TSTP Solution File: LAT334+4 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : LAT334+4 : TPTP v8.2.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 23:29:25 EDT 2024
% Result : Timeout 296.99s 68.02s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1544
% Syntax : Number of formulae : 3616 ( 657 unt; 352 typ; 0 def)
% Number of atoms : 16860 (2009 equ; 0 cnn)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 54898 (4472 ~; 968 |;7018 &;37056 @)
% ( 224 <=>;5160 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 666 ( 666 >; 0 *; 0 +; 0 <<)
% Number of symbols : 355 ( 352 usr; 53 con; 0-9 aty)
% Number of variables : 7097 ( 0 ^6755 !; 342 ?;7097 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_type,type,
v10_lattices: $i > $o ).
thf(l3_lattices_type,type,
l3_lattices: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(m2_lattice4_type,type,
m2_lattice4: $i > $i > $o ).
thf(v12_lattices_type,type,
v12_lattices: $i > $o ).
thf(k23_filter_2_type,type,
k23_filter_2: $i > $i > $i ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(v1_trees_1_type,type,
v1_trees_1: $i > $o ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(v1_realset1_type,type,
v1_realset1: $i > $o ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(v1_tex_2_type,type,
v1_tex_2: $i > $i > $o ).
thf(v17_lattices_type,type,
v17_lattices: $i > $o ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
thf(k8_lopclset_type,type,
k8_lopclset: $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(a_2_0_lopclset_type,type,
a_2_0_lopclset: $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(k3_relat_1_type,type,
k3_relat_1: $i > $i ).
thf(v4_lattice3_type,type,
v4_lattice3: $i > $o ).
thf(v13_lattices_type,type,
v13_lattices: $i > $o ).
thf(k5_lattices_type,type,
k5_lattices: $i > $i ).
thf(k15_lattice3_type,type,
k15_lattice3: $i > $i > $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(k13_lopclset_type,type,
k13_lopclset: $i > $i ).
thf(k16_coh_sp_type,type,
k16_coh_sp: $i > $i ).
thf(r4_lattice3_type,type,
r4_lattice3: $i > $i > $i > $o ).
thf(r1_lattices_type,type,
r1_lattices: $i > $i > $i > $o ).
thf(k1_funct_2_type,type,
k1_funct_2: $i > $i > $i ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $i > $i > $i ).
thf(k5_finsub_1_type,type,
k5_finsub_1: $i > $i ).
thf(k10_afinsq_1_type,type,
k10_afinsq_1: $i > $i ).
thf(r1_relat_2_type,type,
r1_relat_2: $i > $i > $o ).
thf(k2_pre_topc_type,type,
k2_pre_topc: $i > $i ).
thf(k1_trees_3_type,type,
k1_trees_3: $i ).
thf(k9_filter_1_type,type,
k9_filter_1: $i > $i ).
thf(r3_lattice3_type,type,
r3_lattice3: $i > $i > $i > $o ).
thf(k1_lattice4_type,type,
k1_lattice4: $i > $i > $i ).
thf(m2_card_fil_type,type,
m2_card_fil: $i > $i > $o ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(k1_pre_topc_type,type,
k1_pre_topc: $i > $i ).
thf(r3_lattices_type,type,
r3_lattices: $i > $i > $i > $o ).
thf(k16_lattice3_type,type,
k16_lattice3: $i > $i > $i ).
thf(k9_lopclset_type,type,
k9_lopclset: $i > $i ).
thf(a_2_1_lattice4_type,type,
a_2_1_lattice4: $i > $i > $i ).
thf(k2_lattice4_type,type,
k2_lattice4: $i > $i > $i ).
thf(k4_lattice4_type,type,
k4_lattice4: $i > $i > $i ).
thf(r8_relat_2_type,type,
r8_relat_2: $i > $i > $o ).
thf(v14_lattices_type,type,
v14_lattices: $i > $o ).
thf(k6_lattices_type,type,
k6_lattices: $i > $i ).
thf(k2_filter_0_type,type,
k2_filter_0: $i > $i > $i ).
thf(a_2_0_filter_0_type,type,
a_2_0_filter_0: $i > $i > $i ).
thf(v2_setfam_1_type,type,
v2_setfam_1: $i > $o ).
thf(k4_lattice3_type,type,
k4_lattice3: $i > $i > $i ).
thf(k3_lattice3_type,type,
k3_lattice3: $i > $i ).
thf(v1_matrix_2_type,type,
v1_matrix_2: $i > $o ).
thf(m3_matrix_2_type,type,
m3_matrix_2: $i > $i > $o ).
thf(m1_filter_0_type,type,
m1_filter_0: $i > $i > $o ).
thf(v1_filter_0_type,type,
v1_filter_0: $i > $i > $o ).
thf(r1_filter_0_type,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(k10_filter_0_type,type,
k10_filter_0: $i > $i > $i ).
thf(k5_filter_0_type,type,
k5_filter_0: $i > $i > $i > $i ).
thf(m1_lattice4_type,type,
m1_lattice4: $i > $i > $i > $o ).
thf(v2_lattice4_type,type,
v2_lattice4: $i > $i > $i > $o ).
thf(r2_lattice4_type,type,
r2_lattice4: $i > $i > $i > $o ).
thf(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(u2_lattices_type,type,
u2_lattices: $i > $i ).
thf(u1_lattices_type,type,
u1_lattices: $i > $i ).
thf(r1_boolealg_type,type,
r1_boolealg: $i > $i > $i > $o ).
thf(k1_boolealg_type,type,
k1_boolealg: $i > $i > $i > $i ).
thf(r1_filter_2_type,type,
r1_filter_2: $i > $i > $i > $o ).
thf(k19_filter_2_type,type,
k19_filter_2: $i > $i > $i ).
thf(m2_filter_2_type,type,
m2_filter_2: $i > $i > $o ).
thf(v3_filter_0_type,type,
v3_filter_0: $i > $o ).
thf(k3_lattice4_type,type,
k3_lattice4: $i > $i > $i ).
thf(v15_lattices_type,type,
v15_lattices: $i > $o ).
thf(v16_lattices_type,type,
v16_lattices: $i > $o ).
thf(r4_lattice4_type,type,
r4_lattice4: $i > $i > $i > $o ).
thf(k8_filter_1_type,type,
k8_filter_1: $i > $i > $i ).
thf(k10_filter_1_type,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(k3_lattices_type,type,
k3_lattices: $i > $i > $i > $i ).
thf(k8_filter_0_type,type,
k8_filter_0: $i > $i > $i ).
thf(v11_lattices_type,type,
v11_lattices: $i > $o ).
thf(k9_openlatt_type,type,
k9_openlatt: $i > $i ).
thf(k11_openlatt_type,type,
k11_openlatt: $i > $i > $i > $i ).
thf(k7_lattices_type,type,
k7_lattices: $i > $i > $i ).
thf(a_2_0_lattice3_type,type,
a_2_0_lattice3: $i > $i > $i ).
thf(a_2_1_domain_1_type,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k12_lopclset_type,type,
k12_lopclset: $i > $i ).
thf(k3_boolealg_type,type,
k3_boolealg: $i > $i > $i > $i ).
thf(k4_lattices_type,type,
k4_lattices: $i > $i > $i > $i ).
thf(k3_filter_0_type,type,
k3_filter_0: $i > $i > $i ).
thf(k4_filter_0_type,type,
k4_filter_0: $i > $i > $i > $i ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(k7_lopclset_type,type,
k7_lopclset: $i > $i ).
thf(k2_filter_2_type,type,
k2_filter_2: $i > $i > $i ).
thf(v6_group_1_type,type,
v6_group_1: $i > $o ).
thf(k17_filter_2_type,type,
k17_filter_2: $i > $i ).
thf(k1_struct_0_type,type,
k1_struct_0: $i > $i > $i ).
thf(v1_lattice2_type,type,
v1_lattice2: $i > $o ).
thf(a_1_1_openlatt_type,type,
a_1_1_openlatt: $i > $i ).
thf(k9_filter_0_type,type,
k9_filter_0: $i > $i > $i > $i ).
thf(l2_lang1_type,type,
l2_lang1: $i > $o ).
thf(k1_lattice2_type,type,
k1_lattice2: $i > $i ).
thf(k6_lopclset_type,type,
k6_lopclset: $i > $i ).
thf(k11_lopclset_type,type,
k11_lopclset: $i > $i ).
thf(k5_filter_1_type,type,
k5_filter_1: $i > $i > $i ).
thf(k6_filter_1_type,type,
k6_filter_1: $i > $i > $i > $i ).
thf(r1_lattice4_type,type,
r1_lattice4: $i > $i > $i > $o ).
thf(r2_filter_2_type,type,
r2_filter_2: $i > $i > $o ).
thf(r2_lattices_type,type,
r2_lattices: $i > $i > $i > $o ).
thf(k20_filter_2_type,type,
k20_filter_2: $i > $i > $i > $i ).
thf(k10_lopclset_type,type,
k10_lopclset: $i > $i ).
thf(k5_filter_2_type,type,
k5_filter_2: $i > $i > $i ).
thf(k6_filter_2_type,type,
k6_filter_2: $i > $i > $i ).
thf(k8_openlatt_type,type,
k8_openlatt: $i > $i ).
thf(a_2_0_openlatt_type,type,
a_2_0_openlatt: $i > $i > $i ).
thf(k10_openlatt_type,type,
k10_openlatt: $i > $i > $i ).
thf(v5_grcat_1_type,type,
v5_grcat_1: $i > $o ).
thf(m3_grcat_1_type,type,
m3_grcat_1: $i > $i > $o ).
thf(k3_filter_2_type,type,
k3_filter_2: $i > $i > $i ).
thf(r3_lattice4_type,type,
r3_lattice4: $i > $i > $i > $o ).
thf(k18_filter_2_type,type,
k18_filter_2: $i > $i > $i ).
thf(k11_filter_0_type,type,
k11_filter_0: $i > $i > $i ).
thf(v5_ringcat1_type,type,
v5_ringcat1: $i > $o ).
thf(m3_ringcat1_type,type,
m3_ringcat1: $i > $i > $o ).
thf(a_2_0_lattice4_type,type,
a_2_0_lattice4: $i > $i > $i ).
thf(v1_lattice4_type,type,
v1_lattice4: $i > $i > $i > $o ).
thf(m1_unialg_2_type,type,
m1_unialg_2: $i > $i > $o ).
thf(m2_unialg_2_type,type,
m2_unialg_2: $i > $i > $i > $o ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(k2_boolealg_type,type,
k2_boolealg: $i > $i > $i > $i ).
thf(k4_filter_2_type,type,
k4_filter_2: $i > $i > $i > $i ).
thf(k22_filter_2_type,type,
k22_filter_2: $i > $i > $i > $i ).
thf(v2_lang1_type,type,
v2_lang1: $i > $o ).
thf(k12_openlatt_type,type,
k12_openlatt: $i > $i > $i > $i ).
thf(r3_boolealg_type,type,
r3_boolealg: $i > $i > $i > $o ).
thf(k11_gate_1_type,type,
k11_gate_1: $i > $i > $i > $i ).
thf(k21_filter_2_type,type,
k21_filter_2: $i > $i > $i > $i ).
thf(k1_rlvect_2_type,type,
k1_rlvect_2: $i > $i > $i ).
thf(k2_struct_0_type,type,
k2_struct_0: $i > $i > $i > $i ).
thf(k15_openlatt_type,type,
k15_openlatt: $i > $i ).
thf(k16_openlatt_type,type,
k16_openlatt: $i > $i ).
thf(k8_rlvect_2_type,type,
k8_rlvect_2: $i > $i > $i > $i ).
thf(r1_rlvect_1_type,type,
r1_rlvect_1: $i > $i > $o ).
thf(a_1_1_lopclset_type,type,
a_1_1_lopclset: $i > $i ).
thf(k2_filter_1_type,type,
k2_filter_1: $i > $i > $i > $i ).
thf(k2_trees_3_type,type,
k2_trees_3: $i ).
thf(l1_orders_2_type,type,
l1_orders_2: $i > $o ).
thf(v5_orders_2_type,type,
v5_orders_2: $i > $i > $o ).
thf(m2_filter_1_type,type,
m2_filter_1: $i > $i > $i > $o ).
thf(k1_filter_0_type,type,
k1_filter_0: $i > $i ).
thf(m1_rfunct_3_type,type,
m1_rfunct_3: $i > $i > $i > $o ).
thf(m2_rfunct_3_type,type,
m2_rfunct_3: $i > $i > $i > $i > $o ).
thf(v1_quantal1_type,type,
v1_quantal1: $i > $i > $o ).
thf(v3_lattice4_type,type,
v3_lattice4: $i > $i > $i > $o ).
thf(a_3_1_filter_2_type,type,
a_3_1_filter_2: $i > $i > $i > $i ).
thf(k15_filter_2_type,type,
k15_filter_2: $i > $i > $i ).
thf(r1_lattice2_type,type,
r1_lattice2: $i > $i > $i > $o ).
thf(r2_boolealg_type,type,
r2_boolealg: $i > $i > $i > $o ).
thf(m2_nat_lat_type,type,
m2_nat_lat: $i > $i > $o ).
thf(v1_filter_2_type,type,
v1_filter_2: $i > $i > $o ).
thf(a_3_0_filter_0_type,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(v1_setwiseo_type,type,
v1_setwiseo: $i > $i > $o ).
thf(m1_filter_2_type,type,
m1_filter_2: $i > $i > $o ).
thf(k7_openlatt_type,type,
k7_openlatt: $i > $i ).
thf(a_3_1_filter_0_type,type,
a_3_1_filter_0: $i > $i > $i > $i ).
thf(l1_funcsdom_type,type,
l1_funcsdom: $i > $o ).
thf(r3_zfrefle1_type,type,
r3_zfrefle1: $i > $i > $o ).
thf(r2_zfrefle1_type,type,
r2_zfrefle1: $i > $i > $o ).
thf(m3_lattice4_type,type,
m3_lattice4: $i > $i > $o ).
thf(k13_filter_2_type,type,
k13_filter_2: $i > $i > $i ).
thf(r1_filter_1_type,type,
r1_filter_1: $i > $i > $o ).
thf(a_3_2_filter_2_type,type,
a_3_2_filter_2: $i > $i > $i > $i ).
thf(v2_filter_0_type,type,
v2_filter_0: $i > $i > $o ).
thf(r6_binop_1_type,type,
r6_binop_1: $i > $i > $i > $o ).
thf(k7_filter_2_type,type,
k7_filter_2: $i > $i > $i ).
thf(k8_filter_2_type,type,
k8_filter_2: $i > $i > $i ).
thf(k7_filter_0_type,type,
k7_filter_0: $i > $i > $i > $i ).
thf(v1_struct_0_type,type,
v1_struct_0: $i > $o ).
thf(g1_struct_0_type,type,
g1_struct_0: $i > $i ).
thf(a_1_0_filter_1_type,type,
a_1_0_filter_1: $i > $i ).
thf(k1_filter_1_type,type,
k1_filter_1: $i > $i > $i > $i ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(k16_filter_2_type,type,
k16_filter_2: $i > $i > $i ).
thf(l1_prelamb_type,type,
l1_prelamb: $i > $o ).
thf(k3_prelamb_type,type,
k3_prelamb: $i > $i > $i > $i ).
thf(k14_filter_2_type,type,
k14_filter_2: $i > $i > $i ).
thf(k17_grcat_1_type,type,
k17_grcat_1: $i > $i > $i ).
thf(k4_card_fil_type,type,
k4_card_fil: $i > $i ).
thf(k1_filter_2_type,type,
k1_filter_2: $i > $i ).
thf(k13_lang1_type,type,
k13_lang1: $i > $i ).
thf(k18_openlatt_type,type,
k18_openlatt: $i > $i ).
thf(m1_struct_0_type,type,
m1_struct_0: $i > $i > $i > $o ).
thf(k12_domain_1_type,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k24_filter_2_type,type,
k24_filter_2: $i > $i > $i ).
thf(k2_prelamb_type,type,
k2_prelamb: $i > $i > $i > $i ).
thf(a_2_0_filter_2_type,type,
a_2_0_filter_2: $i > $i > $i ).
thf(a_1_2_domain_1_type,type,
a_1_2_domain_1: $i > $i ).
thf(k6_filter_0_type,type,
k6_filter_0: $i > $i > $i > $i ).
thf(k3_gate_1_type,type,
k3_gate_1: $i > $i > $i ).
thf(k18_gate_1_type,type,
k18_gate_1: $i > $i > $i > $i > $i > $i ).
thf(a_1_0_domain_1_type,type,
a_1_0_domain_1: $i > $i ).
thf(r4_wellord1_type,type,
r4_wellord1: $i > $i > $o ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(k1_finsub_1_type,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(v1_funcsdom_type,type,
v1_funcsdom: $i > $o ).
thf(k13_funcsdom_type,type,
k13_funcsdom: $i > $i ).
thf(k8_lattice3_type,type,
k8_lattice3: $i > $i > $i ).
thf(a_2_1_openlatt_type,type,
a_2_1_openlatt: $i > $i > $i ).
thf(k1_tex_1_type,type,
k1_tex_1: $i > $i ).
thf(k1_lopclset_type,type,
k1_lopclset: $i > $i ).
thf(k1_prelamb_type,type,
k1_prelamb: $i > $i > $i > $i ).
thf(k13_nat_lat_type,type,
k13_nat_lat: $i ).
thf(k6_nat_lat_type,type,
k6_nat_lat: $i ).
thf(a_3_0_filter_2_type,type,
a_3_0_filter_2: $i > $i > $i > $i ).
thf(a_1_0_openlatt_type,type,
a_1_0_openlatt: $i > $i ).
thf(k11_domain_1_type,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k13_domain_1_type,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(l2_quantal1_type,type,
l2_quantal1: $i > $o ).
thf(k3_sgraph1_type,type,
k3_sgraph1: $i > $i ).
thf(k14_gate_1_type,type,
k14_gate_1: $i > $i > $i > $i > $i ).
thf(k12_gate_1_type,type,
k12_gate_1: $i > $i > $i > $i ).
thf(k4_modal_1_type,type,
k4_modal_1: $i ).
thf(k5_gate_1_type,type,
k5_gate_1: $i > $i > $i ).
thf(k12_filter_2_type,type,
k12_filter_2: $i > $i > $i ).
thf(k10_filter_2_type,type,
k10_filter_2: $i > $i > $i ).
thf(k8_gate_1_type,type,
k8_gate_1: $i > $i > $i > $i ).
thf(k9_filter_2_type,type,
k9_filter_2: $i > $i > $i ).
thf(k1_heyting1_type,type,
k1_heyting1: $i > $i ).
thf(r2_subset_1_type,type,
r2_subset_1: $i > $i > $o ).
thf(k9_gate_1_type,type,
k9_gate_1: $i > $i > $i > $i ).
thf(k15_gate_1_type,type,
k15_gate_1: $i > $i > $i > $i > $i ).
thf(m1_modal_1_type,type,
m1_modal_1: $i > $i > $o ).
thf(k17_gate_1_type,type,
k17_gate_1: $i > $i > $i > $i > $i ).
thf(k2_lattice3_type,type,
k2_lattice3: $i > $i ).
thf(k14_lattice3_type,type,
k14_lattice3: $i > $i ).
thf(k23_gate_1_type,type,
k23_gate_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k19_gate_1_type,type,
k19_gate_1: $i > $i > $i > $i > $i > $i ).
thf(k22_gate_1_type,type,
k22_gate_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k16_gate_1_type,type,
k16_gate_1: $i > $i > $i > $i > $i ).
thf(k24_gate_1_type,type,
k24_gate_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k11_filter_2_type,type,
k11_filter_2: $i > $i > $i ).
thf(m2_prelamb_type,type,
m2_prelamb: $i > $i > $i > $o ).
thf(k3_zf_model_type,type,
k3_zf_model: $i > $i ).
thf(k2_topreal1_type,type,
k2_topreal1: $i ).
thf(k7_real_lat_type,type,
k7_real_lat: $i > $i ).
