_0 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(1884,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1177,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v2_filter_0 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_0) ).
thf(6617,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) )
=> ( A @ ( B @ v2_filter_0 ) ) )
& ( ( A @ ( B @ v2_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(339,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tops_1) ).
thf(2789,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(500,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_4) ).
thf(3519,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1313,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_0) ).
thf(7233,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(489,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_lattice2) ).
thf(3472,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1267,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ! [E: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( ( C @ ( B @ ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ k2_lattices ) ) )
= ( E @ ( D @ ( A @ k3_lopclset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lopclset) ).
thf(7073,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ! [E: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( ( C @ ( B @ ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ k2_lattices ) ) )
= ( E @ ( D @ ( A @ k3_lopclset ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(1282,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k10_lopclset @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lopclset) ).
thf(7134,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k10_lopclset @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(14992,plain,
! [B: $i,A: $i] :
( ( A != sk376 )
| ( B != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7900]) ).
thf(14993,plain,
! [A: $i] :
( ( A != sk129 )
| ( A @ k1_tarski @ ( sk376 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14992:[bind(A,$thf( sk376 ))]]) ).
thf(15320,plain,
sk129 @ k1_tarski @ ( sk376 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14993]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(1752,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ k2_xboole_0 ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(2393,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_4) ).
thf(3086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(4926,plain,
sk217 @ l2_lattices,
inference(cnf,[status(esa)],[4925]) ).
thf(971,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_tops_1) ).
thf(5627,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k6_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_lattices ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(2674,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_lattices ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1402,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( E @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) )
| ~ ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1401]) ).
thf(1403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( A @ v1_xboole_0 )
| ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( E @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ),
inference(lifteq,[status(thm)],[1402]) ).
thf(484,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_0) ).
thf(3458,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
thf(6344,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(7503,plain,
( ( ( sk20 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4637,1824]) ).
thf(7504,plain,
( ( sk20 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7503]) ).
thf(7511,plain,
sk20 != k1_xboole_0,
inference(simp,[status(thm)],[7504]) ).
thf(14544,plain,
! [B: $i,A: $i] :
( ( A != sk20 )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7511]) ).
thf(14545,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk20 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14544:[bind(A,$thf( sk20 ))]]) ).
thf(15158,plain,
k1_xboole_0 @ k1_tarski @ ( sk20 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14545]) ).
thf(16727,plain,
k1_xboole_0 @ k5_finsub_1 @ ( sk20 @ k1_tarski @ r1_xboole_0 ),
inference(rewrite,[status(thm)],[15158,1896]) ).
thf(19200,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ ( sk20 @ k1_tarski @ r1_xboole_0 ) )
!= ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16727,19130]) ).
thf(19201,plain,
( ( k1_xboole_0 @ k5_finsub_1 @ ( sk20 @ k1_tarski @ r1_xboole_0 ) )
!= ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[19200]) ).
thf(19250,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ( ( sk20 @ k1_tarski )
!= ( k1_xboole_0 @ k5_finsub_1 ) ) ),
inference(simp,[status(thm)],[19201]) ).
thf(19296,plain,
( ( sk20 @ k1_tarski )
!= ( k1_xboole_0 @ k5_finsub_1 ) ),
inference(simp,[status(thm)],[19250]) ).
thf(1427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[1426]) ).
thf(1428,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) ) ) ),
inference(lifteq,[status(thm)],[1427]) ).
thf(102,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(1786,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(410,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_4) ).
thf(3118,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1118,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(6385,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(964,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(5595,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(14548,plain,
! [B: $i,A: $i] :
( ( A != sk257 )
| ( B != sk20 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7586]) ).
thf(14549,plain,
! [A: $i] :
( ( A != sk20 )
| ( A @ k1_tarski @ ( sk257 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14548:[bind(A,$thf( sk257 ))]]) ).
thf(15160,plain,
sk20 @ k1_tarski @ ( sk257 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14549]) ).
thf(1278,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(7109,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(731,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(4573,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k9_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(412,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ? [F: $i] :
( ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( F @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_lattice2) ).
thf(3123,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ? [F: $i] :
( ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( F @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1342,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v12_lattices )
& ( A @ v12_lattices ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v12_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_1) ).
thf(7347,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v12_lattices )
=> ( ( B @ v12_lattices )
& ( A @ v12_lattices ) ) )
& ( ( ( B @ v12_lattices )
& ( A @ v12_lattices ) )
=> ( B @ ( A @ k8_filter_1 ) @ v12_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(556,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( G @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(3832,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( G @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1104,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_borsuk_1 ) )
=> ( ( A @ ( B @ v2_borsuk_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ v6_compts_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_borsuk_1) ).
thf(6334,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_borsuk_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ v6_compts_1 ) ) ) )
=> ( A @ ( B @ v2_borsuk_1 ) ) )
& ( ( A @ ( B @ v2_borsuk_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ v6_compts_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(405,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tops_1) ).
thf(3091,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(10341,plain,
! [A: $i] :
( ( ( A @ sk104 @ v1_xboole_0 )
!= ( sk379 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,6996]) ).
thf(10342,plain,
! [A: $i] :
( ( A @ sk104 @ v1_xboole_0 )
!= ( sk379 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10341]) ).
thf(10361,plain,
! [A: $i] :
( ( A @ sk104 )
!= sk379 ),
inference(simp,[status(thm)],[10342]) ).
thf(961,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( D @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r2_hidden ) )
=> ( D @ ( A @ k3_filter_0 ) @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_0) ).
thf(5578,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( D @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r2_hidden ) )
=> ( D @ ( A @ k3_filter_0 ) @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(4978,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(544,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( E @ ( D @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice2) ).
thf(3773,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( E @ ( D @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( D @ ( C @ ( B @ a_3_1_borsuk_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( C @ ( F @ v3_pre_topc ) )
& ( B @ ( E @ v3_pre_topc ) )
& ( D @ ( F @ ( E @ ( C @ ( B @ k7_borsuk_1 ) ) ) @ r1_tarski ) )
& ( A
= ( F @ ( E @ ( C @ ( B @ k7_borsuk_1 ) ) ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_borsuk_1) ).
thf(5363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( ? [E: $i,F: $i] :
( ( C @ ( F @ v3_pre_topc ) )
& ( B @ ( E @ v3_pre_topc ) )
& ( D @ ( F @ ( E @ ( C @ ( B @ k7_borsuk_1 ) ) ) @ r1_tarski ) )
& ( A
= ( F @ ( E @ ( C @ ( B @ k7_borsuk_1 ) ) ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_borsuk_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_borsuk_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( C @ ( F @ v3_pre_topc ) )
& ( B @ ( E @ v3_pre_topc ) )
& ( D @ ( F @ ( E @ ( C @ ( B @ k7_borsuk_1 ) ) ) @ r1_tarski ) )
& ( A
= ( F @ ( E @ ( C @ ( B @ k7_borsuk_1 ) ) ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(2922,plain,
( ~ ? [A: $i] :
( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ? [A: $i] :
( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[2921]) ).
thf(2923,plain,
! [B: $i,A: $i] :
( ( ~ ( B @ ( B @ r1_xboole_0 ) )
| ( B = k1_xboole_0 ) )
& ( ( A != k1_xboole_0 )
| ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[2922]) ).
thf(2924,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ ( A @ r1_xboole_0 ) ) ),
inference(cnfConj,[status(thm)],[2923]) ).
thf(2926,plain,
! [A: $i] :
( ( A @ ( A @ r1_xboole_0 ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2924]) ).
thf(2927,plain,
k1_xboole_0 @ ( k1_xboole_0 @ r1_xboole_0 ),
inference(simp,[status(thm)],[2926]) ).
thf(8547,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( k1_xboole_0 @ r1_xboole_0 ) )
!= ( B @ ( A @ r1_xboole_0 ) ) )
| ~ $true
| ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[2927,1422]) ).
thf(8548,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( k1_xboole_0 @ r1_xboole_0 ) )
!= ( B @ ( A @ r1_xboole_0 ) ) )
| ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= A ) ),
inference(simp,[status(thm)],[8547]) ).
thf(8549,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_xboole_0 ) @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[8548:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(778,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(4796,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_relat_1) ).
thf(2891,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1323,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 @ ( A @ k8_filter_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_0) ).
thf(7270,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 @ ( A @ k8_filter_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(2308,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(743,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k2_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_0) ).
thf(4645,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k2_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(6667,plain,
sk342 @ v3_lattices,
inference(cnfConj,[status(thm)],[6665]) ).
thf(8276,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6115,8267]) ).
thf(8277,plain,
( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8276]) ).
thf(8286,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
!= sk304 ),
inference(simp,[status(thm)],[8277]) ).
thf(432,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(3208,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_partfun1) ).
thf(4236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l1_struct_0 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_struct_0 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_borsuk_1 ) ) @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_borsuk_1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_borsuk_1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_borsuk_1) ).
thf(3663,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l1_struct_0 )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_struct_0 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_borsuk_1 ) ) @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_borsuk_1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_borsuk_1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(1635,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ m1_pre_topc ) )
& ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ v1_borsuk_1 ) )
& ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k21_borsuk_1) ).
thf(1733,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ m1_pre_topc ) )
& ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ v1_borsuk_1 ) )
& ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(2442,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(482,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m1_borsuk_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_connsp_2 ) ) )
=> ? [E: $i] :
( ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( ( E @ ( F @ r1_tarski ) )
| ( E @ ( F @ r1_xboole_0 ) ) ) ) )
& ( D @ ( E @ r1_tarski ) )
& ( E @ ( C @ r1_tarski ) )
& ( A @ ( E @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_borsuk_1) ).
thf(3436,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_connsp_2 ) ) )
=> ? [E: $i] :
( ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( ( E @ ( F @ r1_tarski ) )
| ( E @ ( F @ r1_xboole_0 ) ) ) ) )
& ( D @ ( E @ r1_tarski ) )
& ( E @ ( C @ r1_tarski ) )
& ( A @ ( E @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) )
=> ( A @ ( B @ m1_borsuk_1 ) ) )
& ( ( A @ ( B @ m1_borsuk_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_connsp_2 ) ) )
=> ? [E: $i] :
( ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( ( E @ ( F @ r1_tarski ) )
| ( E @ ( F @ r1_xboole_0 ) ) ) ) )
& ( D @ ( E @ r1_tarski ) )
& ( E @ ( C @ r1_tarski ) )
& ( A @ ( E @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(1897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(7675,plain,
( ( ( sk302 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6101,4161]) ).
thf(7676,plain,
( ( sk302 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7675]) ).
thf(7680,plain,
sk302 != sk161,
inference(simp,[status(thm)],[7676]) ).
thf(14796,plain,
! [B: $i,A: $i] :
( ( A != sk302 )
| ( B != sk161 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7680]) ).
thf(14797,plain,
! [A: $i] :
( ( A != sk161 )
| ( A @ k1_tarski @ ( sk302 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14796:[bind(A,$thf( sk302 ))]]) ).
thf(15244,plain,
sk161 @ k1_tarski @ ( sk302 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14797]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(3641,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(1067,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( D
= ( E @ ( A @ k1_struct_0 ) ) )
& ~ ( B @ k2_pre_topc @ ( E @ r2_hidden ) ) ) )
& ~ ( C @ ( D @ r2_hidden ) )
& ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_borsuk_1) ).
thf(6123,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( D
= ( E @ ( A @ k1_struct_0 ) ) )
& ~ ( B @ k2_pre_topc @ ( E @ r2_hidden ) ) ) )
& ~ ( C @ ( D @ r2_hidden ) )
& ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(661,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_1) ).
thf(4273,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1086,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(6248,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(1638,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( B != C )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1354,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k1_lopclset @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lopclset) ).
thf(7394,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k1_lopclset @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k1_funct_4) ).
thf(4245,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(953,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattices) ).
thf(5556,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(962,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lopclset) ).
thf(5580,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).
thf(2346,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relat_1) ).
thf(5870,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(265,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) )
= ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_lattice2) ).
thf(2478,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) )
= ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(419,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(3155,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1268,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
thf(7077,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(1524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(3419,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(211,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k2_funct_1 ) )
<=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(2257,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B
= ( A @ k2_funct_1 ) ) )
& ( ( B
= ( A @ k2_funct_1 ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(2246,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1327,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset @ u1_struct_0 )
= ( A @ k1_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_lopclset) ).
thf(7282,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset @ u1_struct_0 )
= ( A @ k1_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(6340,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(4139,plain,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(535,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(3710,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k21_borsuk_1 ) ) )
= ( C @ ( B @ k16_borsuk_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k21_borsuk_1) ).
thf(4300,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k21_borsuk_1 ) ) )
= ( C @ ( B @ k16_borsuk_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( B @ ( A @ k2_lopclset ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_lopclset) ).
thf(6061,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( B @ ( A @ k2_lopclset ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1166,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k10_filter_0 ) @ k3_relat_1 )
= ( A @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_filter_0) ).
thf(6585,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k10_filter_0 ) @ k3_relat_1 )
= ( A @ u1_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(231,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( B @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tops_1) ).
thf(2361,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( B @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice2) ).
thf(2311,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_mcart_1) ).
thf(2679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(5143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ r2_hidden ) )
& ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_setwiseo) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ r2_hidden ) )
& ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(2084,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(2214,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A ) )
& ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= A )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ k3_tarski ) )
=> ( C @ ( B @ k3_subset_1 ) @ k3_tarski @ ( D @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_borsuk_1) ).
thf(2624,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= A )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ k3_tarski ) )
=> ( C @ ( B @ k3_subset_1 ) @ k3_tarski @ ( D @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_lattice2) ).
thf(5325,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ ( B @ ( A @ k2_borsuk_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( B @ ( A @ k2_borsuk_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k2_borsuk_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_borsuk_1) ).
thf(2422,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ ( B @ ( A @ k2_borsuk_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( B @ ( A @ k2_borsuk_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k2_borsuk_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(892,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
<=> ( B
= ( B @ ( A @ k2_tops_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_tops_1) ).
thf(5303,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( ( B
= ( B @ ( A @ k2_tops_1 ) ) )
=> ( A @ ( B @ v3_tops_1 ) ) )
& ( ( A @ ( B @ v3_tops_1 ) )
=> ( B
= ( B @ ( A @ k2_tops_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1367,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
<=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice4) ).
thf(7438,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) )
=> ( B @ ( A @ ( C @ v3_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(1071,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
<=> ( A @ u1_pre_topc @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_pre_topc) ).
thf(6154,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ u1_pre_topc @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( A @ u1_pre_topc @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(3500,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).
thf(3066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(365,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_tops_1) ).
thf(2896,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(1035,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(5972,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(773,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(4770,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(4771,plain,
( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(miniscope,[status(thm)],[4770]) ).
thf(4772,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[4771]) ).
thf(4773,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4772]) ).
thf(1134,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tops_1) ).
thf(6460,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_3) ).
thf(2197,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(3160,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(1073,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k1_lattice4 ) )
= ( A @ k5_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattice4) ).
thf(6165,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k1_lattice4 ) )
= ( A @ k5_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_subset_1) ).
thf(4541,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(2605,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_1) ).
thf(4009,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(449,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tops_1) ).
thf(3298,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(669,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v5_tops_1 ) )
=> ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_tops_1) ).
thf(4296,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v5_tops_1 ) )
=> ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(1254,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
<=> ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_0) ).
thf(7023,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
=> ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(1952,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(72,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
<=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
thf(1667,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( ( D @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= D ) )
& ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(951,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tops_1) ).
thf(5552,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( A @ k1_pre_topc @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(639,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k6_filter_1 ) ) @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ ( B @ ( A @ k5_filter_1 ) @ r3_lattices ) ) )
<=> ( B @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_filter_1) ).
thf(4203,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
=> ( D @ ( B @ ( A @ k6_filter_1 ) ) @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ ( B @ ( A @ k5_filter_1 ) @ r3_lattices ) ) ) )
& ( ( D @ ( B @ ( A @ k6_filter_1 ) ) @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ ( B @ ( A @ k5_filter_1 ) @ r3_lattices ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ l1_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_borsuk_1) ).
thf(6087,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ l1_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k6_borsuk_1 ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1010,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( A @ k7_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lopclset) ).
thf(5816,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( A @ k7_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(992,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(5730,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(14076,plain,
! [B: $i,A: $i] :
( ( A != sk152 )
| ( B != sk1 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7476]) ).
thf(14077,plain,
! [A: $i] :
( ( A != sk1 )
| ( A @ k1_tarski @ ( sk152 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14076:[bind(A,$thf( sk152 ))]]) ).
thf(15813,plain,
sk1 @ k1_tarski @ ( sk152 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14077]) ).
thf(16305,plain,
( ( ( sk152 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1896,15813]) ).
thf(16338,plain,
( ( sk152 != k1_xboole_0 )
| ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[16305]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(2111,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1212,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_0 ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(6849,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_0 ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(1630,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1188,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
<=> ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice4) ).
thf(6710,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) )
=> ( B @ ( A @ ( C @ v2_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(4028,plain,
sk153 @ l1_struct_0,
inference(cnf,[status(esa)],[4027]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(5335,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(5439,plain,
sk257 @ v2_funct_1,
inference(cnfConj,[status(thm)],[5436]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(4264,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(14930,plain,
! [B: $i,A: $i] :
( ( B != sk257 )
| ( A != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7584]) ).
thf(14931,plain,
! [A: $i] :
( ( A != sk129 )
| ( sk257 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14930:[bind(A,$thf( A )),bind(B,$thf( sk257 ))]]) ).
thf(15297,plain,
sk257 @ k1_tarski @ ( sk129 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14931]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(4897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(826,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( k1_xboole_0 @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_4) ).
thf(4985,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( k1_xboole_0 @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).
thf(4277,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1257,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v11_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_0) ).
thf(7033,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v11_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(423,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( ( B @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ u1_struct_0 @ k6_setfam_1 ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_pre_topc) ).
thf(3165,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( ( B @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ u1_struct_0 @ k6_setfam_1 ) ) )
& ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ r1_tarski ) )
& ( A @ ( D @ v4_pre_topc ) ) ) ) ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(1862,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(2785,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(792,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_tops_1) ).
thf(4850,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( C @ v1_tops_1 ) )
& ( A @ ( B @ v1_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1211,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_lopclset @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lopclset) ).