thf(k27_gate_1_type,type,
k27_gate_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k26_gate_1_type,type,
k26_gate_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k15_coh_sp_type,type,
k15_coh_sp: $i > $i ).
thf(k29_gate_1_type,type,
k29_gate_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k13_gate_1_type,type,
k13_gate_1: $i > $i > $i > $i ).
thf(k21_gate_1_type,type,
k21_gate_1: $i > $i > $i > $i > $i > $i ).
thf(k30_gate_1_type,type,
k30_gate_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k20_gate_1_type,type,
k20_gate_1: $i > $i > $i > $i > $i > $i ).
thf(k33_gate_1_type,type,
k33_gate_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k7_gate_1_type,type,
k7_gate_1: $i > $i > $i ).
thf(k6_metric_1_type,type,
k6_metric_1: $i > $i ).
thf(v1_metric_1_type,type,
v1_metric_1: $i > $o ).
thf(k32_gate_1_type,type,
k32_gate_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_1_0_card_fil_type,type,
a_1_0_card_fil: $i > $i ).
thf(k6_gate_1_type,type,
k6_gate_1: $i > $i > $i ).
thf(k34_gate_1_type,type,
k34_gate_1: $i > $i > $i ).
thf(k28_gate_1_type,type,
k28_gate_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k25_gate_1_type,type,
k25_gate_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k31_gate_1_type,type,
k31_gate_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $o ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(sk11_type,type,
sk11: $i > $i > $i ).
thf(sk12_type,type,
sk12: $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(sk14_type,type,
sk14: $i > $i > $i ).
thf(sk15_type,type,
sk15: $i > $i > $i ).
thf(sk16_type,type,
sk16: $i > $i > $i > $i ).
thf(sk17_type,type,
sk17: $i > $i ).
thf(sk18_type,type,
sk18: $i > $i > $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk21_type,type,
sk21: $i ).
thf(sk27_type,type,
sk27: $i > $i ).
thf(sk38_type,type,
sk38: $i > $i > $i ).
thf(sk44_type,type,
sk44: $i ).
thf(sk60_type,type,
sk60: $i ).
thf(sk72_type,type,
sk72: $i ).
thf(sk75_type,type,
sk75: $i ).
thf(sk89_type,type,
sk89: $i ).
thf(sk90_type,type,
sk90: $i > $i ).
thf(sk101_type,type,
sk101: $i ).
thf(sk113_type,type,
sk113: $i > $i ).
thf(sk130_type,type,
sk130: $i ).
thf(sk133_type,type,
sk133: $i ).
thf(sk135_type,type,
sk135: $i ).
thf(sk139_type,type,
sk139: $i ).
thf(sk145_type,type,
sk145: $i ).
thf(sk149_type,type,
sk149: $i ).
thf(sk156_type,type,
sk156: $i ).
thf(sk179_type,type,
sk179: $i ).
thf(sk183_type,type,
sk183: $i ).
thf(sk195_type,type,
sk195: $i > $i ).
thf(sk201_type,type,
sk201: $i ).
thf(sk213_type,type,
sk213: $i > $i ).
thf(sk223_type,type,
sk223: $i > $i ).
thf(sk225_type,type,
sk225: $i ).
thf(sk235_type,type,
sk235: $i ).
thf(sk236_type,type,
sk236: $i ).
thf(sk244_type,type,
sk244: $i ).
thf(sk248_type,type,
sk248: $i ).
thf(sk249_type,type,
sk249: $i ).
thf(sk250_type,type,
sk250: $i ).
thf(sk267_type,type,
sk267: $i ).
thf(sk280_type,type,
sk280: $i ).
thf(sk291_type,type,
sk291: $i ).
thf(sk293_type,type,
sk293: $i ).
thf(sk305_type,type,
sk305: $i ).
thf(sk310_type,type,
sk310: $i ).
thf(sk316_type,type,
sk316: $i ).
thf(sk318_type,type,
sk318: $i ).
thf(sk319_type,type,
sk319: $i ).
thf(sk321_type,type,
sk321: $i > $i > $i ).
thf(sk324_type,type,
sk324: $i ).
thf(sk328_type,type,
sk328: $i ).
thf(sk330_type,type,
sk330: $i ).
thf(sk331_type,type,
sk331: $i ).
thf(sk334_type,type,
sk334: $i ).
thf(sk336_type,type,
sk336: $i ).
thf(sk338_type,type,
sk338: $i ).
thf(sk339_type,type,
sk339: $i ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m3_lattice4 @ ( k3_lattice4 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(3962,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m3_lattice4 @ ( k3_lattice4 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(220,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(2276,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(2278,plain,
v2_funct_1 @ sk89,
inference(cnf,[status(esa)],[2276]) ).
thf(2277,plain,
v1_xboole_0 @ sk89,
inference(cnf,[status(esa)],[2276]) ).
thf(21,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(1282,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1283,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1282]) ).
thf(1284,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[1283]) ).
thf(12907,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk89 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2277,1284]) ).
thf(12908,plain,
sk89 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[12907:[bind(A,$thf( sk89 ))]]) ).
thf(13955,plain,
v2_funct_1 @ k1_xboole_0,
inference(rewrite,[status(thm)],[2278,12908]) ).
thf(875,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v3_lattice4 @ C @ B @ A )
=> ( ( v3_filter_0 @ A )
& ( r1_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lattice4) ).
thf(4909,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v3_lattice4 @ C @ B @ A )
=> ( ( v3_filter_0 @ A )
& ( r1_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(702,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) @ ( k3_lattices @ A @ B @ C ) )
=> ( ( r2_boolealg @ A @ B @ ( k7_lattices @ A @ B ) )
| ( r2_boolealg @ A @ C @ ( k7_lattices @ A @ C ) )
| ( ( r1_boolealg @ A @ B @ ( k7_lattices @ A @ C ) )
& ( r1_boolealg @ A @ C @ ( k7_lattices @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_boolealg) ).
thf(4262,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) @ ( k3_lattices @ A @ B @ C ) )
=> ( ( r2_boolealg @ A @ B @ ( k7_lattices @ A @ B ) )
| ( r2_boolealg @ A @ C @ ( k7_lattices @ A @ C ) )
| ( ( r1_boolealg @ A @ B @ ( k7_lattices @ A @ C ) )
& ( r1_boolealg @ A @ C @ ( k7_lattices @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(993,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_tops_1) ).
thf(5390,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(1069,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_filter_1) ).
thf(5676,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(1152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k20_gate_1 @ A @ B @ C @ D @ E ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
& ( v1_xboole_0 @ ( k20_gate_1 @ A @ B @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_gate_1) ).
thf(6074,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k20_gate_1 @ A @ B @ C @ D @ E ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
& ( v1_xboole_0 @ ( k20_gate_1 @ A @ B @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(873,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ D ) ) @ ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_filter_1) ).
thf(4904,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ D ) ) @ ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(991,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(5385,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(1102,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_nat_lat @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_nat_lat) ).
thf(5810,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_nat_lat @ B @ A )
=> ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(32,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(1321,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1322,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[1321]) ).
thf(94,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k1_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k2_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k3_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_filter_1) ).
thf(1665,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k1_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k2_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k3_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1071,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v14_lattices @ A )
& ( v14_lattices @ B ) )
<=> ( v14_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_filter_1) ).
thf(5686,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v14_lattices @ A )
& ( v14_lattices @ B ) )
=> ( v14_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v14_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v14_lattices @ A )
& ( v14_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(345,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_filter_2) ).
thf(2822,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( r2_filter_2 @ A @ B )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) )
=> ( r2_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(184,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_relat_1) ).
thf(2094,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_rfunct_3 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_rfunct_3) ).
thf(5469,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_rfunct_3 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(629,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k1_boolealg @ A @ B @ C ) ) @ ( k4_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_boolealg) ).
thf(3944,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k1_boolealg @ A @ B @ C ) ) @ ( k4_lattices @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) )
& ( v1_funct_1 @ ( k4_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_grfunc_1) ).
thf(1411,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) )
& ( v1_funct_1 @ ( k4_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(74,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
thf(1508,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1515,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1508]) ).
thf(1518,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( v1_relat_1 @ ( sk27 @ A ) ) ),
inference(lifteq,[status(thm)],[1515]) ).
thf(149,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(1917,plain,
! [A: $i] :
( ( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1918,plain,
( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(miniscope,[status(thm)],[1917]) ).
thf(1919,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(cnf,[status(esa)],[1918]) ).
thf(1921,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( v1_xboole_0 @ A ) ),
inference(lifteq,[status(thm)],[1919]) ).
thf(1922,plain,
v1_xboole_0 @ k1_xboole_0,
inference(simp,[status(thm)],[1921]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( v12_lattices @ A )
=> ( v12_lattices @ ( k23_filter_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_filter_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( v12_lattices @ A )
=> ( v12_lattices @ ( k23_filter_2 @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1192,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( v12_lattices @ A )
=> ( v12_lattices @ ( k23_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1195,plain,
m2_lattice4 @ sk2 @ sk1,
inference(cnf,[status(esa)],[1192]) ).
thf(12943,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( m2_lattice4 @ sk2 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1284,1195]) ).
thf(12944,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( m2_lattice4 @ sk2 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[12943:[bind(A,$thf( sk1 ))]]) ).
thf(14975,plain,
( ( m2_lattice4 @ sk2 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,12944]) ).
thf(14996,plain,
( ( m2_lattice4 @ sk2 @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14975]) ).
thf(25927,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( m2_lattice4 @ sk2 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1518,14996]) ).
thf(25928,plain,
( ( v1_relat_1 @ ( sk27 @ sk1 ) )
| ( m2_lattice4 @ sk2 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25927:[bind(A,$thf( sk1 ))]]) ).
thf(664,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k1_boolealg @ A @ C @ D ) ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_boolealg) ).
thf(4094,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k1_boolealg @ A @ C @ D ) ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1076,axiom,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( v13_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_nat_lat) ).
thf(5707,plain,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( v13_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(5708,plain,
l3_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[5707]) ).
thf(26015,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ( A != k6_nat_lat ) ),
inference(paramod_ordered,[status(thm)],[1518,5708]) ).
thf(26016,plain,
( ( v1_relat_1 @ ( sk27 @ k6_nat_lat ) )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26015:[bind(A,$thf( k6_nat_lat ))]]) ).
thf(1124,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k7_real_lat @ A ) )
& ( v10_lattices @ ( k7_real_lat @ A ) )
& ( v11_lattices @ ( k7_real_lat @ A ) )
& ( l3_lattices @ ( k7_real_lat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_real_lat) ).
thf(5918,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k7_real_lat @ A ) )
& ( v10_lattices @ ( k7_real_lat @ A ) )
& ( v11_lattices @ ( k7_real_lat @ A ) )
& ( l3_lattices @ ( k7_real_lat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(66,axiom,
! [A: $i] :
( ( ( v1_finset_1 @ A )
& ! [B: $i,C: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B ) ) )
=> ( ( A = k1_xboole_0 )
| ( r2_hidden @ ( k3_tarski @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_card_2) ).
thf(1469,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
& ! [B: $i,C: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ C @ B ) ) )
=> ( ( A = k1_xboole_0 )
| ( r2_hidden @ ( k3_tarski @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) )
<=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(5088,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) )
=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) )
& ( ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) )
=> ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(45,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(1369,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(850,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_filter_1) ).
thf(4835,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(227,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k5_lattices @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_boolealg) ).
thf(2295,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k5_lattices @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(231,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(2306,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_boolealg @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_boolealg) ).
thf(4571,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_boolealg @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(365,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(2924,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(2925,plain,
v1_finset_1 @ sk133,
inference(cnf,[status(esa)],[2924]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finset_1) ).
thf(1216,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1217,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(miniscope,[status(thm)],[1216]) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ~ ( v1_finset_1 @ A )
| ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[1217]) ).
thf(6876,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk133 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2925,1218]) ).
thf(6877,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk133 @ A ) ),
inference(pattern_uni,[status(thm)],[6876:[bind(A,$thf( sk133 ))]]) ).
thf(6917,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk133 @ A ) ),
inference(simp,[status(thm)],[6877]) ).
thf(15266,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k4_xboole_0 @ sk133 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6917,1218]) ).
thf(15267,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk133 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[15266:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ sk133 @ E )),bind(C,$thf( C ))]]) ).
thf(15278,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk133 @ B ) @ A ) ),
inference(simp,[status(thm)],[15267]) ).
thf(475,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(3345,plain,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(927,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v1_struct_0 @ A )
& ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_1) ).
thf(5133,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v1_struct_0 @ A )
& ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(5136,plain,
v1_struct_0 @ sk293,
inference(cnf,[status(esa)],[5133]) ).
thf(1184,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k10_afinsq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_afinsq_1) ).
thf(6231,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k10_afinsq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(871,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( v3_filter_0 @ ( k5_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_1) ).
thf(4899,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( v3_filter_0 @ ( k5_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_filter_2 @ A @ B @ C )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
thf(3798,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( r1_filter_2 @ A @ B @ C )
=> ( B = C ) )
& ( ( B = C )
=> ( r1_filter_2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(646,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
& ( B = D )
& ( C = E ) )
=> ( r3_lattices @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_lattice2) ).
thf(4022,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
& ( B = D )
& ( C = E ) )
=> ( r3_lattices @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice4) ).
thf(1729,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(492,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( C = D )
=> ( ( ( r3_lattice3 @ A @ C @ E )
=> ( r3_lattice3 @ B @ D @ E ) )
& ( ( r3_lattice3 @ B @ D @ E )
=> ( r3_lattice3 @ A @ C @ E ) )
& ( ( r4_lattice3 @ A @ C @ E )
=> ( r4_lattice3 @ B @ D @ E ) )
& ( ( r4_lattice3 @ B @ D @ E )
=> ( r4_lattice3 @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_quantal1) ).
thf(3434,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( C = D )
=> ( ( ( r3_lattice3 @ A @ C @ E )
=> ( r3_lattice3 @ B @ D @ E ) )
& ( ( r3_lattice3 @ B @ D @ E )
=> ( r3_lattice3 @ A @ C @ E ) )
& ( ( r4_lattice3 @ A @ C @ E )
=> ( r4_lattice3 @ B @ D @ E ) )
& ( ( r4_lattice3 @ B @ D @ E )
=> ( r4_lattice3 @ A @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(429,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r2_hidden @ ( k6_lattices @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_0) ).
thf(3167,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r2_hidden @ ( k6_lattices @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(1394,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1395,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(cnf,[status(esa)],[1394]) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(lifteq,[status(thm)],[1395]) ).
thf(57,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A )
& ( v1_trees_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_trees_1) ).
thf(1414,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A )
& ( v1_trees_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1416,plain,
v1_finset_1 @ sk19,
inference(cnf,[status(esa)],[1414]) ).
thf(6899,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk19 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1416,1218]) ).
thf(6900,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk19 @ A ) ),
inference(pattern_uni,[status(thm)],[6899:[bind(A,$thf( sk19 ))]]) ).
thf(6913,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk19 @ A ) ),
inference(simp,[status(thm)],[6900]) ).
thf(14948,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k4_xboole_0 @ sk19 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6913,1218]) ).
thf(14949,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[14948:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ sk19 @ E )),bind(C,$thf( C ))]]) ).
thf(14961,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A ) ),
inference(simp,[status(thm)],[14949]) ).
thf(383,axiom,
? [A: $i] :
~ ( v1_finset_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_card_5) ).
thf(2990,plain,
? [A: $i] :
~ ( v1_finset_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(2991,plain,
~ ! [A: $i] : ( v1_finset_1 @ A ),
inference(miniscope,[status(thm)],[2990]) ).
thf(2992,plain,
~ ( v1_finset_1 @ sk139 ),
inference(cnf,[status(esa)],[2991]) ).
thf(44475,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[14961,2992]) ).
thf(44512,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[44475]) ).
thf(45684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ A @ B )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,44512]) ).
thf(45685,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45684:[bind(A,$thf( k4_xboole_0 @ sk19 @ J )),bind(B,$thf( H )),bind(C,$thf( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ J ) @ H )),bind(D,$thf( J ))]]) ).
thf(45837,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[45685]) ).
thf(11,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k8_lopclset @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( a_2_0_lopclset @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lopclset) ).
thf(1232,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k8_lopclset @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( a_2_0_lopclset @ A @ C ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( a_2_0_lopclset @ A @ C ) ) ) )
=> ( B
= ( k8_lopclset @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1233,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_relat_1 @ B )
!= ( u1_struct_0 @ A ) )
| ( ( k1_funct_1 @ B @ ( sk7 @ B @ A ) )
!= ( a_2_0_lopclset @ A @ ( sk7 @ B @ A ) ) )
| ( B
= ( k8_lopclset @ A ) ) ),
inference(cnf,[status(esa)],[1232]) ).
thf(1237,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= ( u1_struct_0 @ A ) )
| ( ( a_2_0_lopclset @ A @ ( sk7 @ B @ A ) )
!= ( k1_funct_1 @ B @ ( sk7 @ B @ A ) ) )
| ( B
= ( k8_lopclset @ A ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B ) ),
inference(lifteq,[status(thm)],[1233]) ).
thf(364,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice3) ).
thf(2921,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(711,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k2_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(4290,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k2_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(496,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_boolealg @ A @ B @ ( k1_boolealg @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_boolealg) ).
thf(3477,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_boolealg @ A @ B @ ( k1_boolealg @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(552,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relat_1) ).
thf(3698,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).
thf(1840,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(175,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_realset1) ).
thf(2021,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(2022,plain,
v1_realset1 @ sk60,
inference(cnf,[status(esa)],[2021]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( ~ ( v1_realset1 @ A )
& ! [B: $i,C: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) ) )
& ~ ( ? [B: $i,C: $i] :
( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) )
& ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_realset1) ).
thf(1243,plain,
! [A: $i] :
( ~ ( ~ ( v1_realset1 @ A )
& ! [B: $i,C: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) ) )
& ~ ( ? [B: $i,C: $i] :
( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A )
& ( B != C ) )
& ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1244,plain,
( ~ ? [A: $i] :
( ~ ( v1_realset1 @ A )
& ~ ? [B: $i] :
( ( r2_hidden @ B @ A )
& ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( B != C ) ) ) )
& ~ ? [A: $i] :
( ? [B: $i] :
( ( r2_hidden @ B @ A )
& ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( B != C ) ) )
& ( v1_realset1 @ A ) ) ),
inference(miniscope,[status(thm)],[1243]) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ B @ A )
| ~ ( r2_hidden @ C @ A )
| ( B = C )
| ~ ( v1_realset1 @ A ) ),
inference(cnf,[status(esa)],[1244]) ).
thf(1249,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( r2_hidden @ B @ A )
| ~ ( r2_hidden @ C @ A )
| ~ ( v1_realset1 @ A ) ),
inference(lifteq,[status(thm)],[1245]) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( r2_hidden @ B @ A )
| ~ ( r2_hidden @ C @ A )
| ~ ( v1_realset1 @ A ) ),
inference(simp,[status(thm)],[1249]) ).
thf(1196,plain,
~ ( v1_xboole_0 @ sk2 ),
inference(cnf,[status(esa)],[1192]) ).
thf(6316,plain,
( ( v1_xboole_0 @ sk89 )
!= ( v1_xboole_0 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2277,1196]) ).
thf(6328,plain,
sk89 != sk2,
inference(simp,[status(thm)],[6316]) ).
thf(8191,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r2_hidden @ B @ A )
| ~ ( r2_hidden @ C @ A )
| ~ ( v1_realset1 @ A )
| ( C != sk2 )
| ( B != sk89 ) ),
inference(paramod_ordered,[status(thm)],[1250,6328]) ).
thf(8192,plain,
! [B: $i,A: $i] :
( ~ ( r2_hidden @ sk89 @ A )
| ~ ( r2_hidden @ B @ A )
| ~ ( v1_realset1 @ A )
| ( B != sk2 ) ),
inference(pattern_uni,[status(thm)],[8191:[bind(A,$thf( A )),bind(B,$thf( sk89 ))]]) ).