thf(6847,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_lopclset @ ( B @ r2_hidden ) )
=> ( A @ ( B @ v4_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(2252,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(566,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ v2_funct_1 )
=> ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) @ ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_3) ).
thf(3893,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ v2_funct_1 )
=> ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) @ ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(1820,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(491,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
<=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(3480,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) )
=> ( B @ v2_funct_1 ) )
& ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(1926,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1256,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(7030,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(6609,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(935,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_0) ).
thf(5482,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1196,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(6738,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1092,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k8_lopclset @ k1_funct_1 ) )
= ( C @ ( A @ k8_lopclset @ k1_funct_1 ) @ ( B @ ( A @ k8_lopclset @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lopclset) ).
thf(6270,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k8_lopclset @ k1_funct_1 ) )
= ( C @ ( A @ k8_lopclset @ k1_funct_1 ) @ ( B @ ( A @ k8_lopclset @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(4827,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(890,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(5299,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ k2_funct_1 @ ( B @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k1_funct_1 ) @ ( B @ k2_funct_1 @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
thf(2156,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ k2_funct_1 @ ( B @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k1_funct_1 ) @ ( B @ k2_funct_1 @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(8755,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6115,5811]) ).
thf(8756,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8755]) ).
thf(8763,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk304 ),
inference(simp,[status(thm)],[8756]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(3908,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(3490,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(790,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tops_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) @ ( A @ k1_tops_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_tops_1) ).
thf(4844,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tops_1 ) )
=> ( ( B @ ( A @ k2_tops_1 ) @ ( A @ k1_tops_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_relat_1) ).
thf(4832,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(840,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(5057,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(255,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_1 )
= ( A @ k2_funct_1 @ ( B @ k2_funct_1 @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_1) ).
thf(2439,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_1 )
= ( A @ k2_funct_1 @ ( B @ k2_funct_1 @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(323,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_0) ).
thf(2725,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(78,axiom,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(1699,plain,
! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(2171,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1129,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(6449,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tops_1) ).
thf(2481,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) )
= ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(2139,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(5248,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(2064,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(532,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
<=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_tops_1) ).
thf(3674,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ k1_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(8166,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6115,2180]) ).
thf(8167,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8166]) ).
thf(8175,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk304 ),
inference(simp,[status(thm)],[8167]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2797,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k4_xboole_0 ) )
= A )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(10390,plain,
! [A: $i] :
( ( ( A @ sk267 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5653,1824]) ).
thf(10391,plain,
! [A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10390]) ).
thf(10407,plain,
! [A: $i] :
( ( A @ sk267 )
!= sk20 ),
inference(simp,[status(thm)],[10391]) ).
thf(466,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_4) ).
thf(3363,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1365,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k7_lopclset @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lopclset) ).
thf(7434,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k7_lopclset @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(6100,plain,
sk302 @ v1_relat_1,
inference(cnfConj,[status(thm)],[6096]) ).
thf(990,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(5725,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(2535,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B
= ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( A @ ( E @ m2_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( E @ ( D @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_cat_1) ).
thf(2101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( A @ ( E @ m2_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( E @ ( D @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k20_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ k18_borsuk_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k20_borsuk_1) ).
thf(4954,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k20_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ k18_borsuk_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(2390,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1096,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m1_filter_0 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
<=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_0) ).
thf(6293,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m1_filter_0 ) ) )
& ( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(5403,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(4626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(4209,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1195,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattice4) ).
thf(6736,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(166,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) )
<=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
thf(2069,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
=> ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) ) )
& ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(6476,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(765,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(4741,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(107,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(1809,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(945,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k8_lopclset ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ a_2_0_lopclset ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lopclset) ).
thf(5528,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ a_2_0_lopclset ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) )
=> ( B
= ( A @ k8_lopclset ) ) )
& ( ( B
= ( A @ k8_lopclset ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ a_2_0_lopclset ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(1158,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) )
& ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k3_filter_0 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_0) ).
thf(6542,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) )
& ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k3_filter_0 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A )
& ( A
= ( B @ k2_relat_1 ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
thf(2652,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A )
& ( A
= ( B @ k2_relat_1 ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(994,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ k1_lopclset @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_lopclset) ).
thf(5757,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ k1_lopclset @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(360,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_lattice2) ).
thf(2878,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(6852,plain,
( ( sk362 @ v1_funct_1 )
& ( sk362 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[6851]) ).
thf(6853,plain,
sk362 @ v1_relat_1,
inference(cnfConj,[status(thm)],[6852]) ).
thf(1251,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_borsuk_1) ).
thf(7013,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(2005,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1008,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k4_lattice4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(5812,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k4_lattice4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(1319,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k9_lopclset @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lopclset) ).
thf(7260,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k9_lopclset @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(681,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k6_lattices ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattices) ).
thf(4331,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) )
=> ( B
= ( A @ k6_lattices ) ) )
& ( ( B
= ( A @ k6_lattices ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(385,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ k6_filter_1 ) ) @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ ( B @ ( A @ k5_filter_1 ) @ k4_lattices ) ) )
= ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k6_filter_1 ) ) ) )
& ( ( D @ ( B @ ( A @ k6_filter_1 ) ) @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ ( B @ ( A @ k5_filter_1 ) @ k3_lattices ) ) )
= ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k6_filter_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_1) ).
thf(3009,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ k6_filter_1 ) ) @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ ( B @ ( A @ k5_filter_1 ) @ k4_lattices ) ) )
= ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k6_filter_1 ) ) ) )
& ( ( D @ ( B @ ( A @ k6_filter_1 ) ) @ ( C @ ( B @ ( A @ k6_filter_1 ) ) @ ( B @ ( A @ k5_filter_1 ) @ k3_lattices ) ) )
= ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k6_filter_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice2) ).
thf(2054,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(640,axiom,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(4207,plain,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1223,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_0) ).
thf(6890,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(754,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tops_1) ).
thf(4690,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v4_pre_topc ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(1662,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(4394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(2614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_setwiseo ) ) )
= ( B @ ( C @ ( A @ k5_setwiseo ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_setwiseo) ).
thf(1873,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_setwiseo ) ) )
= ( B @ ( C @ ( A @ k5_setwiseo ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(480,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(3427,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1157,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_0) ).
thf(6540,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_setwiseo ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setwiseo) ).
thf(1758,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_setwiseo ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(4813,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(834,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice2) ).
thf(5025,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(7669,plain,
( ( ( sk302 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6101,1824]) ).
thf(7670,plain,
( ( sk302 @ v1_xboole_0 )
!= ( sk20 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7669]) ).
thf(7681,plain,
sk302 != sk20,
inference(simp,[status(thm)],[7670]) ).
thf(705,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tops_1 ) )
<=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) )
& ( B @ ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tops_1) ).
thf(4456,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) )
& ( B @ ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ r1_tarski ) ) )
=> ( A @ ( B @ v4_tops_1 ) ) )
& ( ( A @ ( B @ v4_tops_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) )
& ( B @ ( B @ ( A @ k6_pre_topc ) @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(531,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(3672,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(8096,plain,
( ( ( sk391 @ v2_pre_topc )
!= ( k22_borsuk_1 @ v2_pre_topc ) )
| ~ ( sk391 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| ( sk391 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7312,8018]) ).
thf(8097,plain,
( ( ( sk391 @ v2_pre_topc )
!= ( k22_borsuk_1 @ v2_pre_topc ) )
| ~ ( sk391 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ( sk391 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[8096]) ).
thf(8099,plain,
( ( sk391 != k22_borsuk_1 )
| ~ ( sk391 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ( sk391 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[8097]) ).
thf(204,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(2234,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(1990,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ( C = k1_xboole_0 )
& ( B
= ( A @ k1_tarski ) ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B = k1_xboole_0 ) )
& ~ ( ( C
= ( A @ k1_tarski ) )
& ( B
= ( A @ k1_tarski ) ) )
& ( ( A @ k1_tarski )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(2202,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(753,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(4688,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1031,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattices) ).
thf(5916,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(1162,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k10_filter_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_0) ).
thf(6564,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k10_filter_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(4355,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(1006,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v14_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_0) ).
thf(5807,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v14_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(3292,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(1246,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relat_1) ).
thf(6998,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(905,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( A @ k1_struct_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_borsuk_1) ).
thf(5358,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( A @ k1_struct_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(5133,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k1_lattice4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice4) ).
thf(4168,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k1_lattice4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1181,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(6641,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) )
=> ( B
= ( A @ k1_zfmisc_1 ) ) )
& ( ( B
= ( A @ k1_zfmisc_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(1012,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k4_filter_0 ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_0) ).
thf(5822,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k4_filter_0 ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(1066,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_0 ) @ v3_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_filter_0) ).
thf(6120,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_0 ) @ v3_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_3) ).
thf(3082,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(1566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
& ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(3260,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
& ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(722,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lopclset) ).
thf(4534,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(769,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice4) ).
thf(4754,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(2407,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( A @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_1) ).
thf(5790,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( A @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(1311,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_lattice4) ).
thf(7228,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(1045,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_0) ).
thf(6012,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_funct_1) ).
thf(4658,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(4749,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(653,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(4255,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(5570,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(16355,plain,
( ( ( sk152 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( k1_xboole_0 @ k5_finsub_1 @ ( sk1 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1896,15814]) ).
thf(16389,plain,
( ( sk152 != k1_xboole_0 )
| ( k1_xboole_0 @ k5_finsub_1 @ ( sk1 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[16355]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_realset2 )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ~ ( ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ k7_lopclset )
!= ( C @ k3_tarski ) ) )
& ( B @ k10_lopclset @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
& ( ( B @ k7_lopclset )
= ( A @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lopclset) ).
thf(5607,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_realset2 )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ~ ( ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ k7_lopclset )
!= ( C @ k3_tarski ) ) )
& ( B @ k10_lopclset @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
& ( ( B @ k7_lopclset )
= ( A @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1140,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_lattice4 ) ) )
<=> ( C @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice4) ).
thf(6472,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ v1_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_lattice4 ) ) )
=> ( C @ v2_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(687,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
= B ) ) )
=> ( ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) )
= B )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice2) ).
thf(4360,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
= B ) ) )
=> ( ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) )
= B )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(5294,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(4937,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(2975,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[2973]) ).
thf(2977,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2975]) ).
thf(848,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_tops_1) ).
thf(5111,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v3_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(934,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k6_lattices )
= ( B @ k6_lattices @ ( A @ k6_lattices @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_1) ).
thf(5478,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_1 ) @ k6_lattices )
= ( B @ k6_lattices @ ( A @ k6_lattices @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(912,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( B @ ( B @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_tops_1) ).
thf(5399,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( B @ ( B @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1170,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_borsuk_1) ).
thf(6597,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1208,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v17_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_filter_0) ).
thf(6826,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v17_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(485,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(3462,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(5074,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(1038,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r3_lattice4 ) ) )
<=> ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice4) ).
thf(5980,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) )
=> ( C @ ( B @ ( A @ r3_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattice4 ) ) )
=> ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(14452,plain,
! [B: $i,A: $i] :
( ( A != sk302 )
| ( B != sk20 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7681]) ).
thf(14453,plain,
! [A: $i] :
( ( A != sk20 )
| ( A @ k1_tarski @ ( sk302 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14452:[bind(A,$thf( sk302 ))]]) ).
thf(15122,plain,
sk20 @ k1_tarski @ ( sk302 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14453]) ).
thf(7962,plain,
( ( ( sk365 @ v2_pre_topc )
!= ( k22_borsuk_1 @ v2_pre_topc ) )
| ~ ( sk365 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| ( sk365 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7312,7888]) ).
thf(7963,plain,
( ( ( sk365 @ v2_pre_topc )
!= ( k22_borsuk_1 @ v2_pre_topc ) )
| ~ ( sk365 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ( sk365 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[7962]) ).
thf(7967,plain,
( ( sk365 != k22_borsuk_1 )
| ~ ( sk365 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ( sk365 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[7963]) ).
thf(690,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_lattice2) ).
thf(4377,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(679,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k5_lopclset @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k5_lopclset @ v1_funct_2 ) ) )
& ( A @ k5_lopclset @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lopclset) ).
thf(4324,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k5_lopclset @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( A @ k5_lopclset @ v1_funct_2 ) ) )
& ( A @ k5_lopclset @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(7682,plain,
( ( ( sk379 @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6115,6996]) ).
thf(7683,plain,
( ( sk379 @ v1_xboole_0 )
!= ( sk304 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7682]) ).
thf(7693,plain,
sk379 != sk304,
inference(simp,[status(thm)],[7683]) ).
thf(14556,plain,
! [B: $i,A: $i] :
( ( A != sk379 )
| ( B != sk304 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7693]) ).
thf(14557,plain,
! [A: $i] :
( ( A != sk304 )
| ( A @ k1_tarski @ ( sk379 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14556:[bind(A,$thf( sk379 ))]]) ).
thf(15163,plain,
sk304 @ k1_tarski @ ( sk379 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14557]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_subset_1) ).
thf(1484,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1263,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(7055,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(720,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( D
= ( C @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_borsuk_1) ).
thf(4522,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( D
= ( C @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(872,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(5235,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1449,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1446]) ).
thf(1452,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( C = F )
| ( ( C @ ( B @ ( A @ g3_lattices ) ) )
!= ( F @ ( E @ ( D @ g3_lattices ) ) ) ) ),
inference(lifteq,[status(thm)],[1449]) ).
thf(1368,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(7443,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( ( C @ ( E @ ( D @ k5_relat_1 ) @ k1_funct_1 ) )
= ( C @ ( D @ k1_funct_1 ) @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
thf(3412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( ( C @ ( E @ ( D @ k5_relat_1 ) @ k1_funct_1 ) )
= ( C @ ( D @ k1_funct_1 ) @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(88,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
=> ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( A @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_partfun1) ).
thf(1738,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ k2_xboole_0 ) )
= C )
=> ! [D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( A @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(4164,plain,
sk161 @ v1_finset_1,
inference(cnfConj,[status(thm)],[4160]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(2656,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_1) ).
thf(3019,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(4409,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(2569,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
= ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1119,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_lattices @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_filter_0) ).
thf(6389,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_lattices @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(3246,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(728,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(4561,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(683,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ k17_borsuk_1 ) @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_borsuk_1) ).
thf(4346,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ k17_borsuk_1 ) @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(2092,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(4092,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(1987,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(919,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_pre_topc )
=> ( A
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).
thf(5420,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v1_pre_topc )
=> ( A
= ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ g1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(6981,plain,
sk376 @ v1_relat_1,
inference(cnfConj,[status(thm)],[6980]) ).
thf(1321,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(7264,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(259,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ m2_relset_1 ) ) )
& ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ v1_funct_2 ) ) )
& ( A @ k3_funct_3 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_3) ).
thf(2454,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ m2_relset_1 ) ) )
& ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ v1_funct_2 ) ) )
& ( A @ k3_funct_3 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(4190,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v5_tops_1 ) )
<=> ( B
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_tops_1) ).
thf(2165,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) )
=> ( A @ ( B @ v5_tops_1 ) ) )
& ( ( A @ ( B @ v5_tops_1 ) )
=> ( B
= ( B @ ( A @ k1_tops_1 ) @ ( A @ k6_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(396,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( A @ k1_setwiseo @ ( B @ ( A @ k10_setwiseo ) ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_setwiseo) ).
thf(3063,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( A @ k1_setwiseo @ ( B @ ( A @ k10_setwiseo ) ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(10349,plain,
! [B: $i,A: $i] :
( ( ( A @ sk104 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,5811]) ).
thf(10350,plain,
! [B: $i,A: $i] :
( ( A @ sk104 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10349]) ).
thf(10360,plain,
! [B: $i,A: $i] :
( ( A @ sk104 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[10350]) ).
thf(1277,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_filter_1 ) )
<=> ( B @ k9_filter_1 @ ( A @ k9_filter_1 @ r4_wellord1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_1) ).
thf(7105,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ k9_filter_1 @ ( A @ k9_filter_1 @ r4_wellord1 ) )
=> ( B @ ( A @ r1_filter_1 ) ) )
& ( ( B @ ( A @ r1_filter_1 ) )
=> ( B @ k9_filter_1 @ ( A @ k9_filter_1 @ r4_wellord1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(831,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_filter_0) ).
thf(5015,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(539,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k1_tops_1 ) @ ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tops_1) ).
thf(3722,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k1_tops_1 ) @ ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(510,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ k2_tops_1 ) @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_tops_1) ).
thf(3554,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ k2_tops_1 ) @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1030,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v3_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
thf(5912,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v3_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(528,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_lattice2) ).
thf(3655,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1152,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r1_relat_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_filter_0) ).
thf(6513,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r1_relat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(550,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relat_1) ).
thf(3801,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(1980,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( ~ ( A @ ( C @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
& ~ ( ~ ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
& ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_finset_1) ).
thf(5309,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(10357,plain,
! [A: $i] :
( ( ( A @ sk104 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,4161]) ).
thf(10358,plain,
! [A: $i] :
( ( A @ sk104 @ v1_xboole_0 )
!= ( sk161 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10357]) ).
thf(10365,plain,
! [A: $i] :
( ( A @ sk104 )
!= sk161 ),
inference(simp,[status(thm)],[10358]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k3_tarski @ ( D @ ( C @ ( A @ k2_funct_2 ) ) ) )
= ( B @ ( D @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_3) ).
thf(3127,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k3_tarski @ ( D @ ( C @ ( A @ k2_funct_2 ) ) ) )
= ( B @ ( D @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(620,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ? [B: $i,C: $i] : ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_funct_4 @ k1_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_4) ).
thf(4132,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ? [B: $i,C: $i] : ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_funct_4 @ k1_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(947,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tops_1) ).
thf(5543,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(860,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(5152,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_lattice2) ).
thf(1538,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(973,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k1_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice4) ).
thf(5638,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k1_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_relat_1) ).
thf(4117,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(869,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_lattice2) ).
thf(5186,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ k2_funct_4 @ k2_relat_1 )
= ( C @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_4) ).
thf(5277,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ k2_funct_4 @ k2_relat_1 )
= ( C @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(380,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(2992,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(493,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice4) ).
thf(3493,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1333,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ r1_filter_1 ) )
& ( B @ ( A @ r1_filter_1 ) ) )
=> ( C @ ( A @ r1_filter_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_1) ).