thf(9231,plain,
! [A: $i] :
( ~ ( r2_hidden @ sk89 @ A )
| ~ ( r2_hidden @ sk2 @ A )
| ~ ( v1_realset1 @ A ) ),
inference(simp,[status(thm)],[8192]) ).
thf(9863,plain,
! [A: $i] :
( ~ ( r2_hidden @ sk89 @ A )
| ~ ( r2_hidden @ sk2 @ A )
| ( ( v1_realset1 @ sk60 )
!= ( v1_realset1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2022,9231]) ).
thf(9864,plain,
( ~ ( r2_hidden @ sk89 @ sk60 )
| ~ ( r2_hidden @ sk2 @ sk60 ) ),
inference(pattern_uni,[status(thm)],[9863:[bind(A,$thf( sk60 ))]]) ).
thf(13933,plain,
( ~ ( r2_hidden @ k1_xboole_0 @ sk60 )
| ~ ( r2_hidden @ sk2 @ sk60 ) ),
inference(rewrite,[status(thm)],[9864,12908]) ).
thf(637,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ D ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ D ) @ ( k1_boolealg @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_boolealg) ).
thf(3969,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ D ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ D ) @ ( k1_boolealg @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(164,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
thf(1982,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_boolealg @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_boolealg) ).
thf(5028,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_boolealg @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(816,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k5_filter_0 @ A @ D @ E ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k5_filter_0 @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_filter_0) ).
thf(4728,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k5_filter_0 @ A @ D @ E ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k5_filter_0 @ A @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(232,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r8_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_filter_0) ).
thf(2309,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r8_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(54,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_trees_1) ).
thf(1404,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_trees_1 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_trees_1 @ B )
| ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[1404]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(1288,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1289,plain,
! [C: $i,B: $i,A: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(cnf,[status(esa)],[1288]) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] :
( ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) )
= ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(lifteq,[status(thm)],[1289]) ).
thf(968,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ D @ C ) @ ( k1_boolealg @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_boolealg) ).
thf(5297,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ D @ C ) @ ( k1_boolealg @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(885,axiom,
? [A: $i] :
( ( l1_funcsdom @ A )
& ( v1_funcsdom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funcsdom) ).
thf(4959,plain,
? [A: $i] :
( ( l1_funcsdom @ A )
& ( v1_funcsdom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(4960,plain,
v1_funcsdom @ sk280,
inference(cnf,[status(esa)],[4959]) ).
thf(788,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_realset1) ).
thf(4603,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(416,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(3119,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(3120,plain,
v1_finset_1 @ sk149,
inference(cnf,[status(esa)],[3119]) ).
thf(6874,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk149 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3120,1218]) ).
thf(6875,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk149 @ A ) ),
inference(pattern_uni,[status(thm)],[6874:[bind(A,$thf( sk149 ))]]) ).
thf(6916,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk149 @ A ) ),
inference(simp,[status(thm)],[6875]) ).
thf(15099,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k4_xboole_0 @ sk149 @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6916,1218]) ).
thf(15100,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk149 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[15099:[bind(A,$thf( E )),bind(B,$thf( k4_xboole_0 @ sk149 @ E )),bind(C,$thf( C ))]]) ).
thf(15123,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk149 @ B ) @ A ) ),
inference(simp,[status(thm)],[15100]) ).
thf(45765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk149 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1396,15123]) ).
thf(45766,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ sk149 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[45765:[bind(A,$thf( sk149 )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( k4_xboole_0 @ sk149 @ F ))]]) ).
thf(45811,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ sk149 @ B ) @ A ) ),
inference(simp,[status(thm)],[45766]) ).
thf(796,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_lattice2) ).
thf(4623,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1176,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_2 @ A )
= ( k1_filter_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).
thf(6194,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_2 @ A )
= ( k1_filter_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(1855,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(3,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1200,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1006,axiom,
? [A: $i] : ( l2_quantal1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_quantal1) ).
thf(5444,plain,
? [A: $i] : ( l2_quantal1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(506,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_pre_topc) ).
thf(3534,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(111,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(1750,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(202,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(2195,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(2196,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2195]) ).
thf(2197,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2196]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1407,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1408,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[1407]) ).
thf(1409,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ B )
!= ( k4_xboole_0 @ B @ A ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1408]) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ( sk18 @ A @ ( k4_xboole_0 @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk18])]) ).
thf(49474,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk18 @ B @ k1_xboole_0 )
= C )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2197,1410]) ).
thf(49475,plain,
! [A: $i] :
( ( sk18 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[49474:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(1141,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_matrix_2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_matrix_2) ).
thf(6020,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_matrix_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(6022,plain,
~ ( v1_xboole_0 @ sk331 ),
inference(cnf,[status(esa)],[6020]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(3681,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) ) )
=> ( ~ ( v1_xboole_0 @ ( k3_tarski @ A ) )
& ( v1_trees_1 @ ( k3_tarski @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_trees_2) ).
thf(1209,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) ) )
=> ( ~ ( v1_xboole_0 @ ( k3_tarski @ A ) )
& ( v1_trees_1 @ ( k3_tarski @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1211,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( r2_hidden @ ( sk4 @ A ) @ A )
| ( sk3 @ A ) ),
inference(cnf,[status(esa)],[1209]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_openlatt @ B @ C ) )
<=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ ( k7_openlatt @ B ) )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_openlatt) ).
thf(3990,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_openlatt @ B @ C ) )
=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ ( k7_openlatt @ B ) )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ ( k7_openlatt @ B ) )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_openlatt @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(404,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k6_domain_1 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(3072,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k6_domain_1 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(150,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_lopclset) ).
thf(1924,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(468,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(3317,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k20_filter_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k20_filter_2) ).
thf(5168,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k20_filter_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(1106,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k16_openlatt @ A )
= ( k8_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k16_openlatt) ).
thf(5820,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k16_openlatt @ A )
= ( k8_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(720,axiom,
? [A: $i] :
~ ( v2_setfam_1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(4339,plain,
? [A: $i] :
~ ( v2_setfam_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1197,plain,
v10_lattices @ sk1,
inference(cnf,[status(esa)],[1192]) ).
thf(13645,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v10_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1284,1197]) ).
thf(13646,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13645:[bind(A,$thf( sk1 ))]]) ).
thf(14618,plain,
( ( v10_lattices @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,13646]) ).
thf(14625,plain,
( ( v10_lattices @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14618]) ).
thf(302,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(2622,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(70,axiom,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(1492,plain,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1493,plain,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1492]) ).
thf(1201,plain,
( ( k1_tarski @ k1_xboole_0 )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1200]) ).
thf(7008,plain,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[1493,1201]) ).
thf(715,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_filter_0 @ A @ B )
= ( k2_filter_0 @ A @ C ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_filter_1) ).
thf(4311,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_filter_0 @ A @ B )
= ( k2_filter_0 @ A @ C ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(340,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ B @ C ) ) @ ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_boolealg) ).
thf(2808,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ B @ C ) ) @ ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1157,axiom,
( ~ ( v3_struct_0 @ k13_nat_lat )
& ( v10_lattices @ k13_nat_lat )
& ( l3_lattices @ k13_nat_lat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_nat_lat) ).
thf(6106,plain,
( ~ ( v3_struct_0 @ k13_nat_lat )
& ( v10_lattices @ k13_nat_lat )
& ( l3_lattices @ k13_nat_lat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(3813,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(442,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) )
<=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_fin_topo) ).
thf(3230,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ( ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) )
=> ~ ( r2_hidden @ C @ B ) )
& ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1178,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v15_lattices @ A )
& ( v15_lattices @ B ) )
<=> ( v15_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_filter_1) ).
thf(6199,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v15_lattices @ A )
& ( v15_lattices @ B ) )
=> ( v15_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v15_lattices @ A )
& ( v15_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(1022,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v1_struct_0 @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tex_1) ).
thf(5496,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v1_struct_0 @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(5498,plain,
~ ( v3_struct_0 @ sk316 ),
inference(cnf,[status(esa)],[5496]) ).
thf(13061,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk316 ) ),
inference(paramod_ordered,[status(thm)],[1284,5498]) ).
thf(13062,plain,
( ~ ( v1_xboole_0 @ sk316 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13061:[bind(A,$thf( sk316 ))]]) ).
thf(731,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattices) ).
thf(4391,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(425,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k15_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k16_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattice3) ).
thf(3153,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k15_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k16_lattice3 @ A @ ( k2_struct_0 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
thf(1422,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(81,axiom,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k10_afinsq_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_afinsq_1) ).
thf(1568,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k10_afinsq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1569,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k10_afinsq_1 @ A ) ),
inference(cnf,[status(esa)],[1568]) ).
thf(212,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tex_2) ).
thf(2248,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(3648,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(3649,plain,
( ! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
=> ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(miniscope,[status(thm)],[3648]) ).
thf(3652,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k1_tarski @ A ) )
| ( C != A )
| ( r2_hidden @ C @ B ) ),
inference(cnf,[status(esa)],[3649]) ).
thf(3666,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k1_tarski @ A ) )
| ( C != A )
| ( r2_hidden @ C @ B ) ),
inference(lifteq,[status(thm)],[3652]) ).
thf(3667,plain,
! [A: $i] : ( r2_hidden @ A @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[3666]) ).
thf(21971,plain,
! [A: $i] :
( ( r2_hidden @ A @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1201,3667]) ).
thf(21972,plain,
r2_hidden @ k1_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[21971:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(21968,plain,
! [A: $i] :
( ~ ( r2_hidden @ k1_xboole_0 @ sk60 )
| ( ( r2_hidden @ A @ ( k1_tarski @ A ) )
!= ( r2_hidden @ sk2 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[3667,13933]) ).
thf(21991,plain,
! [A: $i] :
( ~ ( r2_hidden @ k1_xboole_0 @ sk60 )
| ( A != sk2 )
| ( ( k1_tarski @ A )
!= sk60 ) ),
inference(simp,[status(thm)],[21968]) ).
thf(21998,plain,
( ~ ( r2_hidden @ k1_xboole_0 @ sk60 )
| ( ( k1_tarski @ sk2 )
!= sk60 ) ),
inference(simp,[status(thm)],[21991]) ).
thf(42543,plain,
( ( ( k1_tarski @ sk2 )
!= sk60 )
| ( ( r2_hidden @ k1_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( r2_hidden @ k1_xboole_0 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[21972,21998]) ).
thf(42632,plain,
( ( ( k1_tarski @ sk2 )
!= sk60 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk60 ) ),
inference(simp,[status(thm)],[42543]) ).
thf(42640,plain,
( ( ( k1_tarski @ sk2 )
!= sk60 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk60 ) ),
inference(simp,[status(thm)],[42632]) ).
thf(368,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(2936,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(2941,plain,
v1_xboole_0 @ sk135,
inference(cnf,[status(esa)],[2936]) ).
thf(1096,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k16_coh_sp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_coh_sp) ).
thf(5785,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k16_coh_sp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(5786,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k16_coh_sp @ A ) ),
inference(miniscope,[status(thm)],[5785]) ).
thf(5787,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k16_coh_sp @ A ) ),
inference(cnf,[status(esa)],[5786]) ).
thf(10711,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k16_coh_sp @ A ) )
!= ( v1_xboole_0 @ sk135 ) ),
inference(paramod_ordered,[status(thm)],[2941,5787]) ).
thf(10719,plain,
! [A: $i] :
( ( k16_coh_sp @ A )
!= sk135 ),
inference(simp,[status(thm)],[10711]) ).
thf(13143,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk135 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2941,1284]) ).
thf(13144,plain,
sk135 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[13143:[bind(A,$thf( sk135 ))]]) ).
thf(15045,plain,
! [A: $i] :
( ( k16_coh_sp @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10719,13144]) ).
thf(616,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ D ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_0) ).
thf(3910,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ D ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(1099,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_unialg_2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_unialg_2) ).
thf(5793,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_unialg_2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(188,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tex_2) ).
thf(2113,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(2114,plain,
v1_realset1 @ sk72,
inference(cnf,[status(esa)],[2113]) ).
thf(999,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( D
= ( k4_filter_0 @ A @ B @ C ) )
<=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_0) ).
thf(5405,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( D
= ( k4_filter_0 @ A @ B @ C ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) )
& ( ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) )
=> ( D
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(121,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finseq_5) ).
thf(1793,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(792,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v3_realset2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_realset2) ).
thf(4612,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v3_realset2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(4614,plain,
l1_struct_0 @ sk250,
inference(cnf,[status(esa)],[4612]) ).
thf(68,axiom,
! [A: $i] :
( ( v1_realset1 @ A )
<=> ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_realset1) ).
thf(1481,plain,
! [A: $i] :
( ( ( v1_realset1 @ A )
=> ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) ) )
& ( ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) )
=> ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1482,plain,
( ! [A: $i] :
( ( v1_realset1 @ A )
=> ~ ( ~ ( v1_xboole_0 @ A )
& ~ ? [B: $i] :
( A
= ( k1_tarski @ B ) ) ) )
& ! [A: $i] :
( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ? [B: $i] :
( A
= ( k1_tarski @ B ) ) )
=> ( v1_realset1 @ A ) ) ),
inference(miniscope,[status(thm)],[1481]) ).
thf(1484,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( v1_realset1 @ A ) ),
inference(cnf,[status(esa)],[1482]) ).
thf(1487,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_tarski @ B ) )
| ( v1_realset1 @ A ) ),
inference(lifteq,[status(thm)],[1484]) ).
thf(1488,plain,
! [A: $i] : ( v1_realset1 @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[1487]) ).
thf(7441,plain,
! [A: $i] :
( ( v1_realset1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1201,1488]) ).
thf(7442,plain,
v1_realset1 @ ( k1_zfmisc_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[7441:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( v1_realset1 @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ( A
= ( k6_domain_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tex_2) ).
thf(1221,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( ( v1_realset1 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ( A
= ( k6_domain_1 @ A @ B ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ( A
= ( k6_domain_1 @ A @ B ) ) )
=> ( v1_realset1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1223,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_realset1 @ A )
| ( m1_subset_1 @ ( sk5 @ A ) @ A ) ),
inference(cnf,[status(esa)],[1221]) ).
thf(7528,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( m1_subset_1 @ ( sk5 @ A ) @ A )
| ( ( v1_realset1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( v1_realset1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7442,1223]) ).
thf(7529,plain,
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( m1_subset_1 @ ( sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[7528:[bind(A,$thf( k1_zfmisc_1 @ k1_xboole_0 ))]]) ).
thf(698,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(4237,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(4238,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(miniscope,[status(thm)],[4237]) ).
thf(4239,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[4238]) ).
thf(18283,plain,
( $false
| ( m1_subset_1 @ ( sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(rewrite,[status(thm)],[7529,4239]) ).
thf(18284,plain,
m1_subset_1 @ ( sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) @ ( k1_zfmisc_1 @ k1_xboole_0 ),
inference(simp,[status(thm)],[18283]) ).
thf(1140,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v5_grcat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_grcat_1) ).
thf(6017,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v5_grcat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(44635,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk149 @ B ) @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[15123,2992]) ).
thf(44671,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ sk149 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[44635]) ).
thf(45674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk149 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1396,44671]) ).
thf(45675,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ sk149 @ B ) @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45674:[bind(A,$thf( sk149 )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( k4_xboole_0 @ sk149 @ F ))]]) ).
thf(45832,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ sk149 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[45675]) ).
thf(25969,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( v10_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1518,14625]) ).
thf(25970,plain,
( ( v1_relat_1 @ ( sk27 @ sk1 ) )
| ( v10_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25969:[bind(A,$thf( sk1 ))]]) ).
thf(1193,plain,
v12_lattices @ sk1,
inference(cnf,[status(esa)],[1192]) ).
thf(13599,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( v12_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1284,1193]) ).
thf(13600,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( v12_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13599:[bind(A,$thf( sk1 ))]]) ).
thf(1199,plain,
~ ( v12_lattices @ ( k23_filter_2 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[1192]) ).
thf(12889,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v12_lattices @ k1_xboole_0 )
| ( A
!= ( k23_filter_2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1284,1199]) ).
thf(12890,plain,
( ~ ( v1_xboole_0 @ ( k23_filter_2 @ sk1 @ sk2 ) )
| ~ ( v12_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[12889:[bind(A,$thf( k23_filter_2 @ sk1 @ sk2 ))]]) ).
thf(15152,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ ( k23_filter_2 @ sk1 @ sk2 ) )
| ( ( v12_lattices @ k1_xboole_0 )
!= ( v12_lattices @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[13600,12890]) ).
thf(15153,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ ( k23_filter_2 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[15152:[]]) ).
thf(822,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
& ~ ( v2_setfam_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_abian) ).
thf(4747,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
& ~ ( v2_setfam_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k11_openlatt @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k11_openlatt) ).
thf(4487,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k11_openlatt @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(6477,plain,
( ( v1_finset_1 @ sk149 )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[3120,2992]) ).
thf(6480,plain,
sk149 != sk139,
inference(simp,[status(thm)],[6477]) ).
thf(784,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4592,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1164,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(6127,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(6130,plain,
l3_lattices @ sk334,
inference(cnf,[status(esa)],[6127]) ).
thf(26065,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ( A != sk334 ) ),
inference(paramod_ordered,[status(thm)],[1518,6130]) ).
thf(26066,plain,
( ( v1_relat_1 @ ( sk27 @ sk334 ) )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26065:[bind(A,$thf( sk334 ))]]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k11_openlatt @ A @ B @ C )
= ( k11_openlatt @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k11_openlatt) ).
thf(5501,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k11_openlatt @ A @ B @ C )
= ( k11_openlatt @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(925,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) )
& ( r1_tarski @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_lattice4) ).
thf(5120,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) )
& ( r1_tarski @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(90,axiom,
! [A: $i] :
( ( A = k1_trees_3 )
<=> ! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_trees_3) ).
thf(1608,plain,
! [A: $i] :
( ( ( A = k1_trees_3 )
=> ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) ) )
& ( ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) )
=> ( r2_hidden @ B @ A ) ) ) )
& ( ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) ) )
& ( ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) )
=> ( r2_hidden @ B @ A ) ) )
=> ( A = k1_trees_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(91,axiom,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).
thf(1634,plain,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1635,plain,
~ ? [A: $i,B: $i] :
( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(miniscope,[status(thm)],[1634]) ).
thf(1642,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_relat_1 @ ( sk38 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1635]) ).
thf(1654,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_relat_1 @ ( sk38 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[1642]) ).
thf(1655,plain,
! [A: $i] : ( v1_relat_1 @ ( sk38 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[1654]) ).
thf(767,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_card_fil) ).
thf(4528,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_filter_2 @ A @ B )
= ( k2_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
thf(2448,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_filter_2 @ A @ B )
= ( k2_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(956,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_filter_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_1) ).
thf(5257,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_filter_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1074,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_0) ).
thf(5701,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(4564,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A ) )
=> ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1068,axiom,
? [A: $i] :
( ( l1_funcsdom @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funcsdom) ).
thf(5673,plain,
? [A: $i] :
( ( l1_funcsdom @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(5674,plain,
~ ( v3_struct_0 @ sk324 ),
inference(cnf,[status(esa)],[5673]) ).
thf(42,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v4_lattice3 @ A )
<=> ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_lattice3) ).
thf(1350,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v4_lattice3 @ A )
=> ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) )
& ( ! [B: $i] :
? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) )
=> ( v4_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1354,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ( m1_subset_1 @ ( sk12 @ B @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(cnf,[status(esa)],[1350]) ).
thf(559,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ A @ B @ C @ D )
<=> ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_filter_0) ).
thf(3717,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_filter_0 @ A @ B @ C @ D )
=> ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
=> ( r1_filter_0 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(826,axiom,
? [A: $i] : ( l1_prelamb @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_prelamb) ).
thf(4761,plain,
? [A: $i] : ( l1_prelamb @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(4762,plain,
l1_prelamb @ sk267,
inference(cnf,[status(esa)],[4761]) ).
thf(459,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k3_xboole_0 @ B @ A ) )
& ( v1_funct_1 @ ( k3_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_grfunc_1) ).