thf(7303,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ r1_filter_1 ) )
& ( B @ ( A @ r1_filter_1 ) ) )
=> ( C @ ( A @ r1_filter_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_setwiseo) ).
thf(1797,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A = C )
| ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(845,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r2_borsuk_1 ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ! [E: $i] :
( ( k22_borsuk_1 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) )
& ( B @ u1_struct_0 @ ( k24_borsuk_1 @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) @ r2_hidden ) )
& ( ( k23_borsuk_1 @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) )
& ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ ( C @ v5_pre_topc ) ) )
& ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_borsuk_1) ).
thf(5083,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ! [E: $i] :
( ( k22_borsuk_1 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) )
& ( B @ u1_struct_0 @ ( k24_borsuk_1 @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) @ r2_hidden ) )
& ( ( k23_borsuk_1 @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) )
& ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ ( C @ v5_pre_topc ) ) )
& ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ r2_borsuk_1 ) ) )
& ( ( B @ ( A @ r2_borsuk_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ! [E: $i] :
( ( k22_borsuk_1 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) )
& ( B @ u1_struct_0 @ ( k24_borsuk_1 @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) @ r2_hidden ) )
& ( ( k23_borsuk_1 @ ( D @ ( k22_borsuk_1 @ ( A @ k8_borsuk_1 ) ) ) @ ( C @ ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k8_funct_2 ) ) ) )
= D ) ) )
& ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ ( C @ v5_pre_topc ) ) )
& ( A @ u1_struct_0 @ ( k22_borsuk_1 @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(573,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
= B ) ) )
=> ( ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) )
= B )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_lattice2) ).
thf(3914,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
= B ) ) )
=> ( ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) )
= B )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(14946,plain,
! [B: $i,A: $i] :
( ( B != sk311 )
| ( A != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7708]) ).
thf(14947,plain,
! [A: $i] :
( ( A != sk129 )
| ( sk311 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14946:[bind(A,$thf( A )),bind(B,$thf( sk311 ))]]) ).
thf(15304,plain,
sk311 @ k1_tarski @ ( sk129 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14947]) ).
thf(858,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(5147,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(5208,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k4_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(1187,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattice4) ).
thf(6701,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m2_lattice4 ) ) )
& ( ( A @ ( B @ m2_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(4959,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1337,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v13_lattices )
& ( A @ v13_lattices ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v13_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_1) ).
thf(7331,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v13_lattices )
=> ( ( B @ v13_lattices )
& ( A @ v13_lattices ) ) )
& ( ( ( B @ v13_lattices )
& ( A @ v13_lattices ) )
=> ( B @ ( A @ k8_filter_1 ) @ v13_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(1180,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v13_lattices )
=> ( ( ( B @ ( A @ k5_filter_1 ) @ k5_lattices )
= ( A @ k5_lattices @ ( B @ ( A @ k6_filter_1 ) ) ) )
& ( B @ ( A @ k5_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v13_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k5_filter_1 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_1) ).
thf(6633,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v13_lattices )
=> ( ( ( B @ ( A @ k5_filter_1 ) @ k5_lattices )
= ( A @ k5_lattices @ ( B @ ( A @ k6_filter_1 ) ) ) )
& ( B @ ( A @ k5_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v13_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k5_filter_1 ) @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(350,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(2838,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(6899,plain,
sk365 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[6897]) ).
thf(581,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ k15_borsuk_1 @ m1_eqrel_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_borsuk_1) ).
thf(3970,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ k15_borsuk_1 @ m1_eqrel_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(476,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
thf(3415,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(6073,plain,
sk300 @ v1_funct_1,
inference(cnfConj,[status(thm)],[6071]) ).
thf(1090,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(6262,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(738,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tops_1) ).
thf(4624,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1172,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ g1_pre_topc ) @ l1_pre_topc )
& ( B @ ( A @ g1_pre_topc ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_pre_topc) ).
thf(6601,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ g1_pre_topc ) @ l1_pre_topc )
& ( B @ ( A @ g1_pre_topc ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(1340,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k10_lopclset )
= ( A @ k11_lopclset @ k1_lopclset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lopclset) ).
thf(7342,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k10_lopclset )
= ( A @ k11_lopclset @ k1_lopclset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_4) ).
thf(4611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(11830,plain,
( ( sk1 != k22_borsuk_1 )
| ( ( k23_borsuk_1 @ k1_tarski @ ( sk1 @ k1_lattice4 ) )
= k23_borsuk_1 )
| ( sk1 @ u1_struct_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8425]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_3) ).
thf(4976,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(280,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice2) ).
thf(2543,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(5613,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1113,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_pre_topc) ).
thf(6369,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1155,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ k1_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_0) ).
thf(6526,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ k1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1142,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v3_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
& ( A @ v3_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice4) ).
thf(6479,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v3_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
& ( A @ v3_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(766,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(4745,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(4746,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[4745]) ).
thf(4748,plain,
k1_xboole_0 @ v1_relat_1,
inference(cnfConj,[status(thm)],[4746]) ).
thf(230,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_funct_3 @ v1_funct_1 )
& ( A @ k3_funct_3 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_3) ).
thf(2357,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_funct_3 @ v1_funct_1 )
& ( A @ k3_funct_3 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(142,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tops_1) ).
thf(1955,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) )
& ( ( A @ ( B @ v2_tops_1 ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 )
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(2320,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 )
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(319,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) @ ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_3) ).
thf(2711,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) @ ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(613,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k8_lopclset @ k1_funct_1 ) )
= ( C @ ( A @ k8_lopclset @ k1_funct_1 ) @ ( B @ ( A @ k8_lopclset @ k1_funct_1 ) @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lopclset) ).
thf(4106,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k8_lopclset @ k1_funct_1 ) )
= ( C @ ( A @ k8_lopclset @ k1_funct_1 ) @ ( B @ ( A @ k8_lopclset @ k1_funct_1 ) @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(625,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(4143,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(601,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k9_filter_1 @ k3_relat_1 )
= ( A @ u1_struct_0 ) )
& ( ( A @ k9_filter_1 @ k2_relat_1 )
= ( A @ u1_struct_0 ) )
& ( ( A @ k9_filter_1 @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_1) ).
thf(4046,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k9_filter_1 @ k3_relat_1 )
= ( A @ u1_struct_0 ) )
& ( ( A @ k9_filter_1 @ k2_relat_1 )
= ( A @ u1_struct_0 ) )
& ( ( A @ k9_filter_1 @ k1_relat_1 )
= ( A @ u1_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k19_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ k18_borsuk_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k19_borsuk_1) ).
thf(4538,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k19_borsuk_1 ) ) )
= ( C @ ( B @ ( A @ k18_borsuk_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(4235,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[4234]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( D @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_3) ).
thf(4267,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( D @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(84,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(1717,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(646,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
<=> ( A @ k3_tarski @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
thf(4225,plain,
! [A: $i] :
( ( ( A @ k3_tarski @ v1_finset_1 )
=> ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) ) )
& ( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
=> ( A @ k3_tarski @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(2939,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1301,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ l3_lattices )
& ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ v10_lattices )
& ~ ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lopclset) ).
thf(7192,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ l3_lattices )
& ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ v10_lattices )
& ~ ( A @ k5_lopclset @ ( A @ k4_lopclset @ ( A @ k1_lopclset @ g3_lattices ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(988,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_0) ).
thf(5717,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(932,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(5472,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( C @ ( B @ a_2_2_borsuk_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( B @ u1_pre_topc @ ( D @ k3_tarski @ r2_hidden ) )
& ( A = D )
& ( C @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_borsuk_1) ).
thf(6105,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ( ( ? [D: $i] :
( ( B @ u1_pre_topc @ ( D @ k3_tarski @ r2_hidden ) )
& ( A = D )
& ( C @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_2_borsuk_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_2_borsuk_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( B @ u1_pre_topc @ ( D @ k3_tarski @ r2_hidden ) )
& ( A = D )
& ( C @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k9_relat_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(3007,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k9_relat_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(654,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v6_compts_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_borsuk_1) ).
thf(4257,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ ( A @ k1_struct_0 ) @ v6_compts_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(751,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( C @ v1_pre_topc ) )
=> ( ( C
= ( B @ ( A @ k16_borsuk_1 ) ) )
<=> ( ( ( C @ u1_pre_topc )
= ( B @ ( A @ a_2_2_borsuk_1 ) ) )
& ( ( C @ u1_struct_0 )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_borsuk_1) ).
thf(4671,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( ( C @ l1_pre_topc )
& ( C @ v2_pre_topc )
& ( C @ v1_pre_topc ) )
=> ( ( ( ( ( C @ u1_pre_topc )
= ( B @ ( A @ a_2_2_borsuk_1 ) ) )
& ( ( C @ u1_struct_0 )
= B ) )
=> ( C
= ( B @ ( A @ k16_borsuk_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k16_borsuk_1 ) ) )
=> ( ( ( C @ u1_pre_topc )
= ( B @ ( A @ a_2_2_borsuk_1 ) ) )
& ( ( C @ u1_struct_0 )
= B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(615,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v2_tops_1 ) )
<=> ( B @ ( A @ k2_tops_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_tops_1) ).
thf(4111,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_tops_1 ) @ ( B @ r1_tarski ) )
=> ( A @ ( B @ v2_tops_1 ) ) )
& ( ( A @ ( B @ v2_tops_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1241,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k9_filter_1 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
<=> ( C @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_1) ).
thf(6975,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( A @ k9_filter_1 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
& ( ( A @ k9_filter_1 @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(1244,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_borsuk_1) ).
thf(6992,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(1309,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( B @ v2_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_pre_topc) ).
thf(7224,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( B @ v2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(694,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(4392,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(445,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
<=> ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
thf(3288,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ v1_finset_1 )
=> ( A @ k1_relat_1 @ v1_finset_1 ) )
& ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1124,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_0) ).
thf(6420,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) )
& ( ( A @ ( B @ v1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(332,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k3_funct_3 ) )
<=> ( ! [C: $i] :
( ( A @ k2_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k10_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 @ k1_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_3) ).
thf(2760,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ k2_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k10_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 @ k1_zfmisc_1 ) ) )
=> ( B
= ( A @ k3_funct_3 ) ) )
& ( ( B
= ( A @ k3_funct_3 ) )
=> ( ! [C: $i] :
( ( A @ k2_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k10_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 @ k1_zfmisc_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(4289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).
thf(3620,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(4606,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(1685,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(10114,plain,
( ( sk1 != k22_borsuk_1 )
| ( ( k24_borsuk_1 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= k24_borsuk_1 ) ),
inference(simp,[status(thm)],[8690]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(4559,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(294,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(2611,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(198,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( A @ ( B @ ( C @ ( A @ ( B @ k3_borsuk_1 ) ) @ v5_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_borsuk_1) ).
thf(2209,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( A @ ( B @ ( C @ ( A @ ( B @ k3_borsuk_1 ) ) @ v5_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(14502,plain,
! [B: $i,A: $i] :
( ( B != sk302 )
| ( A != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7679]) ).
thf(14503,plain,
! [A: $i] :
( ( A != sk129 )
| ( sk302 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14502:[bind(A,$thf( A )),bind(B,$thf( sk302 ))]]) ).
thf(15144,plain,
sk302 @ k1_tarski @ ( sk129 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14503]) ).
thf(1345,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_lopclset @ v2_pre_topc )
& ( A @ k11_lopclset @ v1_pre_topc )
& ~ ( A @ k11_lopclset @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lopclset) ).
thf(7363,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_lopclset @ v2_pre_topc )
& ( A @ k11_lopclset @ v1_pre_topc )
& ~ ( A @ k11_lopclset @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(1275,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
<=> ( A @ k1_lattice2 @ v6_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_lattice2) ).
thf(7099,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k1_lattice2 @ v6_group_1 )
=> ( A @ v6_group_1 ) )
& ( ( A @ v6_group_1 )
=> ( A @ k1_lattice2 @ v6_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( C @ k3_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relset_1) ).
thf(1918,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_xboole_0 ) @ ( C @ k3_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1265,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_pre_topc ) @ v1_pre_topc )
& ~ ( B @ ( A @ k3_pre_topc ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_pre_topc) ).
thf(7061,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_pre_topc ) @ v1_pre_topc )
& ~ ( B @ ( A @ k3_pre_topc ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(1128,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
=> ( A @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_filter_0) ).
thf(6447,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
=> ( A @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(5179,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(10343,plain,
! [A: $i] :
( ( ( A @ sk104 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3406,3670]) ).
thf(10344,plain,
! [A: $i] :
( ( A @ sk104 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10343]) ).
thf(10364,plain,
! [A: $i] :
( ( A @ sk104 )
!= sk129 ),
inference(simp,[status(thm)],[10344]) ).
thf(1297,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v14_lattices )
& ( A @ v14_lattices ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_1) ).
thf(7177,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v14_lattices )
=> ( ( B @ v14_lattices )
& ( A @ v14_lattices ) ) )
& ( ( ( B @ v14_lattices )
& ( A @ v14_lattices ) )
=> ( B @ ( A @ k8_filter_1 ) @ v14_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(1122,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_0) ).
thf(6408,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(1949,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_4) ).
thf(2870,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(4165,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_lopclset ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lopclset) ).
thf(1817,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_lopclset ) ) )
= ( C @ ( B @ k2_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1191,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r2_lattices ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_lattices) ).
thf(6721,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r2_lattices ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) )
=> ( A @ v16_lattices ) )
& ( ( A @ v16_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r2_lattices ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(979,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(5660,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(815,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_group_6) ).
thf(4944,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(2078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(830,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_borsuk_1 ) @ ( C @ v3_pre_topc ) )
<=> ? [D: $i] :
( ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ~ ( ( B @ ( G @ v3_pre_topc ) )
& ( A @ ( F @ v3_pre_topc ) )
& ( E
= ( G @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k12_mcart_1 ) ) ) ) ) ) ) )
& ( D @ ( E @ r2_hidden ) ) )
& ( C
= ( D @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) ) )
& ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_borsuk_1) ).
thf(4997,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ~ ( ( B @ ( G @ v3_pre_topc ) )
& ( A @ ( F @ v3_pre_topc ) )
& ( E
= ( G @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k12_mcart_1 ) ) ) ) ) ) ) )
& ( D @ ( E @ r2_hidden ) ) )
& ( C
= ( D @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) ) )
& ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ ( C @ v3_pre_topc ) ) )
& ( ( B @ ( A @ k6_borsuk_1 ) @ ( C @ v3_pre_topc ) )
=> ? [D: $i] :
( ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ~ ( ( B @ ( G @ v3_pre_topc ) )
& ( A @ ( F @ v3_pre_topc ) )
& ( E
= ( G @ ( F @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k12_mcart_1 ) ) ) ) ) ) ) )
& ( D @ ( E @ r2_hidden ) ) )
& ( C
= ( D @ ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k5_setfam_1 ) ) )
& ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(3188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(5510,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(67,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( D @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_setwiseo) ).
thf(1654,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( D @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(2997,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(4102,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(8280,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5440,8267]) ).
thf(8281,plain,
( ( k1_xboole_0 @ k5_finsub_1 @ v1_xboole_0 )
!= ( sk257 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8280]) ).
thf(8285,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
!= sk257 ),
inference(simp,[status(thm)],[8281]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(1575,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1222,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
& ( B
= ( A @ k1_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_0) ).
thf(6882,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
& ( B
= ( A @ k1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(631,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_lattices) ).
thf(4170,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) )
=> ( A @ v12_lattices ) )
& ( ( A @ v12_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_1) ).
thf(6743,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(936,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).
thf(5485,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(8751,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6101,5811]) ).
thf(8752,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk302 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8751]) ).
thf(8761,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk302 ),
inference(simp,[status(thm)],[8752]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(2643,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(2775,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(1866,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(8094,plain,
( ( ( sk391 @ v2_pre_topc )
!= ( sk389 @ v2_pre_topc ) )
| ~ ( sk391 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ~ $true
| ( sk391 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[7385,8018]) ).
thf(8095,plain,
( ( ( sk391 @ v2_pre_topc )
!= ( sk389 @ v2_pre_topc ) )
| ~ ( sk391 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ( sk391 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[8094]) ).
thf(8098,plain,
( ( sk391 != sk389 )
| ~ ( sk391 @ k6_lopclset @ ( sk1 @ r1_filter_1 ) )
| ( sk391 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[8095]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_3) ).
thf(1807,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(603,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ v1_funct_2 ) ) )
& ( A @ k5_lattice4 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice4) ).
thf(4061,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ v1_funct_2 ) ) )
& ( A @ k5_lattice4 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(868,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tops_1) ).
thf(5184,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( C @ ( A @ k1_tops_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(4310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(2792,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(549,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
<=> ( A @ ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
thf(3797,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v3_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1281,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k13_lopclset @ k2_relat_1 )
= ( A @ k12_lopclset @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lopclset) ).
thf(7131,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k13_lopclset @ k2_relat_1 )
= ( A @ k12_lopclset @ u1_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(879,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_pre_topc) ).
thf(5258,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( C @ ( A @ k6_pre_topc ) @ ( B @ ( A @ k6_pre_topc ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(5315,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(572,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_pre_topc @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
thf(3911,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_pre_topc @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(1174,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ v1_tops_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_borsuk_1) ).
thf(6607,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ ( C @ ( B @ ( A @ k11_borsuk_1 ) ) @ v1_tops_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(6689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(16306,plain,
( ( ( sk1 @ k1_tarski )
!= ( k1_xboole_0 @ k1_tarski ) )
| ( k1_xboole_0 @ k5_finsub_1 @ ( sk152 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1896,15813]) ).
thf(16337,plain,
( ( sk1 != k1_xboole_0 )
| ( k1_xboole_0 @ k5_finsub_1 @ ( sk152 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[16306]) ).
thf(10388,plain,
! [A: $i] :
( ( ( A @ sk267 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5653,3670]) ).
thf(10389,plain,
! [A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
!= ( sk129 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10388]) ).
thf(10411,plain,
! [A: $i] :
( ( A @ sk267 )
!= sk129 ),
inference(simp,[status(thm)],[10389]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_funct_4) ).