thf(3276,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k3_xboole_0 @ B @ A ) )
& ( v1_funct_1 @ ( k3_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(390,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v14_lattices @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k2_filter_2 @ A @ B ) @ ( k22_filter_2 @ A @ B @ ( k6_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_filter_2) ).
thf(3017,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v14_lattices @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k2_filter_2 @ A @ B ) @ ( k22_filter_2 @ A @ B @ ( k6_lattices @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(770,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_relat_1 @ ( k8_openlatt @ A ) )
& ( v1_funct_1 @ ( k8_openlatt @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_openlatt) ).
thf(4543,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_relat_1 @ ( k8_openlatt @ A ) )
& ( v1_funct_1 @ ( k8_openlatt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1002,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k7_lattices @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l70_filter_2) ).
thf(5425,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k7_lattices @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1103,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
=> ( r1_filter_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_1) ).
thf(5814,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
=> ( r1_filter_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(696,axiom,
m1_subset_1 @ k2_trees_3 @ ( k1_zfmisc_1 @ k1_trees_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_trees_3) ).
thf(4234,plain,
m1_subset_1 @ k2_trees_3 @ ( k1_zfmisc_1 @ k1_trees_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(28,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k13_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_lopclset) ).
thf(1308,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k13_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1309,plain,
! [A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ( ( k13_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
inference(cnf,[status(esa)],[1308]) ).
thf(1310,plain,
! [A: $i] :
( ( ( k13_lopclset @ A )
= ( k8_lopclset @ A ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A ) ),
inference(lifteq,[status(thm)],[1309]) ).
thf(26003,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l1_prelamb @ k1_xboole_0 )
| ( A != sk267 ) ),
inference(paramod_ordered,[status(thm)],[1518,4762]) ).
thf(26004,plain,
( ( v1_relat_1 @ ( sk27 @ sk267 ) )
| ( l1_prelamb @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26003:[bind(A,$thf( sk267 ))]]) ).
thf(1187,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(6246,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(479,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v13_lattices @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k18_filter_2 @ A @ B ) @ ( k22_filter_2 @ A @ ( k5_lattices @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_filter_2) ).
thf(3367,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v13_lattices @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k18_filter_2 @ A @ B ) @ ( k22_filter_2 @ A @ ( k5_lattices @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1087,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_lattice4) ).
thf(5755,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(647,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(4026,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(395,axiom,
? [A: $i] :
( ( l2_lang1 @ A )
& ( v2_lang1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lang1) ).
thf(3042,plain,
? [A: $i] :
( ( l2_lang1 @ A )
& ( v2_lang1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(3044,plain,
l2_lang1 @ sk145,
inference(cnf,[status(esa)],[3042]) ).
thf(966,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_filter_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_filter_2) ).
thf(5288,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_filter_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(107,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_trees_1) ).
thf(1733,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1735,plain,
~ ( v1_xboole_0 @ sk44 ),
inference(cnf,[status(esa)],[1733]) ).
thf(19,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_partfun1) ).
thf(1268,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1269,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( r2_hidden @ ( sk10 @ B @ A ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
| ( ( k2_xboole_0 @ A @ B )
= ( sk11 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1268]) ).
thf(1275,plain,
! [B: $i,A: $i] :
( ( ( sk11 @ B @ A )
= ( k2_xboole_0 @ A @ B ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( r2_hidden @ ( sk10 @ B @ A ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ),
inference(lifteq,[status(thm)],[1269]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(2141,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(1400,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1401,plain,
~ ? [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 ),
inference(miniscope,[status(thm)],[1400]) ).
thf(1402,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(cnf,[status(esa)],[1401]) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1402]) ).
thf(38066,plain,
! [B: $i,A: $i] :
( ( ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ B )
!= k1_xboole_0 )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1201,1403]) ).
thf(38067,plain,
! [A: $i] :
( ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[38066:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(38135,plain,
! [A: $i] :
( ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[38067]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(39,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funcop_1) ).
thf(1342,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
& ( ( k1_relat_1 @ B )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(3121,plain,
v1_funct_1 @ sk149,
inference(cnf,[status(esa)],[3119]) ).
thf(1115,axiom,
~ ( v1_xboole_0 @ k1_trees_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_trees_3) ).
thf(5875,plain,
~ ( v1_xboole_0 @ k1_trees_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(5876,plain,
~ ( v1_xboole_0 @ k1_trees_3 ),
inference(polarity_switch,[status(thm)],[5875]) ).
thf(6675,plain,
( ( v1_xboole_0 @ k1_trees_3 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,5876]) ).
thf(6680,plain,
k1_trees_3 != k1_xboole_0,
inference(simp,[status(thm)],[6675]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_lattice4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(4247,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_lattice4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_prelamb @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_prelamb @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_prelamb) ).
thf(5005,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_prelamb @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_prelamb @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1159,axiom,
~ ( v1_xboole_0 @ k2_trees_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_trees_3) ).
thf(6116,plain,
~ ( v1_xboole_0 @ k2_trees_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(6117,plain,
~ ( v1_xboole_0 @ k2_trees_3 ),
inference(polarity_switch,[status(thm)],[6116]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
<=> ~ ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(1954,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
=> ~ ( r2_hidden @ A @ B ) )
& ( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
thf(3577,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(180,axiom,
! [A: $i] :
( ( v2_setfam_1 @ A )
=> ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_abian) ).
thf(2042,plain,
! [A: $i] :
( ( v2_setfam_1 @ A )
=> ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_realset1) ).
thf(1693,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1694,plain,
( ~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) )
& ! [A: $i] : ( v1_realset1 @ ( k1_tarski @ A ) ) ),
inference(miniscope,[status(thm)],[1693]) ).
thf(1696,plain,
! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[1694]) ).
thf(1699,plain,
! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ),
inference(simp,[status(thm)],[1696]) ).
thf(9821,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( ( k1_tarski @ k1_xboole_0 )
!= ( k1_tarski @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1201,1699]) ).
thf(9822,plain,
v1_finset_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[9821:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(10022,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9822,1218]) ).
thf(10023,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) ),
inference(pattern_uni,[status(thm)],[10022:[bind(A,$thf( k1_zfmisc_1 @ k1_xboole_0 )),bind(B,$thf( B ))]]) ).
thf(10028,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) ),
inference(simp,[status(thm)],[10023]) ).
thf(45744,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,10028]) ).
thf(45745,plain,
! [A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) ),
inference(pattern_uni,[status(thm)],[45744:[bind(A,$thf( k1_zfmisc_1 @ k1_xboole_0 )),bind(B,$thf( F )),bind(C,$thf( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ F ))]]) ).
thf(45801,plain,
! [A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) ),
inference(simp,[status(thm)],[45745]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(2046,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(1914,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(5711,plain,
~ ( v3_struct_0 @ k6_nat_lat ),
inference(cnf,[status(esa)],[5707]) ).
thf(13097,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != k6_nat_lat ) ),
inference(paramod_ordered,[status(thm)],[1284,5711]) ).
thf(13098,plain,
( ~ ( v1_xboole_0 @ k6_nat_lat )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13097:[bind(A,$thf( k6_nat_lat ))]]) ).
thf(1017,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ D ) @ ( k1_boolealg @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boolealg) ).
thf(5476,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ D ) @ ( k1_boolealg @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_2 @ ( k4_filter_2 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_filter_2) ).
thf(3898,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_2 @ ( k4_filter_2 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(77,axiom,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_5) ).
thf(1529,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(344,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
<=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_filter_0) ).
thf(2819,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) )
& ( ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B )
=> ( r2_hidden @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(374,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k7_lattices @ A @ ( k1_boolealg @ A @ B @ C ) ) @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_boolealg) ).
thf(2957,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k7_lattices @ A @ ( k1_boolealg @ A @ B @ C ) ) @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(654,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( ( k1_funct_1 @ ( k8_openlatt @ A ) @ B )
= ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_openlatt) ).
thf(4047,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ( ( k1_funct_1 @ ( k8_openlatt @ A ) @ B )
= ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( v1_xboole_0 @ ( k25_gate_1 @ A @ B @ C @ D @ E @ F ) )
<=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_gate_1) ).
thf(6236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ ( k25_gate_1 @ A @ B @ C @ D @ E @ F ) )
=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F ) ) )
& ( ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F ) )
=> ~ ( v1_xboole_0 @ ( k25_gate_1 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(840,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_filter_0) ).
thf(4792,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(131,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(1835,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(596,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice2) ).
thf(3836,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(721,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(4342,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(4343,plain,
~ ( v3_struct_0 @ sk236 ),
inference(cnf,[status(esa)],[4342]) ).
thf(444,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ C @ B ) )
=> ( r1_boolealg @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_boolealg) ).
thf(3236,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ C @ B ) )
=> ( r1_boolealg @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(3545,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(324,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_pre_topc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(2723,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(994,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ ( k3_lattices @ A @ B @ C ) ) @ ( k4_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_boolealg) ).
thf(5393,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ ( k3_lattices @ A @ B @ C ) ) @ ( k4_lattices @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(617,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D )
& ( r1_boolealg @ A @ ( k4_lattices @ A @ C @ D ) @ ( k5_lattices @ A ) ) )
=> ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_boolealg) ).
thf(3915,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D )
& ( r1_boolealg @ A @ ( k4_lattices @ A @ C @ D ) @ ( k5_lattices @ A ) ) )
=> ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(288,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k10_filter_0 @ A @ B ) )
<=> ( ( r1_tarski @ ( k3_relat_1 @ C ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C )
<=> ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_filter_0) ).
thf(2548,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k10_filter_0 @ A @ B ) )
=> ( ( r1_tarski @ ( k3_relat_1 @ C ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C )
=> ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B ) )
& ( ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C ) ) ) ) ) ) )
& ( ( ( r1_tarski @ ( k3_relat_1 @ C ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C )
=> ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B ) )
& ( ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C ) ) ) ) ) )
=> ( C
= ( k10_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(272,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k15_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B )
& ( ( k16_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattice3) ).
thf(2491,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k15_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B )
& ( ( k16_lattice3 @ A @ ( k1_struct_0 @ A @ B ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(2985,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(756,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v5_orders_2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_orders_2) ).
thf(4496,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v5_orders_2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(1391,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_openlatt @ B ) )
<=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( C
!= ( u1_struct_0 @ B ) )
& ( v2_filter_0 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_openlatt) ).
thf(5123,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_openlatt @ B ) )
=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( C
!= ( u1_struct_0 @ B ) )
& ( v2_filter_0 @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( C
!= ( u1_struct_0 @ B ) )
& ( v2_filter_0 @ C @ B ) )
=> ( r2_hidden @ A @ ( a_1_0_openlatt @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ ( k22_filter_2 @ A @ B @ C ) )
& ( m2_lattice4 @ ( k22_filter_2 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k22_filter_2) ).
thf(5518,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ ( k22_filter_2 @ A @ B @ C ) )
& ( m2_lattice4 @ ( k22_filter_2 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(450,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tops_1) ).
thf(3249,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(660,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( r2_hidden @ D @ ( k7_openlatt @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_openlatt) ).
thf(4079,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( r2_hidden @ D @ ( k7_openlatt @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1085,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_modal_1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_modal_1) ).
thf(5745,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_modal_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_rfunct_3 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m2_rfunct_3 @ D @ A @ B @ C )
<=> ( m1_subset_1 @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_rfunct_3) ).
thf(5195,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_rfunct_3 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( m2_rfunct_3 @ D @ A @ B @ C )
=> ( m1_subset_1 @ D @ C ) )
& ( ( m1_subset_1 @ D @ C )
=> ( m2_rfunct_3 @ D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1643,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( r1_tarski @ ( k2_relat_1 @ ( sk38 @ B @ A ) ) @ A ) ),
inference(cnf,[status(esa)],[1635]) ).
thf(1649,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( r1_tarski @ ( k2_relat_1 @ ( sk38 @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[1643]) ).
thf(1650,plain,
! [A: $i] : ( r1_tarski @ ( k2_relat_1 @ ( sk38 @ k1_xboole_0 @ A ) ) @ A ),
inference(simp,[status(thm)],[1649]) ).
thf(1108,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k1_lattice2 @ ( k8_filter_1 @ A @ B ) )
= ( k8_filter_1 @ ( k1_lattice2 @ A ) @ ( k1_lattice2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_filter_1) ).
thf(5825,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k1_lattice2 @ ( k8_filter_1 @ A @ B ) )
= ( k8_filter_1 @ ( k1_lattice2 @ A ) @ ( k1_lattice2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(1640,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( B
= ( k1_relat_1 @ ( sk38 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[1635]) ).
thf(1644,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( ( k1_relat_1 @ ( sk38 @ B @ A ) )
= B ) ),
inference(lifteq,[status(thm)],[1640]) ).
thf(1645,plain,
! [A: $i] :
( ( k1_relat_1 @ ( sk38 @ k1_xboole_0 @ A ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1644]) ).
thf(564,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_rfunct_3 @ C @ A @ B ) )
=> ? [D: $i] : ( m2_rfunct_3 @ D @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_rfunct_3) ).
thf(3730,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_rfunct_3 @ C @ A @ B ) )
=> ? [D: $i] : ( m2_rfunct_3 @ D @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(5137,plain,
l1_struct_0 @ sk293,
inference(cnf,[status(esa)],[5133]) ).
thf(26185,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk293 ) ),
inference(paramod_ordered,[status(thm)],[1518,5137]) ).
thf(26186,plain,
( ( v1_relat_1 @ ( sk27 @ sk293 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26185:[bind(A,$thf( sk293 ))]]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_unialg_2 @ B @ A ) )
=> ? [C: $i] : ( m2_unialg_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_unialg_2) ).
thf(2886,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_unialg_2 @ B @ A ) )
=> ? [C: $i] : ( m2_unialg_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1222,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_realset1 @ A )
| ( A
= ( k6_domain_1 @ A @ ( sk5 @ A ) ) ) ),
inference(cnf,[status(esa)],[1221]) ).
thf(1225,plain,
! [A: $i] :
( ( ( k6_domain_1 @ A @ ( sk5 @ A ) )
= A )
| ( v1_xboole_0 @ A )
| ~ ( v1_realset1 @ A ) ),
inference(lifteq,[status(thm)],[1222]) ).
thf(6961,plain,
! [A: $i] :
( ( ( k6_domain_1 @ A @ ( sk5 @ A ) )
= A )
| ( v1_xboole_0 @ A )
| ( ( v1_realset1 @ sk60 )
!= ( v1_realset1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2022,1225]) ).
thf(6962,plain,
( ( ( k6_domain_1 @ sk60 @ ( sk5 @ sk60 ) )
= sk60 )
| ( v1_xboole_0 @ sk60 ) ),
inference(pattern_uni,[status(thm)],[6961:[bind(A,$thf( sk60 ))]]) ).
thf(2023,plain,
~ ( v1_xboole_0 @ sk60 ),
inference(cnf,[status(esa)],[2021]) ).
thf(11023,plain,
( ( ( k6_domain_1 @ sk60 @ ( sk5 @ sk60 ) )
= sk60 )
| $false ),
inference(rewrite,[status(thm)],[6962,2023]) ).
thf(11024,plain,
( ( k6_domain_1 @ sk60 @ ( sk5 @ sk60 ) )
= sk60 ),
inference(simp,[status(thm)],[11023]) ).
thf(1352,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk13 @ A ) )
| ~ ( r1_lattices @ A @ B @ ( sk14 @ B @ A ) )
| ( v4_lattice3 @ A ) ),
inference(cnf,[status(esa)],[1350]) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk13 @ A ) )
| ~ ( r1_lattices @ A @ B @ ( sk14 @ B @ A ) )
| ( v4_lattice3 @ A ) ),
inference(simp,[status(thm)],[1352]) ).
thf(88,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relat_1) ).
thf(1601,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(3281,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(970,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_boolealg @ A @ B @ C )
<=> ( ( k4_lattices @ A @ B @ C )
!= ( k5_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_boolealg) ).
thf(5301,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_boolealg @ A @ B @ C )
=> ( ( k4_lattices @ A @ B @ C )
!= ( k5_lattices @ A ) ) )
& ( ( ( k4_lattices @ A @ B @ C )
!= ( k5_lattices @ A ) )
=> ( r2_boolealg @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(421,axiom,
! [A: $i,B: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k1_rlvect_2 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_rlvect_2) ).
thf(3140,plain,
! [A: $i,B: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k1_rlvect_2 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(675,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boolealg) ).
thf(4137,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1417,plain,
~ ( v1_xboole_0 @ sk19 ),
inference(cnf,[status(esa)],[1414]) ).
thf(6285,plain,
( ( v1_xboole_0 @ sk19 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,1417]) ).
thf(6291,plain,
sk19 != k1_xboole_0,
inference(simp,[status(thm)],[6285]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(1265,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(791,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
=> ( v11_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lattice2) ).
thf(4610,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
=> ( v11_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(25939,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( v1_funcsdom @ k1_xboole_0 )
| ( A != sk280 ) ),
inference(paramod_ordered,[status(thm)],[1518,4960]) ).
thf(25940,plain,
( ( v1_relat_1 @ ( sk27 @ sk280 ) )
| ( v1_funcsdom @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25939:[bind(A,$thf( sk280 ))]]) ).
thf(9837,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ B @ C ) )
| ( ( v1_finset_1 @ ( k1_tarski @ A ) )
!= ( v1_finset_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1699,1218]) ).
thf(9838,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[9837:[bind(A,$thf( D )),bind(B,$thf( k1_tarski @ D ))]]) ).
thf(9850,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(simp,[status(thm)],[9838]) ).
thf(882,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_1 @ A @ ( k8_filter_1 @ ( k5_filter_1 @ A @ ( k2_filter_0 @ A @ B ) ) @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_filter_1) ).
thf(4948,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_1 @ A @ ( k8_filter_1 @ ( k5_filter_1 @ A @ ( k2_filter_0 @ A @ B ) ) @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(10,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_tex_2) ).
thf(1227,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1228,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_realset1 @ A )
| ( m1_subset_1 @ ( sk6 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[1227]) ).
thf(525,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r2_lattice4 @ A @ B @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_lattice4) ).
thf(3597,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r2_lattice4 @ A @ B @ C )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) ) )
& ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) )
=> ( r2_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1035,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v5_ringcat1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_ringcat1) ).
thf(5545,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v5_ringcat1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(5547,plain,
~ ( v1_xboole_0 @ sk318 ),
inference(cnf,[status(esa)],[5545]) ).
thf(6650,plain,
( ( v1_xboole_0 @ sk318 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,5547]) ).
thf(6658,plain,
sk318 != k1_xboole_0,
inference(simp,[status(thm)],[6650]) ).
thf(26995,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk318 ) ),
inference(paramod_ordered,[status(thm)],[1518,6658]) ).
thf(26996,plain,
v1_relat_1 @ ( sk27 @ sk318 ),
inference(pattern_uni,[status(thm)],[26995:[bind(A,$thf( sk318 ))]]) ).
thf(14,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( v1_xboole_0 @ B )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tex_2) ).
thf(1254,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( v1_xboole_0 @ B )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(550,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ D ) @ ( k3_boolealg @ A @ B @ ( k3_boolealg @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_boolealg) ).
thf(3688,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ D ) @ ( k3_boolealg @ A @ B @ ( k3_boolealg @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ ( k8_gate_1 @ A @ B @ C ) )
<=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_gate_1) ).
thf(5621,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ ( k8_gate_1 @ A @ B @ C ) )
=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) ) )
& ( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
=> ~ ( v1_xboole_0 @ ( k8_gate_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(701,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( C
= ( k3_filter_0 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_filter_0) ).
thf(4249,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( ( C
= ( k3_filter_0 @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) )
=> ( C
= ( k3_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(984,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ B ) )
<=> ? [D: $i] :
( ( m1_filter_0 @ D @ A )
& ( D = C )
& ( D
!= ( u1_struct_0 @ A ) )
& ( v2_filter_0 @ D @ A )
& ( r2_hidden @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_openlatt) ).
thf(5352,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ B ) )
=> ? [D: $i] :
( ( m1_filter_0 @ D @ A )
& ( D = C )
& ( D
!= ( u1_struct_0 @ A ) )
& ( v2_filter_0 @ D @ A )
& ( r2_hidden @ B @ D ) ) )
& ( ? [D: $i] :
( ( m1_filter_0 @ D @ A )
& ( D = C )
& ( D
!= ( u1_struct_0 @ A ) )
& ( v2_filter_0 @ D @ A )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(610,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ C @ E @ D @ D )
& ( r1_filter_0 @ A @ B @ F @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_filter_0) ).
thf(3891,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ C @ E @ D @ D )
& ( r1_filter_0 @ A @ B @ F @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1697,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(cnf,[status(esa)],[1694]) ).
thf(10273,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tarski @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,1697]) ).
thf(10286,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10273]) ).
thf(1190,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(6274,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(499,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(3493,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(3494,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(miniscope,[status(thm)],[3493]) ).
thf(3495,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(cnf,[status(esa)],[3494]) ).
thf(911,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) )
<=> ( ( r3_lattices @ A @ C @ B )
& ( r3_lattices @ A @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ C @ E )
& ( r3_lattices @ A @ D @ E ) )
=> ( r3_lattices @ A @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_boolealg) ).
thf(5064,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) )
=> ( ( r3_lattices @ A @ C @ B )
& ( r3_lattices @ A @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ C @ E )
& ( r3_lattices @ A @ D @ E ) )
=> ( r3_lattices @ A @ B @ E ) ) ) ) )
& ( ( ( r3_lattices @ A @ C @ B )
& ( r3_lattices @ A @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ C @ E )
& ( r3_lattices @ A @ D @ E ) )
=> ( r3_lattices @ A @ B @ E ) ) ) )
=> ( r1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( v1_realset1 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_rpr_1) ).
thf(1323,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( v1_realset1 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38058,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k2_xboole_0 @ ( k1_tarski @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1518,1403]) ).
thf(38059,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk27 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[38058:[bind(A,$thf( k2_xboole_0 @ ( k1_tarski @ F ) @ E )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).
thf(38131,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk27 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) ) ),
inference(simp,[status(thm)],[38059]) ).
thf(834,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( m1_filter_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_1) ).
thf(4778,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( m1_filter_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(936,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice4) ).
thf(5160,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(1077,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_openlatt @ A )
= ( a_1_0_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_openlatt) ).
thf(5712,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_openlatt @ A )
= ( a_1_0_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(329,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_hahnban) ).
thf(2745,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(22,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_tex_2) ).
thf(1285,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1287,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_realset1 @ A )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ( v1_xboole_0 @ B )
| ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( v1_realset1 @ B ) ),
inference(cnf,[status(esa)],[1285]) ).
thf(771,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ C ) @ ( k1_boolealg @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_boolealg) ).
thf(4546,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ C ) @ ( k1_boolealg @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(1043,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k5_gate_1 @ A @ B ) )
<=> ( ~ ( ~ ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_gate_1) ).
thf(5585,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ ( k5_gate_1 @ A @ B ) )
=> ( ~ ( ~ ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ A ) ) ) )
& ( ( ~ ( ~ ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ A ) ) )
=> ~ ( v1_xboole_0 @ ( k5_gate_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(296,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r4_lattice3 @ A @ B @ C ) )
=> ( ( k15_lattice3 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice3) ).
thf(2603,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r4_lattice3 @ A @ B @ C ) )
=> ( ( k15_lattice3 @ A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(765,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_struct_0) ).
thf(4523,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(4524,plain,
v1_struct_0 @ sk244,
inference(cnf,[status(esa)],[4523]) ).
thf(971,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_struct_0 @ A )
=> ( A
= ( g1_struct_0 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_struct_0) ).
thf(5306,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v1_struct_0 @ A )
=> ( A
= ( g1_struct_0 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_struct_0 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(4866,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_struct_0 @ A @ B @ C )
= ( k2_struct_0 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(540,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(3644,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(179,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ~ ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_realset1) ).
thf(2039,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ~ ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_filter_1) ).
thf(6034,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(659,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( ( ( k3_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) )
= ( k19_filter_2 @ A @ B ) )
& ( ( k3_filter_2 @ A @ B )
= ( k19_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) ) )
& ( ( k3_filter_2 @ A @ ( k8_filter_2 @ A @ C ) )
= ( k19_filter_2 @ ( k1_lattice2 @ A ) @ C ) )
& ( ( k3_filter_2 @ ( k1_lattice2 @ A ) @ C )
= ( k19_filter_2 @ A @ ( k8_filter_2 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_filter_2) ).
thf(4070,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( ( ( k3_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) )
= ( k19_filter_2 @ A @ B ) )
& ( ( k3_filter_2 @ A @ B )
= ( k19_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) ) )
& ( ( k3_filter_2 @ A @ ( k8_filter_2 @ A @ C ) )
= ( k19_filter_2 @ ( k1_lattice2 @ A ) @ C ) )
& ( ( k3_filter_2 @ ( k1_lattice2 @ A ) @ C )
= ( k19_filter_2 @ A @ ( k8_filter_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(773,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(4561,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(4563,plain,
v1_xboole_0 @ sk248,
inference(cnf,[status(esa)],[4561]) ).
thf(1137,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k15_coh_sp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_coh_sp) ).
thf(5986,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k15_coh_sp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(5987,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k15_coh_sp @ A ) ),
inference(miniscope,[status(thm)],[5986]) ).
thf(5988,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k15_coh_sp @ A ) ),
inference(cnf,[status(esa)],[5987]) ).
thf(10730,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k15_coh_sp @ A ) )
!= ( v1_xboole_0 @ sk248 ) ),
inference(paramod_ordered,[status(thm)],[4563,5988]) ).
thf(10741,plain,
! [A: $i] :
( ( k15_coh_sp @ A )
!= sk248 ),
inference(simp,[status(thm)],[10730]) ).
thf(12723,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk248 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4563,1284]) ).
thf(12724,plain,
sk248 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[12723:[bind(A,$thf( sk248 ))]]) ).
thf(15229,plain,
! [A: $i] :
( ( k15_coh_sp @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10741,12724]) ).
thf(803,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_filter_0) ).
thf(4654,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(35,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A )
& ( v1_trees_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k2_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_trees_1) ).
thf(1329,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A )
& ( v1_trees_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k2_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_finset_1 @ A )
| ~ ( v1_trees_1 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_finset_1 @ B )
| ~ ( v1_trees_1 @ B )
| ( v1_trees_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[1329]) ).
thf(17,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(1263,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1264,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(cnf,[status(esa)],[1263]) ).
thf(718,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k4_card_fil @ A ) )
& ( m1_subset_1 @ ( k4_card_fil @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_card_fil) ).
thf(4334,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k4_card_fil @ A ) )
& ( m1_subset_1 @ ( k4_card_fil @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(313,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k6_lattices @ A ) )
= ( k7_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lopclset) ).
thf(2682,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k6_lattices @ A ) )
= ( k7_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(129,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( A = k1_xboole_0 )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_grfunc_1) ).
thf(1826,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( A = k1_xboole_0 )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(931,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( r2_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_boolealg) ).
thf(5150,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( r2_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(29,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(1311,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1312,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[1311]) ).
thf(1313,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[1312]) ).
thf(723,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k7_lattices @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_lattices) ).
thf(4349,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k7_lattices @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(20,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_realset2 @ A )
<=> ( v1_realset1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_realset2) ).
thf(1279,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v3_realset2 @ A )
=> ( v1_realset1 @ ( u1_struct_0 @ A ) ) )
& ( ( v1_realset1 @ ( u1_struct_0 @ A ) )
=> ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(706,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
thf(4275,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(944,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_filter_0) ).
thf(5182,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(408,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ B @ B ) @ ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_boolealg) ).
thf(3089,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ B @ B ) @ ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(2897,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( v1_xboole_0 @ ( k29_gate_1 @ A @ B @ C @ D @ E @ F @ G ) )
<=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_gate_1) ).
thf(5989,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ ( k29_gate_1 @ A @ B @ C @ D @ E @ F @ G ) )
=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G ) ) )
& ( ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G ) )
=> ~ ( v1_xboole_0 @ ( k29_gate_1 @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(2466,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(191,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_tex_2) ).
thf(2126,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(738,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_grcat_1 @ A ) )
=> ! [B: $i] :
( ( m3_grcat_1 @ B @ A )
<=> ( m1_subset_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m3_grcat_1) ).
thf(4428,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_grcat_1 @ A ) )
=> ! [B: $i] :
( ( ( m3_grcat_1 @ B @ A )
=> ( m1_subset_1 @ B @ A ) )
& ( ( m1_subset_1 @ B @ A )
=> ( m3_grcat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k28_gate_1 @ A @ B @ C @ D @ E @ F @ G ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G ) )
& ( v1_xboole_0 @ ( k28_gate_1 @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_gate_1) ).
thf(6208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k28_gate_1 @ A @ B @ C @ D @ E @ F @ G ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G ) )
& ( v1_xboole_0 @ ( k28_gate_1 @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(3043,plain,
v2_lang1 @ sk145,
inference(cnf,[status(esa)],[3042]) ).
thf(963,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( k6_filter_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_filter_2) ).
thf(5279,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( k6_filter_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(45742,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk133 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,6917]) ).
thf(45743,plain,
! [A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ sk133 @ A ) ),
inference(pattern_uni,[status(thm)],[45742:[bind(A,$thf( sk133 )),bind(B,$thf( E )),bind(C,$thf( k4_xboole_0 @ sk133 @ E ))]]) ).
thf(45800,plain,
! [A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ sk133 @ A ) ),
inference(simp,[status(thm)],[45743]) ).
thf(319,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( C
= ( k3_xboole_0 @ A @ B ) )
=> ( ( ~ ( v2_funct_1 @ A )
& ~ ( v2_funct_1 @ B ) )
| ( v2_funct_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_grfunc_1) ).
thf(2703,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( C
= ( k3_xboole_0 @ A @ B ) )
=> ( ( ~ ( v2_funct_1 @ A )
& ~ ( v2_funct_1 @ B ) )
| ( v2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(15149,plain,
( ~ ( v12_lattices @ k1_xboole_0 )
| ( ( v1_xboole_0 @ ( k23_filter_2 @ sk1 @ sk2 ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,12890]) ).
thf(15182,plain,
( ~ ( v12_lattices @ k1_xboole_0 )
| ( ( k23_filter_2 @ sk1 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[15149]) ).
thf(1047,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k10_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lopclset) ).
thf(5605,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k10_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(67,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_trees_2) ).
thf(1479,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k27_gate_1 @ A @ B @ C @ D @ E @ F @ G ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G ) )
& ( v1_xboole_0 @ ( k27_gate_1 @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_gate_1) ).
thf(5925,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k27_gate_1 @ A @ B @ C @ D @ E @ F @ G ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G ) )
& ( v1_xboole_0 @ ( k27_gate_1 @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(806,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_0 @ ( k3_filter_0 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(4675,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_0 @ ( k3_filter_0 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(632,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r3_zfrefle1 @ A @ B )
=> ( r2_zfrefle1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfrefle1) ).
thf(3951,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r3_zfrefle1 @ A @ B )
=> ( r2_zfrefle1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(703,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( k17_grcat_1 @ A @ B )
= ( k1_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d26_grcat_1) ).
thf(4265,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( k17_grcat_1 @ A @ B )
= ( k1_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(914,axiom,
m2_nat_lat @ k13_nat_lat @ k6_nat_lat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_nat_lat) ).
thf(5076,plain,
m2_nat_lat @ k13_nat_lat @ k6_nat_lat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(1052,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice4) ).
thf(5617,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(37648,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1284,15153]) ).
thf(37649,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[37648:[bind(A,$thf( sk1 ))]]) ).
thf(37686,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v1_xboole_0 @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) ) ),
inference(simp,[status(thm)],[37649]) ).
thf(582,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(3788,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_realset1 @ A )
<=> ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_realset1) ).
thf(1800,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( ~ ( v1_realset1 @ A )
=> ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( ! [B: $i] :
~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
=> ~ ( v1_realset1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(5387,plain,
~ ( v1_xboole_0 @ sk305 ),
inference(cnf,[status(esa)],[5385]) ).
thf(6608,plain,
( ( v1_xboole_0 @ sk305 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,5387]) ).
thf(6612,plain,
sk305 != k1_xboole_0,
inference(simp,[status(thm)],[6608]) ).
thf(26969,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk305 ) ),
inference(paramod_ordered,[status(thm)],[1518,6612]) ).
thf(26970,plain,
v1_relat_1 @ ( sk27 @ sk305 ),
inference(pattern_uni,[status(thm)],[26969:[bind(A,$thf( sk305 ))]]) ).
thf(9855,plain,
! [A: $i] :
( ~ ( r2_hidden @ sk89 @ A )
| ~ ( r2_hidden @ sk2 @ A )
| ( ( v1_realset1 @ sk72 )
!= ( v1_realset1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2114,9231]) ).
thf(9856,plain,
( ~ ( r2_hidden @ sk89 @ sk72 )
| ~ ( r2_hidden @ sk2 @ sk72 ) ),
inference(pattern_uni,[status(thm)],[9855:[bind(A,$thf( sk72 ))]]) ).
thf(13961,plain,
( ~ ( r2_hidden @ k1_xboole_0 @ sk72 )
| ~ ( r2_hidden @ sk2 @ sk72 ) ),
inference(rewrite,[status(thm)],[9856,12908]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(3374,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k4_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(2169,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k4_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(538,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_realset2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tex_2) ).
thf(3638,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(794,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( m2_filter_2 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_filter_2) ).
thf(4617,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( m2_filter_2 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(1030,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_2 @ B @ A )
=> ( ( k8_filter_0 @ A @ B )
= ( k23_filter_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_filter_2) ).
thf(5521,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_2 @ B @ A )
=> ( ( k8_filter_0 @ A @ B )
= ( k23_filter_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(6836,plain,
( ( v1_xboole_0 @ k2_trees_3 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,6117]) ).
thf(6842,plain,
k2_trees_3 != k1_xboole_0,
inference(simp,[status(thm)],[6836]) ).
thf(27027,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != k2_trees_3 ) ),
inference(paramod_ordered,[status(thm)],[1518,6842]) ).
thf(27028,plain,
v1_relat_1 @ ( sk27 @ k2_trees_3 ),
inference(pattern_uni,[status(thm)],[27027:[bind(A,$thf( k2_trees_3 ))]]) ).
thf(1247,plain,
! [A: $i] :
( ( v1_realset1 @ A )
| ( r2_hidden @ ( sk9 @ A ) @ A ) ),
inference(cnf,[status(esa)],[1244]) ).
thf(193,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_realset1) ).
thf(2138,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(2139,plain,
~ ( v1_realset1 @ sk75 ),
inference(cnf,[status(esa)],[2138]) ).
thf(6308,plain,
( ( v1_realset1 @ sk75 )
!= ( v1_realset1 @ sk72 ) ),
inference(paramod_ordered,[status(thm)],[2114,2139]) ).
thf(6310,plain,
sk75 != sk72,
inference(simp,[status(thm)],[6308]) ).
thf(805,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_filter_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
<=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_0) ).
thf(4664,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(6278,plain,
( ( v12_lattices @ ( k23_filter_2 @ sk1 @ sk2 ) )
!= ( v12_lattices @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[1193,1199]) ).
thf(6279,plain,
( ( k23_filter_2 @ sk1 @ sk2 )
!= sk1 ),
inference(simp,[status(thm)],[6278]) ).
thf(13103,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( ( k23_filter_2 @ k1_xboole_0 @ sk2 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1284,6279]) ).
thf(13104,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( ( k23_filter_2 @ k1_xboole_0 @ sk2 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[13103:[bind(A,$thf( sk1 ))]]) ).
thf(15398,plain,
( ( ( k23_filter_2 @ k1_xboole_0 @ sk2 )
!= sk1 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,13104]) ).
thf(15425,plain,
( ( ( k23_filter_2 @ k1_xboole_0 @ sk2 )
!= sk1 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[15398]) ).
thf(40409,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( sk1 != k1_xboole_0 )
| ( A
!= ( k23_filter_2 @ k1_xboole_0 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1284,15425]) ).
thf(40410,plain,
( ~ ( v1_xboole_0 @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[40409:[bind(A,$thf( k23_filter_2 @ k1_xboole_0 @ sk2 ))]]) ).
thf(996,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k7_filter_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_2) ).
thf(5397,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k7_filter_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(2373,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(977,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_tarski @ ( k10_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_lopclset) ).
thf(5323,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_tarski @ ( k10_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).
thf(1345,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
| ~ ( r1_tarski @ B @ C )
| ~ ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
| ( B = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1345]) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
| ~ ( r1_tarski @ B @ C )
| ~ ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) ),
inference(lifteq,[status(thm)],[1346]) ).
thf(619,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) @ ( k16_openlatt @ A ) @ ( k6_lattices @ A ) )
= ( k7_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_openlatt) ).
thf(3919,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) @ ( k16_openlatt @ A ) @ ( k6_lattices @ A ) )
= ( k7_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(52,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_realset1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_realset1) ).
thf(1397,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
& ( v1_realset1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1398,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ ( sk17 @ A ) ) ) )
| ~ ( v1_realset1 @ A ) ),
inference(cnf,[status(esa)],[1397]) ).
thf(7057,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= ( u1_struct_0 @ A ) )
| ( ( a_2_0_lopclset @ A @ ( sk7 @ B @ A ) )
!= ( k1_funct_1 @ B @ ( sk7 @ B @ A ) ) )
| ( B
= ( k8_lopclset @ A ) )
| ( v3_struct_0 @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( v10_lattices @ sk1 )
!= ( v10_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1197,1237]) ).
thf(7058,plain,
! [A: $i] :
( ( ( k1_relat_1 @ A )
!= ( u1_struct_0 @ sk1 ) )
| ( ( a_2_0_lopclset @ sk1 @ ( sk7 @ A @ sk1 ) )
!= ( k1_funct_1 @ A @ ( sk7 @ A @ sk1 ) ) )
| ( A
= ( k8_lopclset @ sk1 ) )
| ( v3_struct_0 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( l3_lattices @ sk1 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(pattern_uni,[status(thm)],[7057:[bind(A,$thf( sk1 ))]]) ).
thf(7063,plain,
! [A: $i] :
( ( ( k1_relat_1 @ A )
!= ( u1_struct_0 @ sk1 ) )
| ( ( a_2_0_lopclset @ sk1 @ ( sk7 @ A @ sk1 ) )
!= ( k1_funct_1 @ A @ ( sk7 @ A @ sk1 ) ) )
| ( A
= ( k8_lopclset @ sk1 ) )
| ( v3_struct_0 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( l3_lattices @ sk1 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(simp,[status(thm)],[7058]) ).
thf(1194,plain,
l3_lattices @ sk1,
inference(cnf,[status(esa)],[1192]) ).
thf(1198,plain,
~ ( v3_struct_0 @ sk1 ),
inference(cnf,[status(esa)],[1192]) ).
thf(7074,plain,
! [A: $i] :
( ( ( k1_relat_1 @ A )
!= ( u1_struct_0 @ sk1 ) )
| ( ( a_2_0_lopclset @ sk1 @ ( sk7 @ A @ sk1 ) )
!= ( k1_funct_1 @ A @ ( sk7 @ A @ sk1 ) ) )
| ( A
= ( k8_lopclset @ sk1 ) )
| $false
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ $true
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(rewrite,[status(thm)],[7063,1194,1198]) ).
thf(7075,plain,
! [A: $i] :
( ( ( k1_relat_1 @ A )
!= ( u1_struct_0 @ sk1 ) )
| ( ( a_2_0_lopclset @ sk1 @ ( sk7 @ A @ sk1 ) )
!= ( k1_funct_1 @ A @ ( sk7 @ A @ sk1 ) ) )
| ( A
= ( k8_lopclset @ sk1 ) )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A ) ),
inference(simp,[status(thm)],[7074]) ).
thf(152,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(1931,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1127,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k13_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_filter_2) ).
thf(5942,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k13_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(3014,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(884,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( ( k3_filter_0 @ A @ B )
= ( k1_filter_0 @ A ) )
& ( ( k3_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_0) ).