thf(3331,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(274,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tops_1 ) )
=> ( ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_tops_1 ) )
& ( A @ ( B @ ( A @ k1_tops_1 ) @ v4_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_tops_1) ).
thf(2526,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_tops_1 ) )
=> ( ( A @ ( B @ ( A @ k6_pre_topc ) @ v4_tops_1 ) )
& ( A @ ( B @ ( A @ k1_tops_1 ) @ v4_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1228,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( A @ ( B @ m1_pre_topc ) )
<=> ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ u1_pre_topc @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) )
& ( A @ k2_pre_topc @ ( B @ k2_pre_topc @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_pre_topc) ).
thf(6903,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ( ( ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ u1_pre_topc @ ( C @ r2_hidden ) ) )
& ( ( B @ u1_pre_topc @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ( A @ k2_pre_topc @ ( B @ k2_pre_topc @ r1_tarski ) ) )
=> ( A @ ( B @ m1_pre_topc ) ) )
& ( ( A @ ( B @ m1_pre_topc ) )
=> ( ! [C: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ u1_pre_topc @ ( C @ r2_hidden ) ) )
& ( ( B @ u1_pre_topc @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( B @ k2_pre_topc @ ( D @ k3_xboole_0 ) ) )
& ( A @ u1_pre_topc @ ( D @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) )
& ( A @ k2_pre_topc @ ( B @ k2_pre_topc @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(807,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(4913,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice2) ).
thf(2594,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(1721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1084,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k6_lopclset @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k6_lopclset @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_lopclset @ k4_lattices ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_lopclset) ).
thf(6230,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k6_lopclset @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k6_lopclset @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_lopclset @ k4_lattices ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1100,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(6322,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(1056,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( A @ ( E @ m2_connsp_2 ) ) )
=> ! [F: $i] :
( ( D @ ( B @ ( F @ m2_connsp_2 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ ( F @ ( E @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ m2_connsp_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_borsuk_1) ).
thf(6077,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( A @ ( E @ m2_connsp_2 ) ) )
=> ! [F: $i] :
( ( D @ ( B @ ( F @ m2_connsp_2 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ ( F @ ( E @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ m2_connsp_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(2174,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k10_relat_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc18_finseq_1) ).
thf(4806,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k10_relat_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(1476,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) ) ) )
& ~ ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(213,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_4) ).
thf(2290,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(735,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ? [F: $i] :
( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( D @ ( F @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice2) ).
thf(4615,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ? [F: $i] :
( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( D @ ( F @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(553,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( C @ ( B @ k16_borsuk_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_borsuk_1) ).
thf(3825,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( C @ ( B @ k16_borsuk_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(8757,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6174,5811]) ).
thf(8758,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8757]) ).
thf(8766,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk311 ),
inference(simp,[status(thm)],[8758]) ).
thf(1261,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_lattice4 ) )
= ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice4) ).
thf(7044,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_lattice4 ) )
= ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1238,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( B @ ( A @ k8_borsuk_1 ) ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_borsuk_1) ).
thf(6953,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( B @ ( A @ k8_borsuk_1 ) ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m2_subset_1 ) ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ m2_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lopclset) ).
thf(1508,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m2_subset_1 ) ) )
=> ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ m2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(870,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
<=> ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_0) ).
thf(5191,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
=> ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(3368,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3367]) ).
thf(3369,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3368]) ).
thf(619,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_pre_topc ) )
= ( D @ ( C @ g1_pre_topc ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(4126,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_pre_topc ) )
= ( D @ ( C @ g1_pre_topc ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ m1_eqrel_1 ) )
& ~ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k18_borsuk_1) ).
thf(2823,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ m1_eqrel_1 ) )
& ~ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(1204,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k2_pre_topc @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_pre_topc) ).
thf(6790,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k2_pre_topc @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1293,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v3_filter_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_0) ).
thf(7167,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v3_filter_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(345,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).
thf(2811,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
=> ( A @ v13_lattices ) )
& ( ( A @ v13_lattices )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(760,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relat_1) ).
thf(4715,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1042,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_borsuk_1) ).
thf(6003,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1047,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( B @ ( C @ ( A @ k5_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_0) ).
thf(6023,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( B @ ( C @ ( A @ k5_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(14982,plain,
! [B: $i,A: $i] :
( ( B != sk304 )
| ( A != sk129 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7694]) ).
thf(14983,plain,
! [A: $i] :
( ( A != sk129 )
| ( sk304 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14982:[bind(A,$thf( A )),bind(B,$thf( sk304 ))]]) ).
thf(15315,plain,
sk304 @ k1_tarski @ ( sk129 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14983]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k3_subset_1 ) )
= ( A @ k1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tops_1) ).
thf(2608,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k3_subset_1 ) )
= ( A @ k1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(19414,plain,
( ( ( sk152 @ v3_realset2 )
!= ( k1_xboole_0 @ v3_realset2 ) )
| ( sk1 != k1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3977,19396]) ).
thf(19415,plain,
( ( ( sk152 @ v3_realset2 )
!= ( k1_xboole_0 @ v3_realset2 ) )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[19414]) ).
thf(19424,plain,
( ( sk152 != k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[19415]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(3003,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(911,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( D @ ( F @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) )
=> ( D @ ( C @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_setwiseo) ).
thf(5394,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( D @ ( F @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) )
=> ( D @ ( C @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(7384,plain,
sk389 @ v1_pre_topc,
inference(cnfConj,[status(thm)],[7381]) ).
thf(714,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C
= ( B @ ( A @ k2_borsuk_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_borsuk_1) ).
thf(4495,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( D @ r2_hidden ) ) )
=> ( C
= ( B @ ( A @ k2_borsuk_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_borsuk_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( D @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( D @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_2) ).
thf(5243,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( D @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( D @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(940,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k6_pre_topc ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(5505,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k6_pre_topc ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(820,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
=> ( ( D = E )
| ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_borsuk_1) ).
thf(4969,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
=> ( ( D = E )
| ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(4261,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(704,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k17_borsuk_1 ) @ ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_borsuk_1) ).
thf(4451,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k17_borsuk_1 ) @ ( B @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= C )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(966,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D )
& ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_lattice2) ).
thf(5600,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D )
& ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(7437,plain,
sk395 @ l3_lattices,
inference(cnf,[status(esa)],[7436]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_filter_0 ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(6305,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_filter_0 ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(2399,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(771,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
& ( ( B @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_1) ).
thf(4759,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
& ( ( B @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(567,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ ( A @ k2_pre_topc @ v1_tops_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_tops_1) ).
thf(3896,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ ( A @ k2_pre_topc @ v1_tops_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(692,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_relat_1) ).
thf(4387,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(2183,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(2315,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1020,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_filter_0 ) )
= ( C @ ( A @ k2_filter_0 ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_1) ).
thf(5864,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k2_filter_0 ) )
= ( C @ ( A @ k2_filter_0 ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(1273,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
& ( A @ v17_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice4) ).
thf(7093,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
& ( A @ v17_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(1153,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ ( A @ k5_filter_1 ) @ k8_filter_1 ) @ ( A @ r1_filter_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_1) ).
thf(6516,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ ( A @ k5_filter_1 ) @ k8_filter_1 ) @ ( A @ r1_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(8168,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6174,2180]) ).
thf(8169,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk311 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8168]) ).
thf(8172,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk311 ),
inference(simp,[status(thm)],[8169]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relat_1) ).
thf(1689,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(584,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(3978,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_3) ).
thf(2081,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(3181,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(2384,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(2475,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(4855,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(534,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(3694,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(862,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k2_filter_0 ) @ ( A @ k12_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( D @ r2_hidden ) )
=> ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( B @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ k2_filter_0 ) @ ( A @ k12_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_filter_1) ).
thf(5162,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k2_filter_0 ) @ ( A @ k12_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( D @ r2_hidden ) )
=> ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( B @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( B @ ( C @ ( A @ k2_filter_0 ) @ ( A @ k12_filter_0 ) @ ( A @ u1_struct_0 @ k2_filter_1 ) ) @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(668,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_pre_topc @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) )
= ( A @ k2_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tops_1) ).
thf(4293,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_pre_topc @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) )
= ( A @ k2_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(916,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(5408,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(6854,plain,
sk362 @ v1_funct_1,
inference(cnfConj,[status(thm)],[6852]) ).
thf(1299,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(7187,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(7265,plain,
( ~ ( sk386 @ v3_struct_0 )
& ( sk386 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[7264]) ).
thf(7266,plain,
sk386 @ l2_struct_0,
inference(cnfConj,[status(thm)],[7265]) ).
thf(519,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_funct_3 )
= ( B @ k1_funct_3 @ ( A @ k1_funct_3 @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_3) ).
thf(3585,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_funct_3 )
= ( B @ k1_funct_3 @ ( A @ k1_funct_3 @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(3430,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(100,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(1777,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(439,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ k2_funct_4 @ k2_funct_4 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_4) ).
thf(3267,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ k2_funct_4 @ k2_funct_4 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(5109,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(839,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
<=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_1) ).
thf(5040,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1260,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_lattice2 )
<=> ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice2) ).
thf(7039,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) )
=> ( A @ v1_lattice2 ) )
& ( ( A @ v1_lattice2 )
=> ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(1361,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ k10_lopclset @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lopclset) ).
thf(7416,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ k10_lopclset @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_subset_1) ).
thf(1706,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(985,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B
!= ( A @ k1_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_pre_topc) ).
thf(5699,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B
!= ( A @ k1_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1290,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( D @ ( B @ ( A @ k9_filter_0 ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_1) ).
thf(7157,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( D @ ( B @ ( A @ k9_filter_0 ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(2162,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(957,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattices) ).
thf(5568,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(13135,plain,
! [B: $i,A: $i] :
( ( A != sk379 )
| ( B != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7517]) ).
thf(13136,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( A @ k1_tarski @ ( sk379 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[13135:[bind(A,$thf( sk379 ))]]) ).
thf(15435,plain,
k1_xboole_0 @ k1_tarski @ ( sk379 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[13136]) ).
thf(19537,plain,
k1_xboole_0 @ k5_finsub_1 @ ( sk379 @ k1_tarski @ r1_xboole_0 ),
inference(rewrite,[status(thm)],[15435,1896]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_funct_1) ).
thf(5119,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(159,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v5_tops_1 ) )
& ( A @ ( B @ v5_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v5_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_tops_1) ).
thf(2036,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ ( C @ v5_tops_1 ) )
& ( A @ ( B @ v5_tops_1 ) ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ v5_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(526,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v11_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( B @ ( G @ r2_hidden ) )
=> ( ( G @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) ) ) ) )
=> ( ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) )
= ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_lattice2) ).
thf(3645,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v11_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( B @ ( G @ r2_hidden ) )
=> ( ( G @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) ) ) ) )
=> ( ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) )
= ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1444,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ k1_struct_0 ) @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ ( B @ ( A @ k6_borsuk_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_borsuk_1 ) ) ) ) ) @ m2_connsp_2 ) ) )
| ~ ( D @ ( B @ ( F @ m1_connsp_2 ) ) )
| ~ ( C @ ( A @ ( E @ m2_connsp_2 ) ) )
| ~ ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( B @ l1_pre_topc )
| ~ ( B @ v2_pre_topc )
| ( B @ v3_struct_0 )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc )
| ( A @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1443]) ).
thf(7406,plain,
sk393 @ l3_lattices,
inference(cnfConj,[status(thm)],[7405]) ).
thf(1219,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattices) ).
thf(6871,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).
thf(4869,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m2_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(543,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_lattices ) ) )
<=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_lattices) ).
thf(3761,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) ) )
=> ( C @ ( B @ ( A @ r2_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r2_lattices ) ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(1135,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ ( A @ k2_funct_4 @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_4) ).
thf(6462,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ ( A @ k2_funct_4 @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(3552,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(4927,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1288,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k7_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(7152,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k7_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
<=> ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tops_1) ).
thf(2779,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) )
=> ( A @ ( B @ v1_tops_1 ) ) )
& ( ( A @ ( B @ v1_tops_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= ( A @ k2_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(2287,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(6997,plain,
sk379 @ v1_relat_1,
inference(cnfConj,[status(thm)],[6995]) ).
thf(1206,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k11_lopclset @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k10_lopclset @ ( B @ r2_hidden ) )
=> ( A @ k11_lopclset @ ( B @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l38_lopclset) ).
thf(6822,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k11_lopclset @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k10_lopclset @ ( B @ r2_hidden ) )
=> ( A @ k11_lopclset @ ( B @ v3_pre_topc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_subset_1) ).
thf(2587,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1295,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k1_filter_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_filter_1) ).
thf(7171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k1_filter_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(1069,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m3_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattice4) ).
thf(6131,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m3_lattice4 ) ) )
& ( ( A @ ( B @ m3_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(952,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_0) ).
thf(5554,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(3264,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(762,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( A @ k6_pre_topc ) )
= B )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
thf(4719,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( A @ k6_pre_topc ) )
= B )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( ( B @ ( A @ k6_pre_topc ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(997,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( E @ v1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
<=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice4) ).
thf(5764,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( E @ v1_lattice4 ) ) )
=> ( ( ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) )
=> ( D @ ( C @ ( A @ r3_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(416,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k4_lopclset ) )
<=> ! [C: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k2_lopclset ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lopclset) ).
thf(3132,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k2_lopclset ) ) ) ) ) )
=> ( B
= ( A @ k4_lopclset ) ) )
& ( ( B
= ( A @ k4_lopclset ) )
=> ! [C: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_lopclset @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ ( A @ k1_lopclset @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k2_lopclset ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(1305,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_filter_0) ).
thf(7210,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ u1_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(6580,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(3469,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(372,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k1_tops_1 ) )
= C )
=> ( A @ ( C @ v3_pre_topc ) ) )
& ( ( B @ ( D @ v3_pre_topc ) )
=> ( ( D @ ( B @ k1_tops_1 ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).
thf(2930,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( B @ l1_pre_topc )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k1_tops_1 ) )
= C )
=> ( A @ ( C @ v3_pre_topc ) ) )
& ( ( B @ ( D @ v3_pre_topc ) )
=> ( ( D @ ( B @ k1_tops_1 ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(178,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(2123,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v5_tops_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ k2_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_tops_1) ).
thf(2374,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v5_tops_1 ) )
=> ( ( B @ ( A @ k1_tops_1 ) @ ( A @ k2_tops_1 ) )
= ( B @ ( A @ k2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(800,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t182_relat_1) ).
thf(4880,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(14416,plain,
! [B: $i,A: $i] :
( ( A != sk376 )
| ( B != sk161 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7901]) ).
thf(14417,plain,
! [A: $i] :
( ( A != sk161 )
| ( A @ k1_tarski @ ( sk376 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14416:[bind(A,$thf( sk376 ))]]) ).
thf(15109,plain,
sk161 @ k1_tarski @ ( sk376 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14417]) ).
thf(1307,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_lopclset @ l1_pre_topc )
& ( A @ k11_lopclset @ v2_pre_topc )
& ( A @ k11_lopclset @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_lopclset) ).
thf(7216,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k11_lopclset @ l1_pre_topc )
& ( A @ k11_lopclset @ v2_pre_topc )
& ( A @ k11_lopclset @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(1270,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B
!= ( C @ ( A @ k1_struct_0 ) ) ) )
& ( A @ k15_borsuk_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_borsuk_1) ).
thf(7081,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B
!= ( C @ ( A @ k1_struct_0 ) ) ) )
& ( A @ k15_borsuk_1 @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(63,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k3_funct_3 )
= ( A @ k3_funct_3 @ ( B @ k3_funct_3 @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_3) ).
thf(1642,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k3_funct_3 )
= ( A @ k3_funct_3 @ ( B @ k3_funct_3 @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(982,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_pre_topc ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tops_1) ).
thf(5677,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ ( D @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(1512,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(99,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= k1_xboole_0 )
=> ( D = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_setwiseo) ).
thf(1774,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= k1_xboole_0 )
=> ( D = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1101,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(6326,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(2683,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1080,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ~ ( B @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) )
& ( A @ ( C @ v1_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lopclset) ).
thf(6201,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ~ ( B @ ( A @ k9_lopclset @ ( A @ k7_lopclset @ k1_zfmisc_1 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) )
& ( A @ ( C @ v1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1344,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) )
<=> ( A @ ( B @ v1_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_0) ).
thf(7355,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ ( B @ v1_filter_0 ) )
=> ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) ) )
& ( ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(3785,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(3511,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(7627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) )
!= ( C @ ( D @ m1_subset_1 ) ) )
| ( ( C @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ~ $true
| ( ( D @ ( C @ k2_setwiseo ) @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= ( D @ ( C @ k2_setwiseo ) ) )
| ( C @ v1_xboole_0 )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1385,7596]) ).
thf(7628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) )
!= ( C @ ( D @ m1_subset_1 ) ) )
| ( ( C @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( D @ ( C @ k2_setwiseo ) @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= ( D @ ( C @ k2_setwiseo ) ) )
| ( C @ v1_xboole_0 )
| ~ ( A @ ( B @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7627]) ).
thf(7629,plain,
! [B: $i,A: $i] :
( ( ( B @ k5_finsub_1 @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( A @ ( B @ k2_setwiseo ) @ ( B @ k5_finsub_1 @ k2_setwiseo ) @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= ( A @ ( B @ k2_setwiseo ) @ ( B @ k5_finsub_1 @ k2_setwiseo ) ) )
| ( B @ k5_finsub_1 @ v1_xboole_0 )
| ~ ( B @ ( A @ m1_subset_1 ) )
| ( B @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[7628:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ k5_finsub_1 )),bind(D,$thf( F @ ( G @ k2_setwiseo ) ))]]) ).
thf(7634,plain,
! [B: $i,A: $i] :
( ( ( B @ k5_finsub_1 @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( A @ ( B @ k2_setwiseo ) @ ( B @ k5_finsub_1 @ k2_setwiseo ) @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= ( A @ ( B @ k2_setwiseo ) @ ( B @ k5_finsub_1 @ k2_setwiseo ) ) )
| ( B @ k5_finsub_1 @ v1_xboole_0 )
| ~ ( B @ ( A @ m1_subset_1 ) )
| ( B @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7629]) ).
thf(780,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(4809,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(12114,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ~ $true
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[11676,7588]) ).
thf(12115,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ m1_subset_1 ) )
!= ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) ) )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[12114]) ).