thf(4952,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( ( k3_filter_0 @ A @ B )
= ( k1_filter_0 @ A ) )
& ( ( k3_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_relat_1) ).
thf(2024,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(556,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( k2_filter_0 @ A @ ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_0) ).
thf(3708,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( k2_filter_0 @ A @ ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(71,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( v1_realset1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tex_2) ).
thf(1494,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) )
& ( v1_realset1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(13101,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( sk1 != k1_xboole_0 )
| ( A
!= ( k23_filter_2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1284,6279]) ).
thf(13102,plain,
( ~ ( v1_xboole_0 @ ( k23_filter_2 @ sk1 @ sk2 ) )
| ( sk1 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13101:[bind(A,$thf( k23_filter_2 @ sk1 @ sk2 ))]]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_subset_1) ).
thf(3602,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(734,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) )
=> ( v11_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice2) ).
thf(4400,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) )
=> ( v11_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(831,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ D )
=> ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_boolealg) ).
thf(4771,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ D )
=> ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(915,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= B ) )
& ( ( k2_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_0) ).
thf(5077,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= B ) )
& ( ( k2_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(762,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_openlatt @ A ) @ ( k4_lattices @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ B ) @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_openlatt) ).
thf(4514,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_openlatt @ A ) @ ( k4_lattices @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ B ) @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(6019,plain,
~ ( v1_xboole_0 @ sk330 ),
inference(cnf,[status(esa)],[6017]) ).
thf(6745,plain,
( ( v1_xboole_0 @ sk330 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,6019]) ).
thf(6752,plain,
sk330 != k1_xboole_0,
inference(simp,[status(thm)],[6745]) ).
thf(26402,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk330 ) ),
inference(paramod_ordered,[status(thm)],[1518,6752]) ).
thf(26403,plain,
v1_relat_1 @ ( sk27 @ sk330 ),
inference(pattern_uni,[status(thm)],[26402:[bind(A,$thf( sk330 ))]]) ).
thf(282,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ B )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_grfunc_1) ).
thf(2533,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ B )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(887,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v13_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_filter_0) ).
thf(4967,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v13_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(172,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_setwiseo) ).
thf(2007,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(858,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_boolealg @ A @ B @ C )
& ( r3_lattices @ A @ C @ D ) )
=> ( r3_boolealg @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_boolealg) ).
thf(4857,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_boolealg @ A @ B @ C )
& ( r3_lattices @ A @ C @ D ) )
=> ( r3_boolealg @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(147,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( r1_tarski @ B @ C )
=> ( ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ ( k16_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_lattice3) ).
thf(1911,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( r1_tarski @ B @ C )
=> ( ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) )
& ( r3_lattices @ A @ ( k16_lattice3 @ A @ C ) @ ( k16_lattice3 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(359,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(2893,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(818,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ B @ ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_lattices) ).
thf(4733,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ B @ ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(45676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ A @ B )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k4_xboole_0 @ sk149 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,44671]) ).
thf(45677,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ ( k4_xboole_0 @ sk149 @ B ) @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45676:[bind(A,$thf( k4_xboole_0 @ sk149 @ J )),bind(B,$thf( H )),bind(C,$thf( k4_xboole_0 @ ( k4_xboole_0 @ sk149 @ J ) @ H )),bind(D,$thf( J ))]]) ).
thf(45833,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ ( k4_xboole_0 @ sk149 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[45677]) ).
thf(1173,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k34_gate_1 @ A @ B ) )
<=> ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_gate_1) ).
thf(6176,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ ( k34_gate_1 @ A @ B ) )
=> ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) ) ) )
& ( ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) ) )
=> ~ ( v1_xboole_0 @ ( k34_gate_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(214,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_matrix_2 @ A ) )
=> ? [B: $i] : ( m3_matrix_2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_matrix_2) ).
thf(2254,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_matrix_2 @ A ) )
=> ? [B: $i] : ( m3_matrix_2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(285,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(2540,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(957,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ E @ F ) @ B ) )
=> ( ( r2_hidden @ ( k9_filter_0 @ A @ ( k3_lattices @ A @ C @ E ) @ ( k3_lattices @ A @ D @ F ) ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ ( k4_lattices @ A @ C @ E ) @ ( k4_lattices @ A @ D @ F ) ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_filter_1) ).
thf(5259,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ E @ F ) @ B ) )
=> ( ( r2_hidden @ ( k9_filter_0 @ A @ ( k3_lattices @ A @ C @ E ) @ ( k3_lattices @ A @ D @ F ) ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ ( k4_lattices @ A @ C @ E ) @ ( k4_lattices @ A @ D @ F ) ) @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(1104,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(5816,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(5817,plain,
v1_xboole_0 @ sk328,
inference(cnf,[status(esa)],[5816]) ).
thf(1027,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k3_sgraph1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_sgraph1) ).
thf(5513,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k3_sgraph1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(5514,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k3_sgraph1 @ A ) ),
inference(miniscope,[status(thm)],[5513]) ).
thf(5515,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k3_sgraph1 @ A ) ),
inference(cnf,[status(esa)],[5514]) ).
thf(10616,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k3_sgraph1 @ A ) )
!= ( v1_xboole_0 @ sk328 ) ),
inference(paramod_ordered,[status(thm)],[5817,5515]) ).
thf(10622,plain,
! [A: $i] :
( ( k3_sgraph1 @ A )
!= sk328 ),
inference(simp,[status(thm)],[10616]) ).
thf(13341,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk328 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5817,1284]) ).
thf(13342,plain,
sk328 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[13341:[bind(A,$thf( sk328 ))]]) ).
thf(14438,plain,
! [A: $i] :
( ( k3_sgraph1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10622,13342]) ).
thf(26711,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k3_sgraph1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,14438]) ).
thf(26712,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k3_sgraph1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26711:[bind(A,$thf( k3_sgraph1 @ C )),bind(B,$thf( C ))]]) ).
thf(27087,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k3_sgraph1 @ A ) ) ),
inference(simp,[status(thm)],[26712]) ).
thf(892,axiom,
! [A: $i] : ( m1_subset_1 @ ( k1_tex_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tex_1) ).
thf(4987,plain,
! [A: $i] : ( m1_subset_1 @ ( k1_tex_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(4988,plain,
! [A: $i] : ( m1_subset_1 @ ( k1_tex_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[4987]) ).
thf(1415,plain,
v1_trees_1 @ sk19,
inference(cnf,[status(esa)],[1414]) ).
thf(300,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setwiseo) ).
thf(2616,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m2_lattice4 @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_1_lattice4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k2_lattice4 @ B @ D ) )
& ( r1_tarski @ D @ ( k4_lattice4 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).
thf(1946,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m2_lattice4 @ C @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_lattice4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k2_lattice4 @ B @ D ) )
& ( r1_tarski @ D @ ( k4_lattice4 @ B @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k2_lattice4 @ B @ D ) )
& ( r1_tarski @ D @ ( k4_lattice4 @ B @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_1_lattice4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(502,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k5_lattices @ A ) )
<=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_boolealg) ).
thf(3524,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k5_lattices @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ B ) )
& ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ B )
=> ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(3431,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(1301,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1302,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(cnf,[status(esa)],[1301]) ).
thf(1118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k24_gate_1 @ A @ B @ C @ D @ E @ F ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F ) )
& ( v1_xboole_0 @ ( k24_gate_1 @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_gate_1) ).
thf(5892,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k24_gate_1 @ A @ B @ C @ D @ E @ F ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F ) )
& ( v1_xboole_0 @ ( k24_gate_1 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k11_filter_0 @ A @ B )
= ( k10_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).
thf(2794,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k11_filter_0 @ A @ B )
= ( k10_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(609,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
& ( C = E )
& ( D = F ) )
=> ( ( k5_filter_0 @ A @ C @ D )
= ( k5_filter_0 @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l59_filter_2) ).
thf(3887,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ! [F: $i] :
( ( ~ ( v1_xboole_0 @ F )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
& ( C = E )
& ( D = F ) )
=> ( ( k5_filter_0 @ A @ C @ D )
= ( k5_filter_0 @ B @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(2324,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(1714,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(177,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_filter_0 @ A @ B )
= ( a_2_0_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_filter_0) ).
thf(2027,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_filter_0 @ A @ B )
= ( a_2_0_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(436,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
<=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_filter_2) ).
thf(3199,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) )
& ( ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B )
=> ( r2_hidden @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( v1_xboole_0 @ ( k14_gate_1 @ A @ B @ C @ D ) )
<=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_gate_1) ).
thf(5526,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ ( k14_gate_1 @ A @ B @ C @ D ) )
=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) ) )
& ( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
=> ~ ( v1_xboole_0 @ ( k14_gate_1 @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(625,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ C )
= B ) )
& ( ( k18_filter_2 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_filter_2) ).
thf(3934,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ C )
= B ) )
& ( ( k18_filter_2 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( v3_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_1) ).
thf(4578,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( v3_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k12_openlatt @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_openlatt) ).
thf(3075,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k12_openlatt @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(1044,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_lattice4) ).
thf(5597,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(846,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(4820,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1111,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ( r2_subset_1 @ A @ B )
=> ( r2_subset_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_subset_1) ).
thf(5856,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ( r2_subset_1 @ A @ B )
=> ( r2_subset_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ ( k6_domain_1 @ A @ B ) )
& ( v1_realset1 @ ( k6_domain_1 @ A @ B ) )
& ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_rpr_1) ).
thf(1418,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ ( k6_domain_1 @ A @ B ) )
& ( v1_realset1 @ ( k6_domain_1 @ A @ B ) )
& ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(261,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(2451,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(503,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_boolealg) ).
thf(3527,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(3123,plain,
~ ( v1_xboole_0 @ sk149 ),
inference(cnf,[status(esa)],[3119]) ).
thf(6408,plain,
( ( v1_xboole_0 @ sk149 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,3123]) ).
thf(6410,plain,
sk149 != k1_xboole_0,
inference(simp,[status(thm)],[6408]) ).
thf(554,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3702,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(1858,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(678,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ A )
=> ( A
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(4147,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ A )
=> ( A
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(655,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( r2_hidden @ B @ ( k7_openlatt @ A ) )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ( v2_filter_0 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_openlatt) ).
thf(4050,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( r2_hidden @ B @ ( k7_openlatt @ A ) )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ( v2_filter_0 @ B @ A ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ( v2_filter_0 @ B @ A ) )
=> ( r2_hidden @ B @ ( k7_openlatt @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(639,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v17_lattices @ A )
<=> ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_lattices) ).
thf(3973,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v17_lattices @ A )
=> ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) ) )
& ( ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) )
=> ( v17_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(26011,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != k1_trees_3 ) ),
inference(paramod_ordered,[status(thm)],[1518,6680]) ).
thf(26012,plain,
v1_relat_1 @ ( sk27 @ k1_trees_3 ),
inference(pattern_uni,[status(thm)],[26011:[bind(A,$thf( k1_trees_3 ))]]) ).
thf(1122,axiom,
~ ( v1_xboole_0 @ k2_topreal1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_topreal1) ).
thf(5913,plain,
~ ( v1_xboole_0 @ k2_topreal1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(5914,plain,
~ ( v1_xboole_0 @ k2_topreal1 ),
inference(polarity_switch,[status(thm)],[5913]) ).
thf(5135,plain,
~ ( v3_struct_0 @ sk293 ),
inference(cnf,[status(esa)],[5133]) ).
thf(12793,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk293 ) ),
inference(paramod_ordered,[status(thm)],[1284,5135]) ).
thf(12794,plain,
( ~ ( v1_xboole_0 @ sk293 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[12793:[bind(A,$thf( sk293 ))]]) ).
thf(934,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k5_filter_2 @ A @ B ) @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).
thf(5156,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k5_filter_2 @ A @ B ) @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(410,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(3093,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(1581,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(2335,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(14483,plain,
( ( v12_lattices @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,13600]) ).
thf(14500,plain,
( ( v12_lattices @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14483]) ).
thf(641,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_boolealg) ).
thf(3986,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(6,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(1214,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1215,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finset_1 @ A )
| ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
inference(cnf,[status(esa)],[1214]) ).
thf(489,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v13_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( ( k5_lattices @ ( k5_filter_1 @ A @ B ) )
= ( k6_filter_1 @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_filter_1) ).
thf(3421,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v13_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( ( k5_lattices @ ( k5_filter_1 @ A @ B ) )
= ( k6_filter_1 @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(12669,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk324 ) ),
inference(paramod_ordered,[status(thm)],[1284,5674]) ).
thf(12670,plain,
( ~ ( v1_xboole_0 @ sk324 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[12669:[bind(A,$thf( sk324 ))]]) ).
thf(122,axiom,
( ( k3_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_toler_1) ).
thf(1795,plain,
( ( k3_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1796,plain,
( ( k3_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1795]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(2979,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(848,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( k7_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( C = A )
& ( v1_filter_0 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_lopclset) ).
thf(4825,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( k7_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( C = A )
& ( v1_filter_0 @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( C = A )
& ( v1_filter_0 @ C @ B ) )
=> ( r2_hidden @ A @ ( k7_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(6021,plain,
v1_matrix_2 @ sk331,
inference(cnf,[status(esa)],[6020]) ).
thf(18667,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[10028,2992]) ).
thf(18682,plain,
! [A: $i] :
( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[18667]) ).
thf(45686,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ A @ B )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,18682]) ).
thf(45687,plain,
! [A: $i] :
( ( k3_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45686:[bind(A,$thf( k1_zfmisc_1 @ k1_xboole_0 )),bind(B,$thf( F )),bind(C,$thf( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ F ))]]) ).
thf(45838,plain,
! [A: $i] :
( ( k3_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[45687]) ).
thf(487,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_trees_3 ) )
=> ( ( A = k2_trees_3 )
<=> ! [B: $i] :
( ( r2_hidden @ B @ A )
<=> ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_trees_3) ).
thf(3389,plain,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_trees_3 ) )
=> ( ( ( A = k2_trees_3 )
=> ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) ) )
& ( ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) )
=> ( r2_hidden @ B @ A ) ) ) )
& ( ! [B: $i] :
( ( ( r2_hidden @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) ) )
& ( ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) )
=> ( r2_hidden @ B @ A ) ) )
=> ( A = k2_trees_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(276,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ D ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) @ ( k1_boolealg @ A @ C @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_boolealg) ).
thf(2508,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ D ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) @ ( k1_boolealg @ A @ C @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(376,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ ( k5_lattices @ A ) @ ( k3_filter_0 @ A @ B ) )
& ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ( ( k2_lattice4 @ A @ C )
= ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lopclset) ).
thf(2964,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ ( k5_lattices @ A ) @ ( k3_filter_0 @ A @ B ) )
& ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ( ( k2_lattice4 @ A @ C )
= ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(910,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_1) ).
thf(5059,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(247,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_sgraph1) ).
thf(2367,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).
thf(2437,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1093,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) )
= B )
& ( ( u2_lattices @ ( k23_filter_2 @ A @ B ) )
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( ( u1_lattices @ ( k23_filter_2 @ A @ B ) )
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_filter_2) ).
thf(5773,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) )
= B )
& ( ( u2_lattices @ ( k23_filter_2 @ A @ B ) )
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( ( u1_lattices @ ( k23_filter_2 @ A @ B ) )
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(649,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( k22_filter_2 @ A @ B @ C )
= ( a_3_2_filter_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_filter_2) ).
thf(4033,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( k22_filter_2 @ A @ B @ C )
= ( a_3_2_filter_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(3739,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).
thf(2281,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1158,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k7_gate_1 @ A @ B ) )
<=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_gate_1) ).
thf(6110,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ ( k7_gate_1 @ A @ B ) )
=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) ) )
& ( ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k7_gate_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(989,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k5_filter_0 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k4_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_filter_0) ).
thf(5375,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k5_filter_0 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k4_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(557,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ D )
& ( r3_lattices @ A @ ( k1_boolealg @ A @ C @ B ) @ D ) )
=> ( r3_lattices @ A @ ( k2_boolealg @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_boolealg) ).
thf(3712,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ D )
& ( r3_lattices @ A @ ( k1_boolealg @ A @ C @ B ) @ D ) )
=> ( r3_lattices @ A @ ( k2_boolealg @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(6129,plain,
~ ( v3_struct_0 @ sk334 ),
inference(cnf,[status(esa)],[6127]) ).
thf(13071,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk334 ) ),
inference(paramod_ordered,[status(thm)],[1284,6129]) ).
thf(13072,plain,
( ~ ( v1_xboole_0 @ sk334 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13071:[bind(A,$thf( sk334 ))]]) ).
thf(953,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) )
=> ( ( r3_boolealg @ A @ B @ C )
& ( r3_boolealg @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_boolealg) ).
thf(5246,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) )
=> ( ( r3_boolealg @ A @ B @ C )
& ( r3_boolealg @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(76,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( r1_tarski @ A @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_grfunc_1) ).
thf(1526,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ( r1_tarski @ A @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(976,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ C ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_filter_0) ).
thf(5321,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ C ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(545,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(3676,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(336,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(2797,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(2798,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(cnf,[status(esa)],[2797]) ).
thf(2799,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(lifteq,[status(thm)],[2798]) ).
thf(186,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( k1_tarski @ B )
!= A )
& ! [C: $i,D: $i] :
~ ( ( C != D )
& ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_collsp) ).
thf(2103,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
( ( ( k1_tarski @ B )
!= A )
& ! [C: $i,D: $i] :
~ ( ( C != D )
& ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1405,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_trees_1 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_trees_1 @ B )
| ( v1_trees_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[1404]) ).
thf(799,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
=> ( ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ D )
& ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_boolealg) ).
thf(4643,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
=> ( ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ D )
& ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(1943,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1168,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k4_card_fil @ A )
= ( a_1_0_card_fil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_card_fil) ).
thf(6156,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k4_card_fil @ A )
= ( a_1_0_card_fil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(809,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ ( k1_boolealg @ A @ C @ B ) ) @ ( k3_lattices @ A @ B @ C ) )
& ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k1_boolealg @ A @ C @ B ) @ B ) @ ( k3_lattices @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_boolealg) ).
thf(4707,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ ( k1_boolealg @ A @ C @ B ) ) @ ( k3_lattices @ A @ B @ C ) )
& ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k1_boolealg @ A @ C @ B ) @ B ) @ ( k3_lattices @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(38189,plain,
! [B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A
!= ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1284,38135]) ).
thf(38190,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) ),
inference(pattern_uni,[status(thm)],[38189:[bind(A,$thf( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ D )),bind(B,$thf( D ))]]) ).
thf(38246,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) ),
inference(simp,[status(thm)],[38190]) ).
thf(1236,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( B
!= ( k8_lopclset @ A ) )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
| ( ( k1_funct_1 @ B @ C )
= ( a_2_0_lopclset @ A @ C ) ) ),
inference(cnf,[status(esa)],[1232]) ).
thf(1241,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( k8_lopclset @ A ) )
| ( ( k1_funct_1 @ B @ C )
= ( a_2_0_lopclset @ A @ C ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ),
inference(lifteq,[status(thm)],[1236]) ).
thf(1242,plain,
! [B: $i,A: $i] :
( ( ( a_2_0_lopclset @ A @ B )
= ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ ( k8_lopclset @ A ) )
| ~ ( v1_funct_1 @ ( k8_lopclset @ A ) )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ),
inference(simp,[status(thm)],[1241]) ).
thf(710,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r3_lattices @ A @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k7_openlatt @ A ) )
& ~ ( r2_hidden @ C @ D )
& ( r2_hidden @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_openlatt) ).
thf(4285,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r3_lattices @ A @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( r2_hidden @ D @ ( k7_openlatt @ A ) )
& ~ ( r2_hidden @ C @ D )
& ( r2_hidden @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(979,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattices) ).
thf(5328,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(688,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( v1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
<=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_lattice4) ).
thf(4211,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( v1_lattice4 @ E @ A @ B )
=> ( ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) )
& ( ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) )
=> ( r3_lattices @ A @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(12891,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v12_lattices @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1284,1199]) ).
thf(12892,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v12_lattices @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[12891:[bind(A,$thf( sk1 ))]]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(2982,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(356,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_lattice4 @ C @ B @ A )
& ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ F ) ) )
=> ( r3_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice4) ).
thf(2884,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_lattice4 @ C @ B @ A )
& ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ F ) ) )
=> ( r3_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k4_filter_2 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_filter_2) ).
thf(2954,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k4_filter_2 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(3582,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(1691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(560,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k22_filter_2 @ A @ B @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_filter_2) ).
thf(3720,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k22_filter_2 @ A @ B @ B ) @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(1148,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v12_lattices @ A )
& ( v12_lattices @ B ) )
<=> ( v12_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_filter_1) ).
thf(6047,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v12_lattices @ A )
& ( v12_lattices @ B ) )
=> ( v12_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v12_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v12_lattices @ A )
& ( v12_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(15101,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ sk149 @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[6916,2992]) ).
thf(15108,plain,
! [A: $i] :
( ( k4_xboole_0 @ sk149 @ A )
!= sk139 ),
inference(simp,[status(thm)],[15101]) ).
thf(45759,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ A @ B )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk149 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,15108]) ).
thf(45760,plain,
! [A: $i] :
( ( k3_xboole_0 @ sk149 @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45759:[bind(A,$thf( sk149 )),bind(B,$thf( E )),bind(C,$thf( k4_xboole_0 @ sk149 @ E ))]]) ).
thf(45808,plain,
! [A: $i] :
( ( k3_xboole_0 @ sk149 @ A )
!= sk139 ),
inference(simp,[status(thm)],[45760]) ).
thf(967,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( k10_openlatt @ A @ B ) )
<=> ( ( m1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_openlatt) ).
thf(5291,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ ( k10_openlatt @ A @ B ) )
=> ( ( m1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( m1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) )
=> ( r2_hidden @ C @ ( k10_openlatt @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1155,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( v13_lattices @ ( k23_filter_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_filter_2) ).
thf(6092,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( v13_lattices @ ( k23_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(3679,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
<=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(1863,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
=> ~ ( r2_hidden @ B @ A ) )
& ( ~ ( r2_hidden @ B @ A )
=> ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(61,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_realset1) ).
thf(1429,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1431,plain,
~ ( v1_xboole_0 @ sk21 ),
inference(cnf,[status(esa)],[1429]) ).
thf(6284,plain,
( ( v1_xboole_0 @ sk21 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,1431]) ).
thf(6289,plain,
sk21 != k1_xboole_0,
inference(simp,[status(thm)],[6284]) ).
thf(26566,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk21 ) ),
inference(paramod_ordered,[status(thm)],[1518,6289]) ).
thf(26567,plain,
v1_relat_1 @ ( sk27 @ sk21 ),
inference(pattern_uni,[status(thm)],[26566:[bind(A,$thf( sk21 ))]]) ).
thf(1131,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_2 @ ( k1_filter_2 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_2) ).
thf(5961,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_2 @ ( k1_filter_2 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(412,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_lopclset @ A ) @ ( k3_lattices @ A @ B @ C ) )
= ( k2_xboole_0 @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_lopclset) ).
thf(3097,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_lopclset @ A ) @ ( k3_lattices @ A @ B @ C ) )
= ( k2_xboole_0 @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(4,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ B @ A ) )
& ( v1_finset_1 @ ( k3_xboole_0 @ B @ A ) )
& ( v1_trees_1 @ ( k3_xboole_0 @ B @ A ) )
& ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
& ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_trees_1) ).
thf(1202,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ B @ A ) )
& ( v1_finset_1 @ ( k3_xboole_0 @ B @ A ) )
& ( v1_trees_1 @ ( k3_xboole_0 @ B @ A ) )
& ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
& ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_trees_1 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_finset_1 @ B )
| ~ ( v1_trees_1 @ B )
| ( v1_finset_1 @ ( k3_xboole_0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1202]) ).
thf(388,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k5_lattices @ A ) )
<=> ( r3_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_boolealg) ).
thf(3011,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k5_lattices @ A ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ A @ B @ C )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(7530,plain,
( ( v1_realset1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( v1_realset1 @ sk75 ) ),
inference(paramod_ordered,[status(thm)],[7442,2139]) ).
thf(7533,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk75 ),
inference(simp,[status(thm)],[7530]) ).
thf(899,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_tops_2) ).
thf(5012,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(684,axiom,
! [A: $i,B: $i] :
( ( ( g1_struct_0 @ A )
= ( g1_struct_0 @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_struct_0) ).
thf(4199,plain,
! [A: $i,B: $i] :
( ( ( g1_struct_0 @ A )
= ( g1_struct_0 @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(690,axiom,
? [A: $i] : ( l1_orders_2 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(4216,plain,
? [A: $i] : ( l1_orders_2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1095,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ ( k15_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_openlatt) ).
thf(5783,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ ( k15_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(870,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r2_boolealg @ A @ B @ B )
<=> ( B
!= ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_boolealg) ).
thf(4893,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_boolealg @ A @ B @ B )
=> ( B
!= ( k5_lattices @ A ) ) )
& ( ( B
!= ( k5_lattices @ A ) )
=> ( r2_boolealg @ A @ B @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(717,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( m2_filter_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
<=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_filter_2) ).
thf(4323,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_filter_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(467,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( m2_card_fil @ B @ A )
<=> ( ~ ( r2_hidden @ A @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
& ( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_card_fil) ).
thf(3301,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
=> ( ( ( m2_card_fil @ B @ A )
=> ( ~ ( r2_hidden @ A @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
& ( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) )
& ( ( ~ ( r2_hidden @ A @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
& ( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_card_fil @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_1) ).
thf(4962,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(600,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(3852,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(27,axiom,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(1303,plain,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1304,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1303]) ).
thf(1306,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1304]) ).
thf(768,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) )
<=> ( ( r3_boolealg @ A @ B @ C )
| ( r3_boolealg @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_boolealg) ).
thf(4531,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) )
=> ( ( r3_boolealg @ A @ B @ C )
| ( r3_boolealg @ A @ B @ D ) ) )
& ( ( ( r3_boolealg @ A @ B @ C )
| ( r3_boolealg @ A @ B @ D ) )
=> ( r3_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(537,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k6_lattices @ A ) )
= ( k5_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lattice4) ).
thf(3635,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k6_lattices @ A ) )
= ( k5_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(2364,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1134,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(5968,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).
thf(1336,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ( ( k1_relat_1 @ B )
!= ( k1_relat_1 @ C ) )
| ( ( k2_relat_1 @ B )
!= ( k1_tarski @ A ) )
| ( ( k2_relat_1 @ C )
!= ( k1_tarski @ A ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[1336]) ).
thf(1338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= ( k1_relat_1 @ C ) )
| ( ( k2_relat_1 @ B )
!= ( k1_tarski @ A ) )
| ( ( k2_relat_1 @ C )
!= ( k1_tarski @ A ) )
| ( B = C )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C ) ),
inference(lifteq,[status(thm)],[1337]) ).
thf(929,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) )
=> ( ( k8_filter_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_filter_2) ).
thf(5142,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) )
=> ( ( k8_filter_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1113,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k13_lang1 @ A ) )
& ( v2_lang1 @ ( k13_lang1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lang1) ).
thf(5862,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k13_lang1 @ A ) )
& ( v2_lang1 @ ( k13_lang1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(778,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_tarski @ ( k9_openlatt @ A ) @ ( k1_zfmisc_1 @ ( k7_openlatt @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_openlatt) ).
thf(4576,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_tarski @ ( k9_openlatt @ A ) @ ( k1_zfmisc_1 @ ( k7_openlatt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(2307,plain,
! [A: $i] :
~ ( v1_tex_2 @ ( sk90 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[2306]) ).
thf(108,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_rpr_1) ).
thf(1736,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(273,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( v1_filter_0 @ B @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lopclset) ).
thf(2496,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( v1_filter_0 @ B @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(566,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(3735,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(877,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattice2) ).
thf(4915,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(49,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r4_lattice3 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattice3) ).
thf(1382,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r4_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) )
=> ( r4_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1383,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( r4_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ D @ B ) ) )
=> ( r4_lattice3 @ A @ B @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[1382]) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ C )
| ~ ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
| ~ ( r2_hidden @ D @ C )
| ( r1_lattices @ A @ D @ B ) ),
inference(cnf,[status(esa)],[1383]) ).
thf(339,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(2805,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( m1_subset_1 @ ( k12_openlatt @ A @ B @ C ) @ ( k9_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_openlatt) ).
thf(4375,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( m1_subset_1 @ ( k12_openlatt @ A @ B @ C ) @ ( k9_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1080,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ A ) )
=> ( m2_lattice4 @ ( k9_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_2) ).
thf(5719,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ A ) )
=> ( m2_lattice4 @ ( k9_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(3233,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(743,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(4449,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(6107,plain,
l3_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[6106]) ).
thf(919,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(5102,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(804,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_boolealg @ A @ B @ C )
=> ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ C ) @ B )
& ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ B ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_boolealg) ).
thf(4661,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_boolealg @ A @ B @ C )
=> ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ C ) @ B )
& ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(3261,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(295,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(2601,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(593,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_rlvect_2) ).
thf(3827,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(6247,plain,
l3_lattices @ sk339,
inference(cnf,[status(esa)],[6246]) ).
thf(1139,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_1) ).
thf(6000,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(6730,plain,
( ( v1_xboole_0 @ k2_topreal1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,5914]) ).
thf(6739,plain,
k2_topreal1 != k1_xboole_0,
inference(simp,[status(thm)],[6730]) ).
thf(27053,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != k2_topreal1 ) ),
inference(paramod_ordered,[status(thm)],[1518,6739]) ).
thf(27054,plain,
v1_relat_1 @ ( sk27 @ k2_topreal1 ),
inference(pattern_uni,[status(thm)],[27053:[bind(A,$thf( k2_topreal1 ))]]) ).
thf(13309,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1284,1198]) ).
thf(13310,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13309:[bind(A,$thf( sk1 ))]]) ).
thf(14342,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,13310]) ).
thf(14357,plain,
( ~ ( v3_struct_0 @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14342]) ).
thf(733,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice2) ).
thf(4397,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(895,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k10_lopclset @ A )
= ( k1_lopclset @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lopclset) ).
thf(5002,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k10_lopclset @ A )
= ( k1_lopclset @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ( r4_lattice3 @ A @ ( sk12 @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[1350]) ).
thf(1144,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_lattice4) ).
thf(6032,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(82,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tex_2) ).
thf(1570,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( v1_relat_1 @ ( k10_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_0) ).
thf(4989,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( v1_relat_1 @ ( k10_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(907,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) )
<=> ( v1_filter_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_filter_0) ).
thf(5044,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) )
=> ( v1_filter_0 @ B @ A ) )
& ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(983,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r2_hidden @ B @ ( k22_filter_2 @ A @ B @ C ) )
& ( r2_hidden @ C @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_filter_2) ).
thf(5349,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r2_hidden @ B @ ( k22_filter_2 @ A @ B @ C ) )
& ( r2_hidden @ C @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(192,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_tex_2) ).
thf(2133,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattice3 @ A @ B ) @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(2147,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_lattice3 @ A @ B ) @ ( u1_struct_0 @ ( k3_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(959,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( B
= ( k1_filter_0 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_0) ).
thf(5266,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( B
= ( k1_filter_0 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(392,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_pre_topc) ).
thf(3022,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1010,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( k10_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ B ) ) @ ( k9_lopclset @ B ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lopclset) ).
thf(5455,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( k10_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ B ) ) @ ( k9_lopclset @ B ) @ C )
= A ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ B ) ) @ ( k9_lopclset @ B ) @ C )
= A ) )
=> ( r2_hidden @ A @ ( k10_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(4344,plain,
l1_struct_0 @ sk236,
inference(cnf,[status(esa)],[4342]) ).
thf(663,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(4091,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(2606,plain,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(837,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r4_wellord1 @ A @ B )
=> ( r4_wellord1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_wellord1) ).
thf(4785,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r4_wellord1 @ A @ B )
=> ( r4_wellord1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(757,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A ) )
=> ( m1_filter_2 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_filter_2) ).
thf(4499,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A ) )
=> ( m1_filter_2 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
thf(3778,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B != A ) )
& ( ( B != A )
=> ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(3646,plain,
v1_xboole_0 @ sk183,
inference(cnf,[status(esa)],[3644]) ).
thf(13249,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( ( v1_xboole_0 @ sk183 )
!= ( v1_xboole_0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3646,1284]) ).
thf(13250,plain,
sk183 = k1_xboole_0,
inference(pattern_uni,[status(thm)],[13249:[bind(A,$thf( sk183 ))]]) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_relat_1 @ B )
!= ( u1_struct_0 @ A ) )
| ( m1_subset_1 @ ( sk7 @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( B
= ( k8_lopclset @ A ) ) ),
inference(cnf,[status(esa)],[1232]) ).
thf(1238,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ B )
!= ( u1_struct_0 @ A ) )
| ( B
= ( k8_lopclset @ A ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( m1_subset_1 @ ( sk7 @ B @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(lifteq,[status(thm)],[1234]) ).
thf(653,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k20_filter_2 @ A @ D @ E ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k20_filter_2 @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_filter_2) ).
thf(4044,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k20_filter_2 @ A @ D @ E ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k20_filter_2 @ A @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).
thf(3286,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k19_gate_1 @ A @ B @ C @ D @ E ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E ) )
& ( v1_xboole_0 @ ( k19_gate_1 @ A @ B @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_gate_1) ).
thf(5843,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k19_gate_1 @ A @ B @ C @ D @ E ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E ) )
& ( v1_xboole_0 @ ( k19_gate_1 @ A @ B @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(458,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_rlvect_1 @ A @ B )
<=> ( r2_hidden @ B @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_rlvect_1) ).
thf(3271,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( ( r1_rlvect_1 @ A @ B )
=> ( r2_hidden @ B @ ( u1_struct_0 @ A ) ) )
& ( ( r2_hidden @ B @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(815,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
<=> ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lattice3) ).
thf(4725,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r3_lattices @ A @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( r4_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(1072,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m3_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(5690,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m3_lattice4 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(729,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_rlvect_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_rlvect_2) ).
thf(4385,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_rlvect_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(25,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( ( k5_lattices @ A )
= ( k15_lattice3 @ A @ k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice3) ).
thf(1294,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( ( k5_lattices @ A )
= ( k15_lattice3 @ A @ k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1296,plain,
! [A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ~ ( l3_lattices @ A )
| ( v13_lattices @ A ) ),
inference(cnf,[status(esa)],[1294]) ).
thf(298,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( C = E )
& ( D = F )
& ( r2_lattices @ A @ C @ D ) )
=> ( r2_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_filter_2) ).
thf(2609,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( C = E )
& ( D = F )
& ( r2_lattices @ A @ C @ D ) )
=> ( r2_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(24,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_relat_1) ).
thf(1291,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(965,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_lattices) ).
thf(5285,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1154,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m1_lattice4 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(6090,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m1_lattice4 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(36,axiom,
( ~ ( v1_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) )
& ( v1_trees_1 @ ( k1_tarski @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_trees_1) ).
thf(1333,plain,
( ~ ( v1_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) )
& ( v1_trees_1 @ ( k1_tarski @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1334,plain,
v1_trees_1 @ ( k1_tarski @ k1_xboole_0 ),
inference(cnf,[status(esa)],[1333]) ).
thf(6926,plain,
v1_trees_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ),
inference(rewrite,[status(thm)],[1334,1201]) ).
thf(265,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) @ ( k5_finsub_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finsub_1) ).
thf(2464,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) @ ( k5_finsub_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(2939,plain,
v1_finset_1 @ sk135,
inference(cnf,[status(esa)],[2936]) ).
thf(6897,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) )
| ( ( v1_finset_1 @ sk135 )
!= ( v1_finset_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2939,1218]) ).
thf(6898,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk135 @ A ) ),
inference(pattern_uni,[status(thm)],[6897:[bind(A,$thf( sk135 ))]]) ).
thf(6912,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ sk135 @ A ) ),
inference(simp,[status(thm)],[6898]) ).
thf(14789,plain,
! [A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ k1_xboole_0 @ A ) ),
inference(rewrite,[status(thm)],[6912,13144]) ).
thf(14950,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ sk19 @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[6913,2992]) ).
thf(14957,plain,
! [A: $i] :
( ( k4_xboole_0 @ sk19 @ A )
!= sk139 ),
inference(simp,[status(thm)],[14950]) ).
thf(45691,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ A @ B )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk19 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,14957]) ).
thf(45692,plain,
! [A: $i] :
( ( k3_xboole_0 @ sk19 @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45691:[bind(A,$thf( sk19 )),bind(B,$thf( E )),bind(C,$thf( k4_xboole_0 @ sk19 @ E ))]]) ).
thf(45840,plain,
! [A: $i] :
( ( k3_xboole_0 @ sk19 @ A )
!= sk139 ),
inference(simp,[status(thm)],[45692]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(2873,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(457,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k18_filter_2 @ A @ B ) @ ( k19_filter_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_filter_2) ).
thf(3269,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k18_filter_2 @ A @ B ) @ ( k19_filter_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_1) ).
thf(3618,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(790,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k9_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_filter_0) ).
thf(4608,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k9_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(41565,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ ( k1_tarski @ B ) @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[9850,2992]) ).
thf(41593,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[41565]) ).
thf(320,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setwiseo) ).
thf(2710,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(2712,plain,
! [A: $i] : ( v1_xboole_0 @ ( sk113 @ A ) ),
inference(cnf,[status(esa)],[2710]) ).
thf(10434,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk113 @ A ) )
!= ( v1_xboole_0 @ ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2712,1697]) ).
thf(10470,plain,
! [B: $i,A: $i] :
( ( sk113 @ A )
!= ( k1_tarski @ B ) ),
inference(simp,[status(thm)],[10434]) ).
thf(12685,plain,
! [B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ( ( v1_xboole_0 @ ( sk113 @ A ) )
!= ( v1_xboole_0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2712,1284]) ).
thf(12686,plain,
! [A: $i] :
( ( sk113 @ A )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12685:[bind(A,$thf( C )),bind(B,$thf( sk113 @ C ))]]) ).
thf(13812,plain,
! [A: $i] :
( ( sk113 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[12686]) ).
thf(24111,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10470,13812]) ).
thf(267,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k1_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_lattice4) ).
thf(2477,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k1_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(236,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v17_lattices @ A )
& ( r4_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice4) ).
thf(2332,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v17_lattices @ A )
& ( r4_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(26282,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ( A != sk339 ) ),
inference(paramod_ordered,[status(thm)],[1518,6247]) ).
thf(26283,plain,
( ( v1_relat_1 @ ( sk27 @ sk339 ) )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26282:[bind(A,$thf( sk339 ))]]) ).
thf(824,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k20_filter_2 @ A @ B @ C ) @ ( k20_filter_2 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_filter_2) ).
thf(4757,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k20_filter_2 @ A @ B @ C ) @ ( k20_filter_2 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(943,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_ringcat1 @ A ) )
=> ! [B: $i] :
( ( m3_ringcat1 @ B @ A )
<=> ( m1_subset_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m3_ringcat1) ).
thf(5177,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_ringcat1 @ A ) )
=> ! [B: $i] :
( ( ( m3_ringcat1 @ B @ A )
=> ( m1_subset_1 @ B @ A ) )
& ( ( m1_subset_1 @ B @ A )
=> ( m3_ringcat1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(26049,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k1_tarski @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,10286]) ).
thf(26050,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_tarski @ A ) ) ),
inference(pattern_uni,[status(thm)],[26049:[bind(A,$thf( k1_tarski @ C )),bind(B,$thf( C ))]]) ).
thf(27188,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_tarski @ A ) ) ),
inference(simp,[status(thm)],[26050]) ).
thf(571,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r3_lattices @ A @ D @ E )
& ( r2_hidden @ E @ C ) ) ) ) )
=> ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_lattice3) ).