thf(12222,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( k1_xboole_0 != A )
| ( ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= A ) ),
inference(simp,[status(thm)],[12115]) ).
thf(12267,plain,
( ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( sk1 @ u1_struct_0 ) )
| ( ( k1_xboole_0 @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( sk1 @ k2_lattice4 ) )
= k1_xboole_0 ) ),
inference(simp,[status(thm)],[12222]) ).
thf(1112,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( A @ ( C @ v6_compts_1 ) )
<=> ( B @ ( D @ v6_compts_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_borsuk_1) ).
thf(6361,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( ( B @ ( D @ v6_compts_1 ) )
=> ( A @ ( C @ v6_compts_1 ) ) )
& ( ( A @ ( C @ v6_compts_1 ) )
=> ( B @ ( D @ v6_compts_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(1316,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k12_lopclset @ ( A @ ( A @ k13_lopclset @ v3_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lopclset) ).
thf(7242,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k12_lopclset @ ( A @ ( A @ k13_lopclset @ v3_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(3987,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(904,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_relat_1) ).
thf(5356,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(3464,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(3521,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(1876,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1132,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(6456,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).
thf(2736,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m1_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(154,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
thf(2008,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(418,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k9_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k9_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) @ ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_1) ).
thf(3145,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k9_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k9_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) @ ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(4029,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(672,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(4303,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(702,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattices) ).
thf(4427,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(924,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_realset2 )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ k8_lopclset @ k1_funct_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ v1_filter_0 ) )
& ( D = A )
& ( B @ ( D @ m1_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_lopclset) ).
thf(5441,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_realset2 )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ v1_filter_0 ) )
& ( D = A )
& ( B @ ( D @ m1_filter_0 ) ) )
=> ( C @ ( B @ k8_lopclset @ k1_funct_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k8_lopclset @ k1_funct_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ r2_hidden ) )
& ( B @ ( D @ v1_filter_0 ) )
& ( D = A )
& ( B @ ( D @ m1_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1325,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_borsuk_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_borsuk_1) ).
thf(7278,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_borsuk_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(599,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ k4_lattices ) ) )
= ( F @ ( E @ ( B @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k10_filter_1 ) ) ) ) )
& ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ k3_lattices ) ) )
= ( F @ ( E @ ( B @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_filter_1) ).
thf(4034,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ k4_lattices ) ) )
= ( F @ ( E @ ( B @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k10_filter_1 ) ) ) ) )
& ( ( F @ ( D @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k10_filter_1 ) ) ) @ ( B @ ( A @ k8_filter_1 ) @ k3_lattices ) ) )
= ( F @ ( E @ ( B @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k10_filter_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1230,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tops_1) ).
thf(6929,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k2_tops_1 ) @ ( A @ k2_tops_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(386,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) )
& ( A @ ( A @ k2_pre_topc @ v3_pre_topc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_tops_1) ).
thf(3015,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ ( A @ k2_pre_topc @ v4_pre_topc ) )
& ( A @ ( A @ k2_pre_topc @ v3_pre_topc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(10400,plain,
! [A: $i] :
( ( ( A @ sk267 @ v1_xboole_0 )
!= ( sk372 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5653,6952]) ).
thf(10401,plain,
! [A: $i] :
( ( A @ sk267 @ v1_xboole_0 )
!= ( sk372 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10400]) ).
thf(10408,plain,
! [A: $i] :
( ( A @ sk267 )
!= sk372 ),
inference(simp,[status(thm)],[10401]) ).
thf(1436,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) )
| ~ ( A @ ( B @ v3_pre_topc ) )
| ~ ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l1_pre_topc ) ),
inference(cnfConj,[status(thm)],[1435]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(1859,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(14454,plain,
! [B: $i,A: $i] :
( ( B != sk302 )
| ( A != sk20 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7681]) ).
thf(14455,plain,
! [A: $i] :
( ( A != sk20 )
| ( sk302 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14454:[bind(A,$thf( A )),bind(B,$thf( sk302 ))]]) ).
thf(15123,plain,
sk302 @ k1_tarski @ ( sk20 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14455]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(5159,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(1657,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(226,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) ) )
=> ( ( B @ ( A @ r2_borsuk_1 ) )
=> ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ r2_borsuk_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_borsuk_1) ).
thf(2334,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ( A @ ( B @ v1_borsuk_1 ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_borsuk_1 ) )
& ( B @ ( C @ v2_borsuk_1 ) ) )
=> ( ( B @ ( A @ r2_borsuk_1 ) )
=> ( C @ ( B @ ( A @ k21_borsuk_1 ) ) @ ( C @ ( B @ ( A @ k20_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ r2_borsuk_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(513,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tops_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( C != k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_tops_1) ).
thf(3560,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( C != k1_xboole_0 ) ) )
=> ( A @ ( B @ v1_tops_1 ) ) )
& ( ( A @ ( B @ v1_tops_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r1_xboole_0 ) )
& ( A @ ( C @ v3_pre_topc ) )
& ( C != k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(191,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k17_borsuk_1 ) )
= ( B @ ( A @ u1_struct_0 @ k2_borsuk_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_borsuk_1) ).
thf(2186,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k17_borsuk_1 ) )
= ( B @ ( A @ u1_struct_0 @ k2_borsuk_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(462,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k1_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tops_1) ).
thf(3347,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ ( A @ u1_struct_0 @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k1_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(666,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_tops_1) ).
thf(4286,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_relat_1) ).
thf(3558,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1040,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r2_hidden ) ) ) )
& ( B
!= ( A @ k5_lattices ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_0) ).
thf(5990,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r2_hidden ) ) ) )
& ( B
!= ( A @ k5_lattices ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_1) ).
thf(4007,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(846,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_4 @ v1_funct_1 )
& ( A @ k2_funct_4 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_4) ).
thf(5105,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_4 @ v1_funct_1 )
& ( A @ k2_funct_4 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_4) ).
thf(4083,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(538,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_1) ).
thf(3716,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_1) ).
thf(2572,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(917,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
<=> ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_filter_0) ).
thf(5413,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
=> ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(5462,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1168,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(6590,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1089,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( D @ ( E @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattice2) ).
thf(6258,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( D @ ( E @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(376,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2961,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_struct_0 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(1710,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_struct_0 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1116,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ m1_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_1) ).
thf(6380,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( A @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ m1_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(245,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relat_1) ).
thf(2404,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k2_xboole_0 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1326,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( A @ v11_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattice4) ).
thf(7280,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( A @ v11_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(5867,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1357,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(7402,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(1331,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_realset2 )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ k7_lopclset @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ v1_filter_0 ) )
& ( C = A )
& ( B @ ( C @ m1_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lopclset) ).
thf(7291,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_realset2 )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( B @ ( C @ v1_filter_0 ) )
& ( C = A )
& ( B @ ( C @ m1_filter_0 ) ) )
=> ( B @ k7_lopclset @ ( A @ r2_hidden ) ) )
& ( ( B @ k7_lopclset @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ v1_filter_0 ) )
& ( C = A )
& ( B @ ( C @ m1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(3045,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(496,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(3506,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(558,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lopclset) ).
thf(3843,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k2_lattice4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice4) ).
thf(5283,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k2_lattice4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ a_2_0_borsuk_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ k3_tarski ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_borsuk_1) ).
thf(6273,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ k3_tarski ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_borsuk_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_borsuk_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ k3_tarski ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_4) ).
thf(5322,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(551,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_1) ).
thf(3805,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(676,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).
thf(4318,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_partfun1) ).
thf(1742,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1148,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
thf(6503,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( B @ ( A @ k1_filter_1 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k1_filter_1) ).
thf(7338,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( B @ ( A @ k1_filter_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(1258,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ u1_pre_topc @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_pre_topc) ).
thf(7035,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ u1_pre_topc @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(563,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t170_relat_1) ).
thf(3886,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1272,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset @ l3_lattices )
& ( A @ k6_lopclset @ v10_lattices )
& ~ ( A @ k6_lopclset @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lopclset) ).
thf(7088,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lopclset @ l3_lattices )
& ( A @ k6_lopclset @ v10_lattices )
& ~ ( A @ k6_lopclset @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(19159,plain,
( ( ( sk161 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) )
!= ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15967,19130]) ).
thf(19160,plain,
( ( sk161 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) )
!= ( k1_xboole_0 @ k5_finsub_1 @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(simp,[status(thm)],[19159]) ).
thf(19255,plain,
( ( ( sk161 @ k1_tarski )
!= ( k1_xboole_0 @ k5_finsub_1 ) )
| ( ( k1_xboole_0 @ k5_finsub_1 )
!= ( k1_xboole_0 @ k5_finsub_1 ) ) ),
inference(simp,[status(thm)],[19160]) ).
thf(19298,plain,
( ( sk161 @ k1_tarski )
!= ( k1_xboole_0 @ k5_finsub_1 ) ),
inference(simp,[status(thm)],[19255]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(3341,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B
= ( A @ k2_pre_topc ) )
& ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) )
!= k1_xboole_0 ) )
& ~ ( ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) )
= k1_xboole_0 )
& ( B
!= ( A @ k2_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_pre_topc) ).
thf(1930,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B
= ( A @ k2_pre_topc ) )
& ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) )
!= k1_xboole_0 ) )
& ~ ( ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) )
= k1_xboole_0 )
& ( B
!= ( A @ k2_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(18041,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( A @ v10_lattices )
| ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1896,13362]) ).
thf(18042,plain,
( ( k1_xboole_0 @ v10_lattices )
| ( sk1 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[18041:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(14798,plain,
! [B: $i,A: $i] :
( ( B != sk302 )
| ( A != sk161 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7680]) ).
thf(14799,plain,
! [A: $i] :
( ( A != sk161 )
| ( sk302 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14798:[bind(A,$thf( A )),bind(B,$thf( sk302 ))]]) ).
thf(15245,plain,
sk302 @ k1_tarski @ ( sk161 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14799]) ).
thf(1220,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k2_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice4) ).
thf(6874,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k2_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
thf(4923,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(3244,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(2502,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ( ( B
= ( A @ k1_tarski ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(14672,plain,
! [B: $i,A: $i] :
( ( A != sk372 )
| ( B != sk257 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7585]) ).
thf(14673,plain,
! [A: $i] :
( ( A != sk257 )
| ( A @ k1_tarski @ ( sk372 @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14672:[bind(A,$thf( sk372 ))]]) ).
thf(15198,plain,
sk257 @ k1_tarski @ ( sk372 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14673]) ).
thf(1079,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(6190,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(2809,plain,
! [A: $i] :
( ( A @ k1_setwiseo )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2808]) ).
thf(2810,plain,
! [A: $i] :
( ( A @ k1_setwiseo )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2809]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(2731,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(114,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D = E )
=> ( ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
= ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k2_lattice2 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
= ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattice2) ).
thf(1829,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D = E )
=> ( ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
= ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k2_lattice2 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
= ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_lattice2) ).
thf(1977,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1004,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(5803,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( C = D ) ) ) )
& ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( A
= ( B @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_1) ).
thf(3025,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( C = D ) ) ) )
& ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( A
= ( B @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1343,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( B @ ( A @ k9_filter_0 ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_1) ).
thf(7352,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) @ ( B @ ( A @ k9_filter_0 ) ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(252,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_4) ).
thf(2430,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(6099,plain,
sk302 @ v1_funct_1,
inference(cnfConj,[status(thm)],[6096]) ).
thf(14546,plain,
! [B: $i,A: $i] :
( ( B != sk20 )
| ( A != k1_xboole_0 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7511]) ).
thf(14547,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( sk20 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14546:[bind(A,$thf( A )),bind(B,$thf( sk20 ))]]) ).
thf(15159,plain,
sk20 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14547]) ).
thf(16859,plain,
sk20 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_xboole_0 ),
inference(rewrite,[status(thm)],[15159,1896]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(2847,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(366,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) )
= ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_3) ).
thf(2898,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) )
= ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(3411,plain,
~ ( sk105 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3409]) ).
thf(821,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_funct_3 @ v1_funct_1 )
& ( A @ k1_funct_3 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_3) ).
thf(4972,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_funct_3 @ v1_funct_1 )
& ( A @ k1_funct_3 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(856,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( B @ k1_funct_4 ) @ ( A @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_4) ).
thf(5140,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( B @ k1_funct_4 ) @ ( A @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(1126,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k3_lattices ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattices) ).
thf(6435,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k3_lattices ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_4) ).
thf(3360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(1083,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( A @ v2_pre_topc )
<=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ u1_pre_topc @ ( C @ r2_hidden ) )
& ( A @ u1_pre_topc @ ( B @ r2_hidden ) ) )
=> ( A @ u1_pre_topc @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) )
& ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ u1_pre_topc @ ( B @ r1_tarski ) )
=> ( A @ u1_pre_topc @ ( B @ ( A @ u1_struct_0 @ k5_setfam_1 ) @ r2_hidden ) ) ) )
& ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_pre_topc) ).
thf(6209,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ u1_pre_topc @ ( C @ r2_hidden ) )
& ( A @ u1_pre_topc @ ( B @ r2_hidden ) ) )
=> ( A @ u1_pre_topc @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) )
& ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ u1_pre_topc @ ( B @ r1_tarski ) )
=> ( A @ u1_pre_topc @ ( B @ ( A @ u1_struct_0 @ k5_setfam_1 ) @ r2_hidden ) ) ) )
& ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ r2_hidden ) ) )
=> ( A @ v2_pre_topc ) )
& ( ( A @ v2_pre_topc )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ u1_pre_topc @ ( C @ r2_hidden ) )
& ( A @ u1_pre_topc @ ( B @ r2_hidden ) ) )
=> ( A @ u1_pre_topc @ ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) )
& ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ u1_pre_topc @ ( B @ r1_tarski ) )
=> ( A @ u1_pre_topc @ ( B @ ( A @ u1_struct_0 @ k5_setfam_1 ) @ r2_hidden ) ) ) )
& ( A @ u1_pre_topc @ ( A @ u1_struct_0 @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k5_finsub_1 @ ( D @ ( C @ ( B @ ( A @ k10_setwiseo ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_setwiseo) ).
thf(2467,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k5_finsub_1 @ ( D @ ( C @ ( B @ ( A @ k10_setwiseo ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(841,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ k3_tarski )
= ( A @ k3_tarski @ ( B @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_3) ).
thf(5061,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ k3_tarski )
= ( A @ k3_tarski @ ( B @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1372,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ v15_lattices )
& ( A @ v15_lattices ) )
<=> ( B @ ( A @ k8_filter_1 ) @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_1) ).
thf(7457,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k8_filter_1 ) @ v15_lattices )
=> ( ( B @ v15_lattices )
& ( A @ v15_lattices ) ) )
& ( ( ( B @ v15_lattices )
& ( A @ v15_lattices ) )
=> ( B @ ( A @ k8_filter_1 ) @ v15_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(287,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v4_pre_topc ) )
<=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
thf(2583,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) )
=> ( A @ ( B @ v4_pre_topc ) ) )
& ( ( A @ ( B @ v4_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(604,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) )
=> ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_lattice2) ).
thf(4066,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) )
=> ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k5_finsub_1 )
= ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finsub_1) ).
thf(5280,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k5_finsub_1 )
= ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(649,axiom,
! [A: $i] :
( ( A @ k5_finsub_1 @ ( A @ k1_setwiseo @ m1_subset_1 ) )
& ( A @ k1_setwiseo @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setwiseo) ).
thf(4239,plain,
! [A: $i] :
( ( A @ k5_finsub_1 @ ( A @ k1_setwiseo @ m1_subset_1 ) )
& ( A @ k1_setwiseo @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1085,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_0) ).
thf(6233,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) )
& ( ( A @ ( B @ v1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1347,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( B @ ( A @ k5_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v17_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k5_filter_1 ) @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_filter_1) ).
thf(7370,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( B @ ( A @ k5_filter_1 ) @ l3_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v17_lattices )
& ( B @ ( A @ k5_filter_1 ) @ v10_lattices )
& ~ ( B @ ( A @ k5_filter_1 ) @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(1109,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r4_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice4) ).
thf(6348,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) )
=> ( C @ ( B @ ( A @ r4_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(998,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k3_pre_topc ) @ m1_pre_topc ) )
& ( B @ ( A @ k3_pre_topc ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pre_topc) ).
thf(5768,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k3_pre_topc ) @ m1_pre_topc ) )
& ( B @ ( A @ k3_pre_topc ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(506,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( A @ ( B @ v1_borsuk_1 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_borsuk_1) ).
thf(3538,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_pre_topc ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) )
=> ( A @ ( B @ v1_borsuk_1 ) ) )
& ( ( A @ ( B @ v1_borsuk_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ u1_struct_0 ) )
=> ( A @ ( C @ v4_pre_topc ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(931,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_filter_0 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_filter_0) ).
thf(5468,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_filter_0 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).
thf(1713,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(903,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ k16_borsuk_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_borsuk_1) ).
thf(5354,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ k16_borsuk_1 ) @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k17_borsuk_1 ) @ ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( A @ k16_borsuk_1 ) @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(605,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k16_borsuk_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_borsuk_1) ).
thf(4071,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k16_borsuk_1 ) @ v2_pre_topc )
& ( B @ ( A @ k16_borsuk_1 ) @ v1_pre_topc )
& ~ ( B @ ( A @ k16_borsuk_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(409,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( E @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_lattice2) ).
thf(3113,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( E @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(908,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( A @ k1_funct_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_funct_4) ).
thf(5376,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( A @ k1_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(471,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k2_pre_topc @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(3394,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ k2_pre_topc @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_lopclset ) ) )
= ( B @ ( C @ ( A @ k2_lopclset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_lopclset) ).
thf(6778,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_lopclset @ ( C @ m1_subset_1 ) )
& ( A @ k1_lopclset @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_lopclset ) ) )
= ( B @ ( C @ ( A @ k2_lopclset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
<=> ( B
= ( A @ k1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(2484,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) )
& ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B
= ( A @ k1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1159,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices )
= ( A @ k1_lattice2 @ k6_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_lattice2) ).
thf(6548,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices )
= ( A @ k1_lattice2 @ k6_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(1505,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(660,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relat_1) ).
thf(4271,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_subset_1) ).
thf(1621,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(644,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relat_1) ).
thf(4221,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(1353,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(7392,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(1017,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k2_pre_topc @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(5845,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( A @ k2_pre_topc @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(775,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_4) ).
thf(4779,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(144,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
thf(1962,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(1945,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k5_finsub_1 @ ( C @ ( B @ ( A @ k5_setwiseo ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setwiseo) ).
thf(1681,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k5_finsub_1 @ ( C @ ( B @ ( A @ k5_setwiseo ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1215,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(6857,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(7462,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ~ $true
| ( A @ v3_struct_0 )
| ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1379,1383]) ).
thf(7463,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ v10_lattices )
!= ( A @ v10_lattices ) )
| ~ ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
| ~ ( A @ l3_lattices )
| ~ ( A @ v17_lattices )
| ( A @ v3_struct_0 )
| ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ),
inference(simp,[status(thm)],[7462]) ).
thf(7464,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ~ ( sk1 @ v17_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( sk1 @ k5_lattice4 @ ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ ( sk1 @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( A @ ( sk1 @ k7_lattices ) @ ( sk1 @ k5_lattice4 @ ( B @ ( sk1 @ ( sk1 @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( sk1 @ k3_lattices ) ) ) ) ),
inference(pattern_uni,[status(thm)],[7463:[bind(A,$thf( sk1 ))]]) ).
thf(7471,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ ( sk1 @ l3_lattices )
| ~ ( sk1 @ v17_lattices )
| ( sk1 @ v3_struct_0 )
| ( ( sk1 @ k5_lattice4 @ ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ ( sk1 @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( A @ ( sk1 @ k7_lattices ) @ ( sk1 @ k5_lattice4 @ ( B @ ( sk1 @ ( sk1 @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( sk1 @ k3_lattices ) ) ) ) ),
inference(simp,[status(thm)],[7464]) ).
thf(7477,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ~ $true
| ~ $true
| $false
| ( ( sk1 @ k5_lattice4 @ ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ ( sk1 @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( A @ ( sk1 @ k7_lattices ) @ ( sk1 @ k5_lattice4 @ ( B @ ( sk1 @ ( sk1 @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( sk1 @ k3_lattices ) ) ) ) ),
inference(rewrite,[status(thm)],[7471,1376,1380,1375]) ).
thf(7478,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
| ~ ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
| ( ( sk1 @ k5_lattice4 @ ( A @ ( sk1 @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( sk1 @ u1_struct_0 @ k5_setwiseo ) ) @ ( sk1 @ ( sk1 @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( A @ ( sk1 @ k7_lattices ) @ ( sk1 @ k5_lattice4 @ ( B @ ( sk1 @ ( sk1 @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( sk1 @ k3_lattices ) ) ) ) ),
inference(simp,[status(thm)],[7477]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_relat_1) ).
thf(3296,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1053,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattices) ).
thf(6067,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(3526,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(3946,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk150 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3942]) ).
thf(3959,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk150 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3946]) ).
thf(3960,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk150 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[3959]) ).
thf(1276,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ v17_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_lopclset) ).
thf(7103,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k6_lopclset @ v17_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(490,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_pre_topc) ).
thf(3474,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ v3_pre_topc ) ) )
& ( ( A @ ( B @ v3_pre_topc ) )
=> ( ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) @ ( A @ k6_pre_topc ) )
= ( B @ ( A @ k2_pre_topc @ ( A @ u1_struct_0 @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(504,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
<=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ~ ( A @ v3_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_pre_topc) ).
thf(3528,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k6_pre_topc ) @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r2_hidden ) )
& ( A @ ( D @ v3_pre_topc ) ) ) )
& ~ ( A @ v3_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_tops_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_tops_1) ).
thf(2754,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_tops_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v1_tops_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(747,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k18_borsuk_1 ) ) )
= ( B @ ( A @ a_2_3_borsuk_1 ) @ ( C @ k2_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_borsuk_1) ).
thf(4655,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k18_borsuk_1 ) ) )
= ( B @ ( A @ a_2_3_borsuk_1 ) @ ( C @ k2_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(311,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(2672,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(2640,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funct_4) ).
thf(3580,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(5877,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1240,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ~ ( ( ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v1_filter_0 ) ) ) )
& ( B != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_0) ).
thf(6961,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ~ ( ( ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v1_filter_0 ) ) ) )
& ( B != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(719,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(4520,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ u1_struct_0 @ k3_subset_1 ) @ v4_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(742,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice2) ).
thf(4642,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m2_lattice4 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_1_lattice4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( B @ k4_lattice4 ) @ ( D @ r1_tarski ) )
& ( A
= ( D @ ( B @ k2_lattice4 ) ) )
& ( B @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).
thf(4702,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m2_lattice4 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( B @ k4_lattice4 ) @ ( D @ r1_tarski ) )
& ( A
= ( D @ ( B @ k2_lattice4 ) ) )
& ( B @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_lattice4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_lattice4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( B @ k4_lattice4 ) @ ( D @ r1_tarski ) )
& ( A
= ( D @ ( B @ k2_lattice4 ) ) )
& ( B @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1039,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
<=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_0) ).
thf(5986,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(894,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k5_subset_1 ) ) @ k3_tarski )
= ( D @ k3_tarski @ ( C @ k3_tarski @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_borsuk_1) ).
thf(5312,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k5_subset_1 ) ) @ k3_tarski )
= ( D @ k3_tarski @ ( C @ k3_tarski @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(14558,plain,
! [B: $i,A: $i] :
( ( B != sk379 )
| ( A != sk304 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7693]) ).
thf(14559,plain,
! [A: $i] :
( ( A != sk304 )
| ( sk379 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[14558:[bind(A,$thf( A )),bind(B,$thf( sk379 ))]]) ).
thf(15164,plain,
sk379 @ k1_tarski @ ( sk304 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[14559]) ).
thf(1072,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ~ ( ( ( C @ ( A @ k2_lattice4 ) )
= ( A @ k5_lattices ) )
& ( B @ ( C @ r1_tarski ) ) ) )
& ( B @ ( A @ k3_filter_0 ) @ ( A @ k5_lattices @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lopclset) ).
thf(6158,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ! [C: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ~ ( ( ( C @ ( A @ k2_lattice4 ) )
= ( A @ k5_lattices ) )
& ( B @ ( C @ r1_tarski ) ) ) )
& ( B @ ( A @ k3_filter_0 ) @ ( A @ k5_lattices @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).
thf(4891,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(725,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relat_1) ).
thf(4555,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(560,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tops_1) ).
thf(3854,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_tops_1 ) @ ( B @ ( A @ k1_tops_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice2) ).
thf(2206,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(867,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(5183,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(13018,plain,
! [B: $i,A: $i] :
( ( B != sk376 )
| ( A != sk372 )
| ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1440,7903]) ).
thf(13019,plain,
! [A: $i] :
( ( A != sk372 )
| ( sk376 @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[13018:[bind(A,$thf( A )),bind(B,$thf( sk376 ))]]) ).
thf(15381,plain,
sk376 @ k1_tarski @ ( sk372 @ k1_tarski @ r1_xboole_0 ),
inference(simp,[status(thm)],[13019]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(6718,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1243,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ~ ( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( B
= ( F @ ( E @ ( A @ k4_lattices ) ) ) ) ) ) )
& ( D @ ( C @ ( A @ k5_filter_0 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_0) ).
thf(6984,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ~ ( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( B
= ( F @ ( E @ ( A @ k4_lattices ) ) ) ) ) ) )
& ( D @ ( C @ ( A @ k5_filter_0 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_filter_0 ) )
& ( B @ ( C @ m1_filter_0 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(5261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_filter_0 ) )
& ( B @ ( C @ m1_filter_0 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k2_pre_topc )
= ( A @ k1_pre_topc @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_pre_topc) ).
thf(2436,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ k2_pre_topc )
= ( A @ k1_pre_topc @ ( A @ u1_struct_0 @ k3_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(768,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(4752,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(2297,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1087,axiom,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(6254,plain,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_partfun1) ).
thf(5255,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(6072,plain,
sk300 @ v1_relat_1,
inference(cnfConj,[status(thm)],[6071]) ).
thf(7267,plain,
~ ( sk386 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[7265]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_3) ).
thf(4423,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(394,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ v3_pre_topc ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ v3_pre_topc ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_borsuk_1) ).
thf(3052,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ v3_pre_topc ) )
& ( A @ ( C @ v3_pre_topc ) ) )
=> ( B @ ( A @ k6_borsuk_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_borsuk_1 ) ) ) @ v3_pre_topc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1121,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
<=> ( A @ k1_lattice2 @ v14_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).
thf(6404,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k1_lattice2 @ v14_lattices )
=> ( A @ v13_lattices ) )
& ( ( A @ v13_lattices )
=> ( A @ k1_lattice2 @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(797,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_setwiseo) ).
thf(4863,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(454,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_4) ).
thf(3316,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(980,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( D @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_0) ).
thf(5664,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( D @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(431,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r1_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice4) ).
thf(3200,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r1_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1184,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(6668,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(2106,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_3) ).
thf(3933,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(795,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ k2_pre_topc @ ( A @ k1_tops_1 ) )
= ( A @ k2_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tops_1) ).
thf(4858,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( A @ k2_pre_topc @ ( A @ k1_tops_1 ) )
= ( A @ k2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1364,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc ) )
=> ( ( B
= ( A @ k11_lopclset ) )
<=> ( ( ( B @ u1_pre_topc )
= ( A @ a_1_2_lopclset ) )
& ( ( B @ u1_struct_0 )
= ( A @ k7_lopclset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lopclset) ).
thf(7424,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_realset2 )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l1_pre_topc )
& ( B @ v2_pre_topc )
& ( B @ v1_pre_topc ) )
=> ( ( ( ( ( B @ u1_pre_topc )
= ( A @ a_1_2_lopclset ) )
& ( ( B @ u1_struct_0 )
= ( A @ k7_lopclset ) ) )
=> ( B
= ( A @ k11_lopclset ) ) )
& ( ( B
= ( A @ k11_lopclset ) )
=> ( ( ( B @ u1_pre_topc )
= ( A @ a_1_2_lopclset ) )
& ( ( B @ u1_struct_0 )
= ( A @ k7_lopclset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(392,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(3047,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1248,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ k2_pre_topc @ ( B @ r1_tarski ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_pre_topc) ).
thf(7003,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ k2_pre_topc @ ( B @ r1_tarski ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1236,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] : ( A @ ( B @ m1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pre_topc) ).
thf(6948,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] : ( A @ ( B @ m1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k3_pre_topc ) @ v2_pre_topc )
& ( B @ ( A @ k3_pre_topc ) @ v1_pre_topc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_pre_topc) ).
thf(5574,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( ( B @ ( A @ k3_pre_topc ) @ v2_pre_topc )
& ( B @ ( A @ k3_pre_topc ) @ v1_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(3575,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(670,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( D @ ( A @ k1_struct_0 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_borsuk_1) ).
thf(4298,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pre_topc ) )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ u1_struct_0 @ ( D @ r2_hidden ) )
=> ( C @ ( B @ ( A @ k18_borsuk_1 ) ) @ ( D @ ( A @ k1_struct_0 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1232,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( B @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
thf(6933,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( B @ ( A @ k1_tops_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(31007,plain,
$false,
inference(e,[status(thm)],[2630,7766,1633,4899,4729,2921,2427,6566,2199,5437,1665,1586,4201,2452,6836,1411,3883,5116,10410,5561,6979,4094,1469,4835,6355,2889,4571,4464,2336,2109,1454,7445,1767,15303,5950,2412,2876,5320,6285,8283,6855,4852,3830,2787,5654,6317,1850,2499,2559,6172,4015,6074,10363,2331,4682,7285,7396,4992,6374,7903,3680,5454,1406,7409,2808,5625,4711,1692,7208,1437,4479,3990,7888,4714,2976,1924,7596,8044,7517,2495,5292,15314,1443,3417,15143,1618,6458,5297,1401,1422,6900,1939,2248,2676,2014,5793,7368,6776,3108,2114,5405,3498,4215,2380,7182,1971,2854,1426,4403,7695,4011,5288,3338,4279,6851,2459,6996,6894,4980,1458,7400,3848,5550,5814,4234,8765,4090,5361,6505,5565,2686,6939,4839,3367,6359,2918,2141,15916,4638,7345,6416,4650,5713,7147,1761,3121,6551,6680,2901,7452,3313,5782,3370,4792,4343,2972,5977,4137,6342,6102,3335,16387,3350,6466,2491,1782,1391,7079,4371,4079,1441,2020,7136,8133,7235,5476,1613,5825,5723,1645,2886,12257,1386,3466,5301,4198,3898,4963,2067,6483,4322,4156,2136,1518,4610,6182,4467,7311,4775,4249,5342,1887,1409,5429,3938,7262,7696,3574,3821,3653,3043,7386,4637,6892,3976,2328,1792,1430,1660,7418,5883,2667,7401,4151,6095,5759,1907,5064,5274,4654,3617,3125,1826,4275,4349,5130,3410,1455,3280,2562,16240,5640,3089,6662,6332,7000,4568,6010,6599,1572,15161,19130,15199,8257,1545,2420,2713,3517,3998,1892,1379,3385,7711,2857,6470,4617,6611,4194,4358,6502,5604,4664,1398,6781,3084,6923,7436,7047,3734,5829,4368,4141,15110,6098,5727,4390,4471,4507,5020,6734,2852,5077,4514,2533,6382,6594,1847,7588,4756,7226,5974,2222,5027,7969,6176,7677,2777,13533,2017,6983,7258,4696,4988,1415,5433,2616,7268,8284,7273,2794,7144,4329,1811,1450,7300,1373,3724,2893,2469,3670,4001,5333,4820,1418,2236,6745,6534,7376,4847,5558,5946,11676,1864,1383,4134,7015,5650,2254,3569,8018,5805,2034,12703,5135,3300,3093,4115,5761,1581,6438,4162,7899,10404,2367,3712,6491,2371,5169,4040,2982,7408,7413,5572,7707,6451,6631,3068,1377,2618,2833,5401,5379,4842,8454,1896,5643,6740,7336,4504,5772,2523,2530,1394,10405,2772,3157,5246,1526,10057,6772,6863,7213,8173,1433,5489,3588,4379,5819,15321,3906,1521,2718,3406,7305,7230,7197,6856,6731,2364,5545,4557,3318,1708,5519,6282,1651,6560,2910,2204,3303,15967,10362,6015,1438,7286,3984,2646,15379,7037,5017,5438,5697,6058,2118,5034,7019,6865,4076,7005,6307,3054,5540,4031,2621,4312,3550,6464,5122,7129,4925,6092,3795,2589,2409,18493,5734,4920,6371,2133,15169,10409,5507,4661,6079,3827,5630,2805,6328,3972,6605,2541,3022,4252,1751,7710,1487,4449,4493,1824,4284,7692,19396,2396,7244,3514,4021,7378,3778,3286,5843,2433,7449,5460,1624,7545,7713,2327,3408,3282,1423,7097,3958,7308,7237,2758,5391,8255,5879,2873,5492,1837,3269,6629,15296,6432,2628,4192,2670,4608,1920,3403,4725,1968,3198,5177,3556,16123,3578,7902,1457,5038,3144,5113,6392,6168,5658,3050,2211,1407,6267,2313,3727,6666,2741,8287,4461,1392,2228,4027,5285,6728,2300,1772,2377,1375,2692,5847,1755,3001,6075,4123,3615,1541,13362,4957,7421,3254,6101,1794,4512,7205,5238,5423,7065,10413,8282,2577,7389,5502,5798,4525,1425,4693,5583,3963,4930,5919,5889,7513,5811,3078,4883,4109,7809,3176,4817,1397,4653,3922,4983,4425,3714,8177,3194,2038,8176,1493,4320,1683,3775,3311,7189,3326,5166,5031,3143,6175,6518,5694,15168,2323,3407,5705,6844,3210,6116,7111,2830,4315,5464,1414,2240,4406,1584,5547,1937,6256,4861,4648,4054,7059,3671,3643,6946,7404,5905,1889,7313,2978,4621,6935,2649,4180,2317,3294,1744,3935,6065,1419,2450,6097,2681,2845,4829,4717,6005,4259,3074,6186,2756,1627,5317,5850,1451,5149,7138,2153,2387,8764,7221,5900,1974,6207,7169,6129,4482,6876,2465,8690,4934,2497,6346,7027,7385,1852,7086,1429,2862,8425,4902,3162,7174,4223,10406,8174,2788,10366,7678,1814,2546,7407,4782,4765,3856,6716,2057,6070,1466,2915,1895,4995,6497,4163,3454,2634,2749,1434,3903,7150,4184,4212,4889,3183,3173,6859,16169,7476,6982,1515,5417,2189,6038,7289,6931,1616,10359,3422,5840,6950,2338,5872,5524,6507,2292,1959,7512,5451,7155,6084,6001,19300,3396,3343,7160,2121,2936,1648,1727,5666,1510,1764,3130,7582,6026,3358,6824,6203,3890,7010,4874,4412,2941,6578,6792,8771,2602,3375,3888,6454,3839,3523,2734,7382,3111,3274,4269,4017,5598,5241,8015,6468,6510,1388,8697,1701,2716,1965,7828,2827,3536,6140,7709,7162,3547,19301,5456,6493,8259,2048,3925,8762,2225,6959,1884,6617,1389,2789,3519,4159,7233,3472,7073,7134,15320,1752,2393,3086,4926,5627,2674,1403,3458,6344,19296,6898,1428,1786,3118,6385,5595,15160,7109,4573,3123,7347,3832,6334,3091,10361,5578,4978,3773,5363,8549,3051,4796,2891,7270,2308,4645,6667,8286,3208,4236,3663,1635,1733,2442,3436,1897,15244,3641,6123,4273,6248,1638,7394,4245,5556,5580,2346,5870,2478,3155,7077,1524,3419,2257,2246,7282,6340,4139,3710,4300,1376,6061,6585,2361,2311,2679,5143,2538,7514,2084,2214,2624,5325,2422,5303,7438,6154,3500,3066,2896,5972,4773,6460,2197,3160,2182,6165,4541,2605,4009,3977,3298,4296,7023,1381,1952,7901,1667,2180,5552,4203,6087,5816,5730,3668,16338,2111,6849,1630,6710,4028,5335,5439,4264,3572,15297,4897,4985,4277,7033,3165,1862,2785,4850,6847,2252,3893,1820,3480,1926,7030,6609,1445,5482,6738,6270,4827,15814,5299,2156,8763,3908,3490,4844,4832,6589,5057,2439,2725,2401,1699,2171,6449,7383,2481,2139,5248,2064,3674,8175,2797,10407,3363,7434,6100,5725,2535,2101,4954,2390,6293,5403,4626,4209,6736,2069,6476,4741,1809,5528,6542,2652,5757,2878,6853,7013,2005,5812,5435,7260,4331,3009,2054,4207,6890,4690,1662,4394,2614,1873,3427,6540,1758,4813,5025,7681,4456,3672,1420,8099,2234,8116,1990,2202,7679,4688,5916,6564,4355,5807,3292,6115,6664,6998,5358,5133,4168,6641,5822,6120,4490,3082,1566,3260,10581,4534,4754,2407,5790,7228,6012,4658,4749,4255,5570,16389,1748,5607,6472,4360,5294,4937,2977,5111,5478,1400,5399,16727,6597,6826,3462,5074,5980,15122,7967,4377,4324,4630,7511,15163,1484,7586,7055,4522,5235,1452,7443,6174,3412,1738,4164,2656,3019,4409,2569,6389,3246,4561,4346,2092,4092,1987,5420,3940,6981,7264,2454,4190,2165,7693,3063,10360,7105,5015,3722,3554,5912,3655,6513,3801,1980,5309,10365,3127,4132,5543,5152,1538,7583,6994,5638,4117,5186,5277,8448,2992,3493,7303,1797,5083,3914,7380,15304,1404,5147,5208,6701,4959,7331,6633,2838,6899,3970,3415,6073,6262,4624,6601,7342,4611,11830,4976,2543,5613,6369,6526,6479,4748,2357,7585,1955,2320,2711,4106,5809,4143,4046,4538,4235,18591,4267,1717,4225,2939,7192,5717,5472,8433,6105,3007,4257,4671,4111,6975,6992,7224,4392,3288,6420,2760,4289,3620,4606,1685,10114,4559,2611,2209,15144,7363,7099,1918,7061,6447,5179,10364,5653,4770,7177,6408,1949,2870,4165,1817,6721,5660,4944,2078,4997,3188,5510,1654,1412,2997,4102,8285,1575,6882,4170,6743,5485,8761,1453,2643,2775,1866,8098,1807,4061,5184,4310,2792,3797,7131,5258,5315,3911,6607,6689,16337,10411,3331,2526,6903,4913,1385,2594,1721,6230,6322,6077,2174,4806,1476,2290,4615,3825,8766,7044,6953,1508,5191,3369,4126,2823,6790,7167,2811,4715,6003,6023,15315,2608,19424,3003,5394,1822,7384,4495,5243,5505,4969,4261,4451,5600,4745,7437,6305,2399,4759,3896,4387,2183,2315,5864,7093,7680,6516,8172,1689,3978,2081,3181,2384,2475,4855,3694,5162,4293,5408,6854,7187,7266,3585,3430,1777,3267,7312,5109,5040,1440,7039,7416,1706,5699,7157,2162,5568,19537,5119,2036,3645,8267,1444,7406,6871,4869,3761,6462,3552,4927,7152,2779,2287,6997,6822,2587,7171,6131,5554,3264,4719,5764,3132,7210,6580,3469,15813,2930,2123,2374,4880,15109,7216,7081,1642,5677,1512,1774,6326,2683,6201,7355,3785,3511,7634,4809,12267,6361,1395,7242,3987,5356,3464,1380,3521,1876,6456,2736,2008,3145,4029,4303,4427,5441,7278,4034,6929,3015,10408,1436,1859,15123,5159,1657,2334,3560,2186,3347,6114,4286,3558,5990,4007,5105,4083,3716,2572,5413,5462,1410,6590,6258,2961,1710,6380,2404,7280,5867,7402,7291,6952,3045,3506,3843,5283,6273,5322,3805,5440,4318,1742,6503,7338,7035,3886,7088,1431,7694,19298,3341,1930,18042,15245,6874,4923,3244,2502,15198,6190,2810,2731,1829,1977,5803,3974,3025,7352,2430,6099,16859,7584,2847,2898,1384,3411,4972,5140,6435,3360,1378,6209,2467,5061,7457,2583,4066,4484,5280,4239,6233,7708,7370,6348,8437,5768,3538,4713,5468,1713,5354,4071,3113,5376,3394,6778,2484,6548,1505,4271,1621,4221,7392,5845,4779,1962,1945,1681,4161,6857,7478,3296,6067,3526,3960,7103,7900,3474,3528,2754,4655,2672,2640,3580,5877,6961,4520,4642,4702,5986,5312,15164,6158,4891,4555,7310,3854,2206,5183,15381,6718,6984,5261,2436,4752,2297,6254,5255,6072,1416,7267,4423,3052,6404,4863,3316,5664,3200,6668,2106,3933,4858,7424,3047,7003,6948,5574,6896,3575,2177,4298,6933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT292+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n006.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 20:30:41 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.39/1.99 % [INFO] Parsing done (996ms).
% 4.39/2.01 % [INFO] Running in sequential loop mode.
% 5.20/2.39 % [INFO] eprover registered as external prover.
% 5.45/2.40 % [INFO] Scanning for conjecture ...
% 7.39/3.00 % [INFO] Found a conjecture (or negated_conjecture) and 6467 axioms. Running axiom selection ...
% 10.32/4.14 % [INFO] Axiom selection finished. Selected 1370 axioms (removed 5097 axioms).
% 12.44/4.62 % [INFO] Problem is first-order (TPTP FOF).
% 12.44/4.67 % [INFO] Type checking passed.
% 12.44/4.67 % [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 ...
% 117.60/33.13 % External prover 'e' found a proof!
% 117.60/33.13 % [INFO] Killing All external provers ...
% 117.60/33.14 % Time passed: 32582ms (effective reasoning time: 31119ms)
% 117.60/33.14 % 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)>
% 117.60/33.15 % Axioms used in derivation (1370): t106_xboole_1, t72_xboole_1, t15_finset_1, t7_filter_0, t28_funct_3, t2_filter_0, t21_zfmisc_1, t175_relat_1, d13_filter_0, dt_k2_borsuk_1, t158_relat_1, t17_lattice4, rc2_lopclset, t38_funct_4, t45_lattice4, t51_filter_1, t42_xboole_1, dt_k1_funct_3, t34_subset_1, t34_funct_3, t30_lopclset, dt_k5_filter_1, t108_tops_1, t50_lattice4, t51_partfun1, redefinition_m2_relset_1, t20_filter_1, t44_xboole_1, t13_zfmisc_1, t24_filter_0, t10_lattice2, t13_relset_1, t70_setwiseo, cc1_tops_1, t181_relat_1, t15_lopclset, dt_k7_filter_0, fc8_tops_1, t177_relat_1, t19_xboole_1, t70_tops_1, t31_filter_0, t43_subset_1, d5_lopclset, t147_funct_1, t84_tops_1, t14_finset_1, t20_lattice4, t39_lattices, t76_lattice2, t67_tops_1, t26_lopclset, t17_xboole_1, t2_lopclset, dt_k1_filter_1, t78_filter_0, t42_subset_1, t36_lopclset, t43_lattice2, dt_m1_lattice4, t15_setwiseo, cc2_finset_1, t20_zfmisc_1, t76_tops_1, t36_funct_3, t35_subset_1, d1_tarski, dt_k2_lattice2, t135_zfmisc_1, t17_zfmisc_1, t54_tops_1, fc11_finseq_1, t148_funct_1, t25_relset_1, fc12_tops_1, t66_funct_2, t143_funct_1, t67_relat_1, t62_filter_0, t66_partfun1, t45_pre_topc, t154_relat_1, t13_funct_3, t70_funct_2, dt_k3_borsuk_1, t80_filter_0, t56_filter_1, l38_lopclset, t53_subset_1, t35_tops_1, t79_tops_1, rc4_finset_1, t35_filter_1, fc2_pre_topc, redefinition_k5_subset_1, t81_filter_0, d12_borsuk_1, t48_filter_1, d13_lattices, dt_k6_filter_1, d6_filter_0, idempotence_k3_lopclset, t97_tops_1, t105_zfmisc_1, t54_filter_1, t41_pre_topc, t140_zfmisc_1, fraenkel_a_1_0_filter_1, dt_k19_borsuk_1, redefinition_k12_mcart_1, t109_xboole_1, idempotence_k3_xboole_0, t1_boole, d6_lattice2, t62_relat_1, t7_subset_1, t2_realset1, t32_funct_2, t66_xboole_1, t23_xboole_1, fraenkel_a_2_1_borsuk_1, t36_lattice4, t15_filter_1, t79_funct_4, symmetry_r1_filter_1, t14_funct_4, t50_relat_1, t91_tops_1, dt_k2_tops_1, t29_filter_0, t24_lattice4, t73_xboole_1, t3_xboole_1, d4_lattice4, t137_funct_1, d3_subset_1, t57_lattice2, t51_borsuk_1, idempotence_k5_setwiseo, t7_lattice2, t113_xboole_1, rc7_finseq_1, t87_tops_1, t56_partfun1, t8_subset_1, existence_l1_lattices, t29_borsuk_1, t29_funct_3, t156_funct_1, t35_borsuk_1, fc1_xboole_0, t53_filter_1, t42_filter_0, t5_borsuk_1, cc6_lattices, t25_funct_1, t16_funct_2, d16_lattices, t113_zfmisc_1, dt_k20_borsuk_1, t34_xboole_1, dt_k7_subset_1, rc4_pre_topc, d13_borsuk_1, t50_borsuk_1, t15_funct_1, rc3_tops_1, fc4_relat_1, t19_lattices, t4_ordinal1, t1_group_6, t39_funct_3, t59_partfun1, t158_funct_1, t43_lattices, redefinition_k10_borsuk_1, t44_relat_1, t1_subset, dt_k1_lattice4, t147_relat_1, t10_partfun1, t47_lattice2, t9_lattice2, t22_funct_1, t43_xboole_1, t81_zfmisc_1, t52_funct_4, t10_relset_1, fc4_tops_1, dt_k1_subset_1, t6_xboole_1, d8_funct_1, fc1_lattice2, d5_xboole_0, t90_tops_1, t38_filter_1, t29_subset_1, dt_k8_borsuk_1, t4_lattice4, t151_funct_1, t52_zfmisc_1, t144_relat_1, dt_k9_lopclset, fc4_subset_1, dt_k1_tops_1, existence_l3_lattices, t53_lattices, dt_k5_lattices, t7_funct_2, fraenkel_a_3_0_borsuk_1, t18_xboole_1, t3_mcart_1, t155_funct_1, d2_group_6, t23_lopclset, t87_filter_0, t16_setwiseo, fc3_relat_1, t96_zfmisc_1, t45_filter_1, t21_lattice2, t19_relat_1, t70_xboole_1, t69_filter_0, redefinition_k13_lopclset, t67_borsuk_1, dt_k2_funct_4, t117_zfmisc_1, t88_tops_1, t61_tops_1, t23_pre_topc, t23_filter_0, t43_zfmisc_1, t47_relat_1, fc9_relat_1, t16_lattice4, t46_lattice4, t68_xboole_1, t19_finset_1, t54_funct_4, existence_m3_lattice4, t25_xboole_1, t2_boole, dt_m1_filter_1, t69_tops_1, t18_filter_0, dt_k3_lattice4, t106_tops_1, t102_tops_1, t5_funct_3, dt_k1_lattice2, t65_partfun1, t29_lopclset, t44_funct_2, fraenkel_a_2_0_lattice4, d10_borsuk_1, d2_funct_3, t117_funct_1, fc11_tops_1, t1_qc_lang1, dt_k4_subset_1, fc6_tops_1, t27_xboole_1, t59_tops_1, t71_xboole_1, t122_zfmisc_1, d13_pre_topc, t83_filter_0, t4_mcart_1, redefinition_k3_lopclset, t50_pre_topc, dt_k1_struct_0, existence_m1_filter_1, t35_lattice4, d6_pre_topc, dt_k16_borsuk_1, t12_pre_topc, t26_lattice4, d11_borsuk_1, t85_filter_0, t82_tops_1, dt_m1_borsuk_1, dt_m1_realset1, t25_pre_topc, cc5_tops_1, t55_funct_4, dt_u2_struct_0, rc2_partfun1, t18_relat_1, fc1_filter_0, fc1_funct_1, t171_relat_1, t45_zfmisc_1, t8_lopclset, t95_zfmisc_1, t63_partfun1, t153_funct_1, t20_funct_3, t15_relset_1, t19_funct_3, t18_funct_3, t14_filter_0, t77_tops_1, t73_tops_1, t56_tops_1, idempotence_k2_lopclset, fraenkel_a_2_0_filter_0, t99_zfmisc_1, l49_lopclset, cc4_lattices, redefinition_k11_filter_0, d8_lopclset, t13_pre_topc, rc3_funct_1, t81_xboole_1, t48_filter_0, d9_lattice4, t6_lopclset, t3_lopclset, t68_borsuk_1, dt_k5_filter_0, dt_k3_filter_0, t32_tops_1, t78_borsuk_1, t69_zfmisc_1, d1_struct_0, t37_xboole_1, cc1_relat_1, rc3_pre_topc, t46_borsuk_1, t36_subset_1, t138_funct_1, t47_filter_1, t17_funct_1, t9_xboole_1, d6_tops_1, t41_zfmisc_1, cc3_tops_1, dt_m2_relset_1, t18_finset_1, t131_zfmisc_1, redefinition_k2_funct_2, idempotence_k5_subset_1, t59_lattice2, t49_zfmisc_1, dt_k1_pre_topc, reflexivity_r1_filter_1, commutativity_k3_xboole_0, t154_funct_1, t29_partfun1, t33_lattice4, t62_funct_2, t55_funct_1, t32_filter_0, dt_k10_filter_1, t70_partfun1, t71_tops_1, dt_k8_lopclset, dt_k4_lopclset, t26_filter_0, t46_pre_topc, fc11_finset_1, t31_lattices, dt_k2_lopclset, rc1_funct_1, t31_relat_1, t168_relat_1, t111_tops_1, redefinition_k6_filter_0, dt_k1_filter_0, t115_zfmisc_1, t80_tops_1, t62_funct_1, t46_lattice2, d3_pre_topc, t65_funct_2, t19_funct_1, t56_setwiseo, dt_m2_lattice4, d11_filter_0, t13_funct_4, t50_tops_1, t29_finset_1, d4_lopclset, dt_k2_binop_1, t137_zfmisc_1, t2_binop_1, t2_partfun1, t34_tops_1, t86_xboole_1, fc5_pre_topc, involutiveness_k3_subset_1, t13_relat_1, t89_xboole_1, t53_filter_0, t25_funct_2, fc2_xboole_0, t16_lopclset, dt_m2_realset1, t9_funct_3, t32_subset_1, rc6_pre_topc, t64_funct_2, t66_tops_1, dt_k12_lopclset, t108_xboole_1, t56_filter_0, t72_filter_0, t24_lopclset, t43_tops_1, fraenkel_a_3_0_filter_0, t46_funct_2, t32_funct_3, t21_funct_4, t15_relat_1, t12_funct_4, t173_relat_1, dt_k6_lopclset, t172_relat_1, t27_relat_1, d16_lattice4, t70_filter_0, t78_funct_4, d1_xboole_0, dt_m1_eqrel_1, t49_funct_1, t65_tops_1, dt_k21_borsuk_1, t46_filter_0, t5_lopclset, t52_pre_topc, t64_relat_1, t138_zfmisc_1, rc6_finseq_1, rc1_tops_1, fraenkel_a_2_0_borsuk_1, t37_filter_0, d14_borsuk_1, t36_filter_1, rc3_lattices, t52_filter_0, t23_funct_1, t130_zfmisc_1, t51_xboole_1, redefinition_k1_filter_1, t57_filter_0, dt_l1_lattices, t14_lopclset, t56_funct_4, t14_relset_1, dt_k11_borsuk_1, t6_mcart_1, t46_zfmisc_1, t31_partfun1, dt_k7_lattices, d15_lattice4, t56_zfmisc_1, t26_borsuk_1, t47_funct_2, t24_finsub_1, t27_relset_1, commutativity_k3_lopclset, d21_borsuk_1, redefinition_k19_borsuk_1, dt_l1_pre_topc, dt_k4_lattice4, t118_zfmisc_1, t55_partfun1, t2_mcart_1, t8_funct_2, fc10_finset_1, t37_funct_3, t19_lopclset, t60_partfun1, existence_m1_realset1, t26_finset_1, t77_borsuk_1, t39_lattice4, t16_relset_1, t38_lattice4, t39_funct_4, t28_lopclset, t49_borsuk_1, fc2_borsuk_1, t6_boole, t12_funct_1, t10_funct_3, t3_funct_2, t18_subset_1, rc2_subset_1, fc9_finset_1, dt_k1_lopclset, fc4_lopclset, existence_l2_lattices, t50_xboole_1, t74_borsuk_1, dt_k6_subset_1, t10_relat_1, t43_pre_topc, t80_borsuk_1, t59_setfam_1, t2_filter_1, t59_filter_0, t26_relset_1, t20_funct_1, t47_lattice4, t16_pre_topc, t41_tops_1, dt_k11_lopclset, t32_partfun1, t22_tops_1, t160_funct_1, t5_subset, t44_filter_1, t1_xboole_1, redefinition_k12_filter_0, dt_k1_funct_4, t86_tops_1, t27_funct_3, t29_relat_1, d14_lattice4, t64_partfun1, t52_relat_1, t77_funct_2, free_g1_pre_topc, t54_borsuk_1, existence_l2_struct_0, t32_lattices, idempotence_k1_filter_1, t55_relat_1, t34_filter_0, t68_partfun1, t5_lattice4, t3_partfun1, t59_setwiseo, t19_filter_0, t52_xboole_1, t44_lattice4, t75_xboole_1, t49_filter_0, t34_relat_1, dt_k10_setwiseo, commutativity_k2_xboole_0, d12_lattices, d17_lattice4, t39_partfun1, t149_funct_1, d2_realset1, t6_lattice2, dt_k13_lopclset, t65_xboole_1, t27_tops_1, t1_zfmisc_1, fc2_tops_1, t53_funct_4, t17_filter_1, t45_funct_2, t53_borsuk_1, t94_zfmisc_1, t8_lattice4, t46_tops_1, t4_xboole_0, t8_tops_1, fc17_finseq_1, t150_relat_1, existence_m1_relset_1, commutativity_k5_subset_1, t79_borsuk_1, t50_lattices, d5_tops_1, dt_l3_lattices, t48_lattice2, t18_pre_topc, t21_filter_1, fraenkel_a_3_1_borsuk_1, t19_relset_1, t64_tops_1, t110_tops_1, t123_zfmisc_1, fc2_subset_1, t79_zfmisc_1, t12_lattice2, t5_funct_2, t176_relat_1, dt_k8_funct_2, redefinition_k5_setwiseo, t18_setwiseo, t75_tops_1, dt_k18_borsuk_1, t24_finset_1, t62_tops_1, t40_funct_2, t57_tops_1, t44_pre_topc, t40_filter_0, t72_partfun1, t27_lattice4, t9_relat_1, t84_lattice2, t2_tops_1, dt_k7_borsuk_1, dt_l2_lattices, t97_zfmisc_1, t121_funct_1, t75_borsuk_1, t2_tarski, t16_funct_1, t14_relat_1, t33_relat_1, dt_k4_filter_0, t33_xboole_1, t75_lattice2, t122_funct_1, t13_setwiseo, t47_lattices, t25_borsuk_1, d20_lattices, d1_filter_1, dt_k15_borsuk_1, t4_filter_0, t2_zfmisc_1, t31_funct_3, t89_filter_0, t114_xboole_1, t1_filter_1, d6_realset1, t39_filter_1, t67_zfmisc_1, t38_filter_0, d1_funct_4, d13_funct_1, t4_cat_1, t98_zfmisc_1, t34_lattice4, fc3_xboole_0, d18_lattices, t70_lattice2, d8_filter_0, t32_xboole_1, t52_subset_1, t60_filter_0, dt_k9_filter_1, t5_ordinal1, t4_boole, t53_xboole_1, d3_lattices, t22_lopclset, t47_borsuk_1, t71_lattice2, t146_funct_1, t84_xboole_1, d2_pre_topc, t125_funct_1, t21_xboole_1, cc5_lattices, d5_pre_topc, t4_subset, d3_lopclset, t34_lopclset, t76_xboole_1, t178_relat_1, t38_subset_1, t53_pre_topc, t81_tops_1, t44_lattices, d2_xboole_0, t30_xboole_1, t18_lopclset, t39_tops_1, dt_k2_funct_1, dt_k8_filter_0, t14_funct_1, dt_k22_borsuk_1, d4_tarski, t56_lattice2, abstractness_v1_pre_topc, t42_filter_1, t61_partfun1, t141_zfmisc_1, t80_xboole_1, t79_xboole_1, t174_relat_1, t41_borsuk_1, d7_realset2, d2_lattice4, t45_lattices, t49_lattice4, t58_funct_1, t25_finset_1, d8_pre_topc, t30_tops_1, t67_xboole_1, d7_filter_0, d2_lopclset, existence_m2_realset1, t52_filter_1, redefinition_k2_lopclset, d7_lopclset, redefinition_k5_setfam_1, t49_tops_1, t58_zfmisc_1, t21_funct_3, t17_funct_2, t85_lattice2, t58_tops_1, t29_xboole_1, t50_funct_4, t75_filter_0, dt_k17_borsuk_1, t13_lattice2, t179_relat_1, t52_tops_1, t72_borsuk_1, t63_tops_1, d10_pre_topc, d9_lopclset, t59_funct_1, t139_zfmisc_1, t32_lopclset, t16_lattice2, t7_boole, fraenkel_a_2_3_borsuk_1, cc1_funct_1, t27_pre_topc, fc9_tops_1, d10_lattice4, fc4_pre_topc, dt_k5_lattice4, rc3_struct_0, fc1_subset_1, t13_finset_1, d1_setwiseo, t3_ordinal1, t4_funct_2, t37_tops_1, dt_g1_pre_topc, dt_k10_borsuk_1, t103_tops_1, d10_setfam_1, t55_filter_0, t50_filter_1, d2_subset_1, t66_zfmisc_1, t33_funct_4, t22_relat_1, dt_k6_borsuk_1, t48_xboole_1, t157_funct_1, t5_setwiseo, d17_lattices, t92_tops_1, dt_k8_filter_1, t37_filter_1, t85_xboole_1, rc1_funct_2, t33_filter_1, d7_tops_1, t34_filter_1, t31_lattice4, t16_subset_1, dt_k2_partfun1, t69_partfun1, t7_ordinal1, t153_relat_1, t41_lopclset, rc2_funct_1, t9_funct_2, t160_relat_1, fc10_relat_1, t31_funct_2, rc1_subset_1, dt_k9_filter_0, t48_funct_1, t90_filter_0, t152_funct_1, t47_funct_1, dt_m1_pre_topc, t31_xboole_1, t4_subset_1, t88_xboole_1, t18_funct_4, t48_lattice4, t68_filter_0, t51_funct_1, t30_funct_4, t22_finset_1, t8_lattice2, d6_lopclset, t21_funct_2, fc3_lopclset, t42_funct_4, t24_xboole_1, d2_tops_1, t116_zfmisc_1, t64_zfmisc_1, t30_filter_0, t27_lopclset, t49_lattices, t65_funct_1, t56_funct_1, t124_zfmisc_1, t6_setwiseo, fraenkel_a_2_2_borsuk_1, t54_xboole_1, t113_funct_2, t71_partfun1, t5_filter_0, t69_xboole_1, d21_lattices, t41_lattices, d7_xboole_0, fc5_relat_1, t151_relat_1, existence_m1_filter_0, t83_xboole_1, t49_filter_1, dt_k3_lattice2, t40_lattice4, t45_relat_1, t2_lattice2, t58_filter_1, t48_lattices, t20_xboole_1, t47_pre_topc, t12_funct_3, dt_k2_lattice4, t70_borsuk_1, t9_filter_0, fc5_borsuk_1, t95_tops_1, t16_zfmisc_1, t40_lattices, t101_zfmisc_1, t17_borsuk_1, t38_funct_3, t55_tops_1, t7_lattice4, t46_filter_1, t82_xboole_1, t93_tops_1, t61_filter_1, t55_xboole_1, t124_funct_1, d9_filter_1, t18_filter_1, t41_funct_4, t22_filter_0, cc2_funct_1, t85_borsuk_1, t120_zfmisc_1, t76_borsuk_1, fraenkel_a_2_1_lattice4, existence_m1_pre_topc, t3_funct_3, t18_funct_1, t5_realset1, t17_finset_1, dt_k8_setfam_1, t4_relset_1, t10_filter_0, t31_subset_1, t3_subset, cc1_relset_1, cc1_eqrel_1, d6_lattice4, t30_lattice4, t12_filter_0, t52_borsuk_1, t55_subset_1, t79_funct_2, t46_funct_1, t41_lattice4, idempotence_k1_funct_4, dt_k6_setfam_1, redefinition_k21_borsuk_1, commutativity_k7_subset_1, t22_lattice4, existence_m1_subset_1, t3_relat_1, t36_borsuk_1, t35_xboole_1, t73_filter_0, redefinition_k4_subset_1, t44_zfmisc_1, t35_funct_3, t155_relat_1, t47_xboole_1, t145_funct_1, t5_lattice2, t44_filter_0, t17_relset_1, t38_tops_1, existence_m2_subset_1, t125_zfmisc_1, t63_borsuk_1, t42_borsuk_1, t30_subset_1, t8_setwiseo, dt_k2_filter_0, dt_k2_funct_2, t14_xboole_1, t44_setfam_1, t11_relset_1, t10_lopclset, d2_filter_0, t11_funct_4, redefinition_k9_lopclset, t5_pre_topc, fc1_finset_1, t15_subset_1, t18_borsuk_1, cc3_lattices, d5_subset_1, t19_lattice2, t72_tops_1, t92_zfmisc_1, t146_relat_1, t9_lattice4, t82_lattice2, d1_filter_0, t15_xboole_1, t11_filter_0, rc2_relat_1, existence_m2_relset_1, t64_filter_0, t48_tops_1, t54_pre_topc, dt_k24_borsuk_1, t114_zfmisc_1, t31_zfmisc_1, t58_partfun1, t60_setwiseo, d1_zfmisc_1, t16_xboole_1, cc2_tops_1, t51_pre_topc, t100_zfmisc_1, t27_filter_0, t26_xboole_1, t63_xboole_1, redefinition_k7_filter_0, t57_setfam_1, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, t62_lattice2, t39_filter_0, dt_k7_lopclset, t11_lattice4, rc2_realset2, dt_k5_subset_1, existence_m2_lattice4, t23_lattice4, dt_k23_borsuk_1, t116_funct_2, d3_lattice4, t25_funct_3, t37_lattice4, t26_subset_1, t65_lattice2, commutativity_k1_filter_1, t6_funct_2, t27_borsuk_1, d4_filter_0, t44_lattice2, t41_subset_1, dt_k12_mcart_1, t157_relat_1, cc3_finsub_1, t96_tops_1, t45_tops_1, t62_setwiseo, d9_pre_topc, t51_filter_0, t142_funct_1, t17_pre_topc, t74_filter_0, t11_lopclset, t51_subset_1, existence_m1_lattice4, t111_xboole_1, d5_filter_0, t15_funct_3, t51_tops_1, t22_xboole_1, t2_funct_3, t60_filter_1, t85_tops_1, t61_lattice2, t84_zfmisc_1, t21_lopclset, t8_xboole_1, t8_realset1, d3_tarski, d1_funct_3, t25_lattice4, rc1_relat_1, t19_setwiseo, t14_setwiseo, t45_lattice2, t36_tops_1, dt_m3_lattice4, t78_xboole_1, t28_xboole_1, t82_borsuk_1, d1_relset_1, t46_subset_1, fc1_struct_0, t62_filter_1, d8_filter_1, t52_lattice2, t78_lattice2, redefinition_k1_struct_0, existence_l1_pre_topc, fc1_lopclset, fraenkel_a_3_1_filter_0, t39_zfmisc_1, d1_realset1, d19_borsuk_1, t5_xboole_0, d15_lattices, t119_zfmisc_1, t13_xboole_1, t60_relat_1, t12_lopclset, t54_funct_1, t40_subset_1, t83_zfmisc_1, t170_relat_1, rc1_lattice4, t77_lattice2, t54_zfmisc_1, t24_lattice2, t19_lattice4, dt_k5_relat_1, t17_subset_1, reflexivity_r1_tarski, t9_funct_1, t6_zfmisc_1, t48_relat_1, t27_finsub_1, t5_mcart_1, t27_finset_1, t52_lattices, t2_xboole_1, fc13_tops_1, t17_funct_4, fraenkel_a_1_0_lopclset, t34_funct_2, rc6_lattices, t67_filter_0, t18_funct_2, t144_funct_1, t121_zfmisc_1, t10_subset_1, t51_funct_4, dt_l2_struct_0, t56_setfam_1, t41_filter_0, rc2_setwiseo, t1_realset1, t38_lopclset, t57_partfun1, t4_xboole_1, d12_funct_1, t9_relset_1, t25_lopclset, dt_g3_lattices, fc6_relat_1, t1_partfun1, t41_xboole_1, t150_funct_1, rc1_pre_topc, t45_borsuk_1, t11_setwiseo, t66_funct_1, d14_lattices, dt_k10_filter_0, dt_k5_lopclset, t54_lattice2, t18_zfmisc_1, t47_filter_0, d7_lattice4, dt_k1_lattices, t49_pre_topc, t90_xboole_1, rc7_pre_topc, t51_relat_1, free_g3_lattices, t20_tops_1, t46_relat_1, t77_filter_0, t30_funct_3, t9_lopclset, d4_xboole_0, t53_tops_1, t48_borsuk_1, t21_lattice4, dt_k5_setfam_1, rc3_finset_1, d6_eqrel_1, rc3_borsuk_1, fc3_pre_topc, dt_k5_setwiseo, commutativity_k5_setwiseo, existence_m1_eqrel_1, fc18_finseq_1, t36_xboole_1, t51_zfmisc_1, t69_lattice2, t47_subset_1, fc2_filter_1, t58_filter_0, t31_tops_1, t47_funct_4, t18_lattice4, dt_m2_subset_1, t40_filter_1, t26_finsub_1, t15_filter_0, t80_zfmisc_1, dt_u1_pre_topc, t54_subset_1, t39_pre_topc, rc1_finset_1, t4_lopclset, d1_lopclset, t64_xboole_1, fc4_borsuk_1, t22_pre_topc, t20_filter_0, t28_finsub_1, t127_zfmisc_1, t123_funct_1, t40_funct_4, t44_subset_1, rc2_tops_1, t49_xboole_1, t7_lopclset, cc1_finset_1, t29_lattices, t16_filter_1, t21_funct_1, t88_filter_0, fc12_finset_1, t51_lattice2, t136_zfmisc_1, t82_filter_0, fc1_relat_1, t77_xboole_1, d6_relat_1, t8_boole, t169_relat_1, rc1_xboole_0, t54_filter_0, t16_funct_3, t1_funct_5, t1_mcart_1, t11_xboole_1, t23_finset_1, t24_partfun1, redefinition_k8_funct_2, fc3_tops_1, t59_filter_1, t47_tops_1, t24_zfmisc_1, t55_lattice2, t68_zfmisc_1, t48_pre_topc, t182_relat_1, d1_borsuk_1, t2_subset, t16_finset_1, fc7_relat_1, t23_finsub_1, t30_finsub_1, t126_zfmisc_1, fc8_relat_1, t40_lopclset, t37_lopclset, rc5_struct_0, t19_filter_1, cc4_tops_1, t46_funct_4, t59_funct_2, t12_xboole_1, t22_funct_3, rc4_borsuk_1, d9_filter_0, t38_funct_2, t33_partfun1, t34_finsub_1, t85_funct_2, d6_borsuk_1, t180_relat_1, t60_funct_1, t37_zfmisc_1, fc2_relat_1, t65_relat_1, t21_relat_1, dt_k6_filter_0, t156_relat_1, d5_borsuk_1, t25_finsub_1, t152_relat_1, dt_k6_lattices, symmetry_r1_xboole_0, t49_funct_4, t134_zfmisc_1, existence_m1_borsuk_1, t25_partfun1, dt_m1_filter_0, t49_relat_1, t161_funct_1, t27_funct_1, t10_realset1, redefinition_k7_borsuk_1, d3_tops_1, t48_funct_4, d1_lattice4, rc1_setwiseo, t15_pre_topc, t33_funct_3, t9_tarski, t34_lattices, t145_relat_1, t51_lattices, t40_tops_1, d10_xboole_0, t74_xboole_1, t7_xboole_1, t115_funct_2, idempotence_k2_xboole_0, t32_finsub_1, t48_subset_1, t28_relat_1, t32_borsuk_1, d4_tops_1, t35_lopclset, t57_filter_1, t32_filter_1, d12_filter_0, t42_lattice4, t50_subset_1, t65_filter_0, t55_borsuk_1, rc2_pre_topc, t46_xboole_1, t71_borsuk_1, t149_relat_1, d15_borsuk_1, redefinition_k20_borsuk_1, t74_tops_1, t33_funct_1, t159_funct_1, t57_funct_1, d19_lattices, t67_partfun1, redefinition_k6_subset_1, t58_setfam_1, t12_relset_1, t14_funct_3, t53_lattice2, existence_l1_struct_0, t5_xboole_1, t45_filter_0, t49_subset_1, t7_tarski, commutativity_k2_lopclset, rc1_partfun1, t71_filter_0, dt_k2_lattices, t3_xboole_0, t28_lattice4, t79_lattice2, dt_k2_setwiseo, t3_boole, redefinition_k2_setwiseo, t13_lopclset, d5_funct_1, t6_ordinal1, t24_funct_3, t20_lopclset, fc1_lattice4, dt_k3_funct_3, redefinition_m2_subset_1, t43_filter_1, t25_relat_1, d1_tops_1, t17_funct_3, t55_filter_1, t6_filter_0, idempotence_k4_subset_1, d14_group_1, t87_xboole_1, d3_filter_0, t24_pre_topc, dt_k3_pre_topc, t41_filter_1, fc14_finset_1, t60_lattice2, t50_filter_0, t26_funct_4, rc4_struct_0, rc5_pre_topc, t39_borsuk_1, dt_k3_lopclset, t49_lattice2, fc13_finset_1, t66_filter_0, t15_funct_4, t43_lattice4, t40_zfmisc_1, d11_lattices, t22_funct_4, rc2_xboole_0, t26_tops_1, t63_lattice2, t55_funct_2, t45_xboole_1, t44_tops_1, d1_pre_topc, dt_k6_pre_topc, t42_lopclset, t8_funct_3, t40_xboole_1, t10_xboole_1, dt_k3_subset_1, t4_funct_3, t6_relat_1, t6_lattice4, t14_lattice2, t159_relat_1, t63_subset_1, t94_tops_1, t42_pre_topc, t26_relat_1, dt_k2_pre_topc, t61_funct_2, t36_funct_4, fc3_lattices, t73_borsuk_1, t33_subset_1, t32_funct_4, t30_partfun1, t65_zfmisc_1, t14_pre_topc, t29_tops_1, fc2_lopclset, t13_filter_0, d3_xboole_0, t38_xboole_1, t19_funct_4, t39_xboole_1, t3_filter_0, t10_lattice4, t20_funct_4, antisymmetry_r2_hidden, t43_lopclset, dt_k1_setwiseo, t68_tops_1, t45_funct_4, d5_lattice4, t21_tops_1, d8_lattice4, t53_relat_1, cc1_pre_topc, t167_relat_1, t69_borsuk_1, t64_lattice2
% 117.60/33.15 % No. of inferences in proof: 3430
% 117.60/33.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32582 ms resp. 31119 ms w/o parsing
% 123.56/34.38 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 124.05/34.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------