thf(3750,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r3_lattices @ A @ D @ E )
& ( r2_hidden @ E @ C ) ) ) ) )
=> ( r3_lattices @ A @ ( k15_lattice3 @ A @ B ) @ ( k15_lattice3 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(64,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(1457,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(833,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_lattice2) ).
thf(4776,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k12_gate_1 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
& ( v1_xboole_0 @ ( k12_gate_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_gate_1) ).
thf(5534,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k12_gate_1 @ A @ B @ C ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
& ( v1_xboole_0 @ ( k12_gate_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(611,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_setwiseo @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_lattice2) ).
thf(3894,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_setwiseo @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(1037,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v6_group_1 @ A )
<=> ( v6_group_1 @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_lattice2) ).
thf(5551,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v6_group_1 @ A )
=> ( v6_group_1 @ ( k1_lattice2 @ A ) ) )
& ( ( v6_group_1 @ ( k1_lattice2 @ A ) )
=> ( v6_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(13255,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( l3_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1284,1194]) ).
thf(13256,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13255:[bind(A,$thf( sk1 ))]]) ).
thf(14331,plain,
( ( l3_lattices @ k1_xboole_0 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,13256]) ).
thf(14338,plain,
( ( l3_lattices @ k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[14331]) ).
thf(735,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_filter_1) ).
thf(4402,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(880,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_lattice3 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lattice3) ).
thf(4942,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k8_lattice3 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1210,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ ( sk4 @ A ) )
| ~ ( v1_trees_1 @ ( sk4 @ A ) )
| ( sk3 @ A ) ),
inference(cnf,[status(esa)],[1209]) ).
thf(92,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(1656,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1041,axiom,
~ ( v1_xboole_0 @ k4_modal_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_modal_1) ).
thf(5566,plain,
~ ( v1_xboole_0 @ k4_modal_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1150,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ ( k8_filter_1 @ A @ B ) @ ( k8_filter_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_filter_1) ).
thf(6060,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ ( k8_filter_1 @ A @ B ) @ ( k8_filter_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattice4) ).
thf(2213,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(820,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice4) ).
thf(4740,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(1171,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_2 @ B @ A )
<=> ( m1_filter_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
thf(6168,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( m1_filter_2 @ B @ A )
=> ( m1_filter_0 @ B @ A ) )
& ( ( m1_filter_0 @ B @ A )
=> ( m1_filter_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(394,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_filter_0) ).
thf(3028,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) )
=> ( v1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(622,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k5_lattices @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattices) ).
thf(3926,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k5_lattices @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1189,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) ) )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( ( k3_lattices @ A @ C @ D )
= ( k3_lattices @ ( k23_filter_2 @ A @ B ) @ E @ F ) )
& ( ( k4_lattices @ A @ C @ D )
= ( k4_lattices @ ( k23_filter_2 @ A @ B ) @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_filter_2) ).
thf(6267,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) ) )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( ( k3_lattices @ A @ C @ D )
= ( k3_lattices @ ( k23_filter_2 @ A @ B ) @ E @ F ) )
& ( ( k4_lattices @ A @ C @ D )
= ( k4_lattices @ ( k23_filter_2 @ A @ B ) @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1112,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k15_openlatt @ A ) )
& ( v10_lattices @ ( k15_openlatt @ A ) )
& ( l3_lattices @ ( k15_openlatt @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_openlatt) ).
thf(5858,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k15_openlatt @ A ) )
& ( v10_lattices @ ( k15_openlatt @ A ) )
& ( l3_lattices @ ( k15_openlatt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(575,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k2_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_0) ).
thf(3763,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k2_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( m1_subset_1 @ ( k8_filter_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_2) ).
thf(4104,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( m1_subset_1 @ ( k8_filter_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(563,axiom,
! [A: $i,B: $i] :
( ( k5_finsub_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finsub_1) ).
thf(3727,plain,
! [A: $i,B: $i] :
( ( k5_finsub_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1281,plain,
! [A: $i] :
( ~ ( l1_struct_0 @ A )
| ~ ( v1_realset1 @ ( u1_struct_0 @ A ) )
| ( v3_realset2 @ A ) ),
inference(cnf,[status(esa)],[1279]) ).
thf(21969,plain,
! [A: $i] :
( ~ ( r2_hidden @ sk2 @ sk72 )
| ( ( r2_hidden @ A @ ( k1_tarski @ A ) )
!= ( r2_hidden @ k1_xboole_0 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[3667,13961]) ).
thf(21988,plain,
! [A: $i] :
( ~ ( r2_hidden @ sk2 @ sk72 )
| ( A != k1_xboole_0 )
| ( ( k1_tarski @ A )
!= sk72 ) ),
inference(simp,[status(thm)],[21969]) ).
thf(21995,plain,
( ~ ( r2_hidden @ sk2 @ sk72 )
| ( ( k1_tarski @ k1_xboole_0 )
!= sk72 ) ),
inference(simp,[status(thm)],[21988]) ).
thf(40469,plain,
( ~ ( r2_hidden @ sk2 @ sk72 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk72 ) ),
inference(rewrite,[status(thm)],[21995,1201]) ).
thf(624,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ! [G: $i] :
( ( m1_filter_0 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( u1_struct_0 @ A ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( u1_struct_0 @ A ) )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r1_filter_0 @ C @ G @ D @ E )
& ( r1_filter_0 @ C @ G @ E @ F ) )
=> ( r1_filter_0 @ C @ G @ D @ F ) )
& ( ( ( r1_filter_0 @ A @ B @ H @ I )
& ( r1_filter_0 @ A @ B @ I @ J ) )
=> ( r1_filter_0 @ A @ B @ H @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_filter_0) ).
thf(3931,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ! [G: $i] :
( ( m1_filter_0 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( u1_struct_0 @ A ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( u1_struct_0 @ A ) )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r1_filter_0 @ C @ G @ D @ E )
& ( r1_filter_0 @ C @ G @ E @ F ) )
=> ( r1_filter_0 @ C @ G @ D @ F ) )
& ( ( ( r1_filter_0 @ A @ B @ H @ I )
& ( r1_filter_0 @ A @ B @ I @ J ) )
=> ( r1_filter_0 @ A @ B @ H @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(109,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
thf(1740,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r1_relat_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_orders_1) ).
thf(1573,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r1_relat_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(2895,plain,
v1_funct_1 @ sk130,
inference(cnf,[status(esa)],[2893]) ).
thf(4525,plain,
l1_struct_0 @ sk244,
inference(cnf,[status(esa)],[4523]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(3386,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(406,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( r2_filter_2 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_filter_2) ).
thf(3078,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( r2_filter_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(8,axiom,
! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_measure1) ).
thf(1219,plain,
! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1220,plain,
! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[1219]) ).
thf(6919,plain,
! [A: $i] : ( m1_subset_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
inference(rewrite,[status(thm)],[1220,1201]) ).
thf(217,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
<=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k10_filter_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_filter_0) ).
thf(2268,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k10_filter_0 @ A @ D ) ) )
& ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k10_filter_0 @ A @ D ) )
=> ( r1_filter_0 @ A @ D @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(843,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
<=> ( v14_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).
thf(4808,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v13_lattices @ A )
=> ( v14_lattices @ ( k1_lattice2 @ A ) ) )
& ( ( v14_lattices @ ( k1_lattice2 @ A ) )
=> ( v13_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(2245,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(672,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_filter_0) ).
thf(4123,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_funct_2) ).
thf(1360,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(946,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) )
= ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattices) ).
thf(5189,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) )
= ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(229,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ( m2_filter_2 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k5_lattices @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_2) ).
thf(2300,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ( m2_filter_2 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k5_lattices @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(580,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ ( k1_boolealg @ A @ C @ B ) )
=> ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_boolealg) ).
thf(3784,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ ( k1_boolealg @ A @ C @ B ) )
=> ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v1_lattice2 @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_1_openlatt @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k9_openlatt @ B ) ) )
& ( A
= ( k3_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_openlatt) ).
thf(2498,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v1_lattice2 @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_1_openlatt @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k9_openlatt @ B ) ) )
& ( A
= ( k3_tarski @ C ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k9_openlatt @ B ) ) )
& ( A
= ( k3_tarski @ C ) ) )
=> ( r2_hidden @ A @ ( a_1_1_openlatt @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_filter_2 @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).
thf(3615,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( r1_filter_2 @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(594,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
<=> ( v1_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_filter_2) ).
thf(3831,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( r2_filter_2 @ A @ B )
=> ( v1_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) )
& ( ( v1_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) )
=> ( r2_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(2115,plain,
~ ( v1_xboole_0 @ sk72 ),
inference(cnf,[status(esa)],[2113]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(3482,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(930,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_matrix_2 @ A ) )
=> ! [B: $i] :
( ( m3_matrix_2 @ B @ A )
<=> ( m1_subset_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m3_matrix_2) ).
thf(5145,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_matrix_2 @ A ) )
=> ! [B: $i] :
( ( ( m3_matrix_2 @ B @ A )
=> ( m1_subset_1 @ B @ A ) )
& ( ( m1_subset_1 @ B @ A )
=> ( m3_matrix_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(115,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k2_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_trees_1) ).
thf(1762,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k2_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(2515,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(452,axiom,
? [A: $i] :
( ( l2_lang1 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_lang1) ).
thf(3254,plain,
? [A: $i] :
( ( l2_lang1 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( C
= ( k2_xboole_0 @ D @ B ) ) )
=> ( ( k1_funct_1 @ C @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_grfunc_1) ).
thf(1851,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( C
= ( k2_xboole_0 @ D @ B ) ) )
=> ( ( k1_funct_1 @ C @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_subset_1) ).
thf(1257,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
| ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[1257]) ).
thf(1259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) )
= ( k6_subset_1 @ A @ B @ C ) )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ),
inference(lifteq,[status(thm)],[1258]) ).
thf(3122,plain,
v1_relat_1 @ sk149,
inference(cnf,[status(esa)],[3119]) ).
thf(370,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k18_filter_2 @ A @ C ) )
<=> ( r3_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_2) ).
thf(2946,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ B @ ( k18_filter_2 @ A @ C ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ A @ B @ C )
=> ( r2_hidden @ B @ ( k18_filter_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(142,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(1873,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) )
& ( ! [B: $i] :
~ ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1874,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( r2_hidden @ B @ A ) )
& ! [A: $i] :
( ~ ? [B: $i] : ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[1873]) ).
thf(1876,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(cnf,[status(esa)],[1874]) ).
thf(1879,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ~ ( r2_hidden @ B @ A ) ),
inference(lifteq,[status(thm)],[1876]) ).
thf(1880,plain,
! [A: $i] :
~ ( r2_hidden @ A @ k1_xboole_0 ),
inference(simp,[status(thm)],[1879]) ).
thf(10294,plain,
! [B: $i,A: $i] :
( ( v1_realset1 @ A )
| ( ( r2_hidden @ ( sk9 @ A ) @ A )
!= ( r2_hidden @ B @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1247,1880]) ).
thf(10295,plain,
v1_realset1 @ k1_xboole_0,
inference(pattern_uni,[status(thm)],[10294:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( sk9 @ k1_xboole_0 ))]]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(2685,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1001,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_setwiseo @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_lattice2) ).
thf(5423,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_setwiseo @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(125,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(1804,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ( r2_zfrefle1 @ A @ B )
=> ( r2_zfrefle1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_zfrefle1) ).
thf(5615,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( ( r2_zfrefle1 @ A @ B )
=> ( r2_zfrefle1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(1326,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1327,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
| ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
inference(cnf,[status(esa)],[1326]) ).
thf(1328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ~ ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ),
inference(lifteq,[status(thm)],[1327]) ).
thf(47,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
<=> ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).
thf(1375,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ A ) )
& ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1056,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_heyting1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_heyting1) ).
thf(5631,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_heyting1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(5632,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_heyting1 @ A ) ),
inference(miniscope,[status(thm)],[5631]) ).
thf(5633,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_heyting1 @ A ) ),
inference(cnf,[status(esa)],[5632]) ).
thf(10687,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_heyting1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,5633]) ).
thf(10697,plain,
! [A: $i] :
( ( k1_heyting1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10687]) ).
thf(26911,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k1_heyting1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,10697]) ).
thf(26912,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_heyting1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26911:[bind(A,$thf( k1_heyting1 @ C )),bind(B,$thf( C ))]]) ).
thf(27139,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_heyting1 @ A ) ) ),
inference(simp,[status(thm)],[26912]) ).
thf(6924,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( m1_subset_1 @ ( sk5 @ A ) @ A )
| ( ( v1_realset1 @ sk60 )
!= ( v1_realset1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2022,1223]) ).
thf(6925,plain,
( ( v1_xboole_0 @ sk60 )
| ( m1_subset_1 @ ( sk5 @ sk60 ) @ sk60 ) ),
inference(pattern_uni,[status(thm)],[6924:[bind(A,$thf( sk60 ))]]) ).
thf(7172,plain,
( $false
| ( m1_subset_1 @ ( sk5 @ sk60 ) @ sk60 ) ),
inference(rewrite,[status(thm)],[6925,2023]) ).
thf(7173,plain,
m1_subset_1 @ ( sk5 @ sk60 ) @ sk60,
inference(simp,[status(thm)],[7172]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_rfunct_3 @ C @ A @ B )
& ~ ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_rfunct_3) ).
thf(5634,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_rfunct_3 @ C @ A @ B )
& ~ ( v1_xboole_0 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(5635,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( sk321 @ B @ A ) ),
inference(cnf,[status(esa)],[5634]) ).
thf(160,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(1970,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(6757,plain,
( ( v1_xboole_0 @ sk331 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,6022]) ).
thf(6765,plain,
sk331 != k1_xboole_0,
inference(simp,[status(thm)],[6757]) ).
thf(26979,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk331 ) ),
inference(paramod_ordered,[status(thm)],[1518,6765]) ).
thf(26980,plain,
v1_relat_1 @ ( sk27 @ sk331 ),
inference(pattern_uni,[status(thm)],[26979:[bind(A,$thf( sk331 ))]]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k1_tarski @ B ) )
<=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(1498,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) )
=> ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(1587,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1003,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v11_lattices @ A )
=> ( v11_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_filter_0) ).
thf(5428,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v11_lattices @ A )
=> ( v11_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(95,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finset_1) ).
thf(1672,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(988,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_filter_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_1) ).
thf(5373,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_filter_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relat_1) ).
thf(1755,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(628,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k5_lattices @ A )
= ( k5_lattices @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_filter_2) ).
thf(3941,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k5_lattices @ A )
= ( k5_lattices @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(6128,plain,
v3_lattices @ sk334,
inference(cnf,[status(esa)],[6127]) ).
thf(669,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( u1_struct_0 @ ( k8_filter_0 @ A @ B ) )
= B )
& ( ( u2_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( ( u1_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_0) ).
thf(4109,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( u1_struct_0 @ ( k8_filter_0 @ A @ B ) )
= B )
& ( ( u2_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u2_lattices @ A ) @ B ) )
& ( ( u1_lattices @ ( k8_filter_0 @ A @ B ) )
= ( k1_realset1 @ ( u1_lattices @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(38091,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A
!= ( k2_xboole_0 @ ( k1_tarski @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1284,1403]) ).
thf(38092,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[38091:[bind(A,$thf( k2_xboole_0 @ ( k1_tarski @ F ) @ E )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).
thf(38119,plain,
! [B: $i,A: $i] :
~ ( v1_xboole_0 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(simp,[status(thm)],[38092]) ).
thf(5497,plain,
v3_realset2 @ sk316,
inference(cnf,[status(esa)],[5496]) ).
thf(401,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(3060,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(264,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(2460,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(15268,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ sk133 @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[6917,2992]) ).
thf(15276,plain,
! [A: $i] :
( ( k4_xboole_0 @ sk133 @ A )
!= sk139 ),
inference(simp,[status(thm)],[15268]) ).
thf(45720,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ A @ B )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk133 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,15276]) ).
thf(45721,plain,
! [A: $i] :
( ( k3_xboole_0 @ sk133 @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45720:[bind(A,$thf( sk133 )),bind(B,$thf( E )),bind(C,$thf( k4_xboole_0 @ sk133 @ E ))]]) ).
thf(45789,plain,
! [A: $i] :
( ( k3_xboole_0 @ sk133 @ A )
!= sk139 ),
inference(simp,[status(thm)],[45721]) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
| ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ),
inference(cnf,[status(esa)],[1360]) ).
thf(1123,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k13_funcsdom @ A ) )
& ( v1_funcsdom @ ( k13_funcsdom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funcsdom) ).
thf(5915,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k13_funcsdom @ A ) )
& ( v1_funcsdom @ ( k13_funcsdom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(921,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r1_boolealg @ A @ ( k4_lattices @ A @ C @ D ) @ ( k5_lattices @ A ) ) )
=> ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ D ) @ ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_boolealg) ).
thf(5107,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r1_boolealg @ A @ ( k4_lattices @ A @ C @ D ) @ ( k5_lattices @ A ) ) )
=> ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ D ) @ ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(45668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ A @ B )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k1_tarski @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,41593]) ).
thf(45669,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ B ) @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45668:[bind(A,$thf( k1_tarski @ H )),bind(B,$thf( G )),bind(C,$thf( k4_xboole_0 @ ( k1_tarski @ H ) @ G )),bind(D,$thf( H ))]]) ).
thf(45829,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[45669]) ).
thf(955,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) )
<=> ( ~ ( r2_boolealg @ A @ B @ C )
& ~ ( r2_boolealg @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_boolealg) ).
thf(5253,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( r2_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) )
=> ( ~ ( r2_boolealg @ A @ B @ C )
& ~ ( r2_boolealg @ A @ B @ D ) ) )
& ( ( ~ ( r2_boolealg @ A @ B @ C )
& ~ ( r2_boolealg @ A @ B @ D ) )
=> ~ ( r2_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(543,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k4_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ C ) @ ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_boolealg) ).
thf(3671,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k4_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ C ) @ ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(6232,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k10_afinsq_1 @ A ) ),
inference(miniscope,[status(thm)],[6231]) ).
thf(6233,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k10_afinsq_1 @ A ) ),
inference(cnf,[status(esa)],[6232]) ).
thf(10753,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k10_afinsq_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,6233]) ).
thf(10763,plain,
! [A: $i] :
( ( k10_afinsq_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10753]) ).
thf(27029,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k10_afinsq_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,10763]) ).
thf(27030,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k10_afinsq_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[27029:[bind(A,$thf( k10_afinsq_1 @ C )),bind(B,$thf( C ))]]) ).
thf(27178,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k10_afinsq_1 @ A ) ) ),
inference(simp,[status(thm)],[27030]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(5166,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A ) )
=> ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(422,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) )
<=> ( r3_lattices @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_filter_0) ).
thf(3143,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) )
=> ( r3_lattices @ A @ C @ B ) )
& ( ( r3_lattices @ A @ C @ B )
=> ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(45682,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk19 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1396,44512]) ).
thf(45683,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ sk19 @ B ) @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45682:[bind(A,$thf( sk19 )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( k4_xboole_0 @ sk19 @ F ))]]) ).
thf(45836,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ sk19 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[45683]) ).
thf(1105,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(5818,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(620,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_lattices) ).
thf(3922,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(916,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( m2_lattice4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_lattice4) ).
thf(5080,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m2_lattice4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(533,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tex_2) ).
thf(3622,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(4092,plain,
! [A: $i] : ( v1_xboole_0 @ ( sk213 @ A ) ),
inference(cnf,[status(esa)],[4091]) ).
thf(10740,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk213 @ A ) )
!= ( v1_xboole_0 @ ( k15_coh_sp @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4092,5988]) ).
thf(10744,plain,
! [B: $i,A: $i] :
( ( sk213 @ A )
!= ( k15_coh_sp @ B ) ),
inference(simp,[status(thm)],[10740]) ).
thf(13427,plain,
! [B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ( ( v1_xboole_0 @ ( sk213 @ A ) )
!= ( v1_xboole_0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4092,1284]) ).
thf(13428,plain,
! [A: $i] :
( ( sk213 @ A )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[13427:[bind(A,$thf( C )),bind(B,$thf( sk213 @ C ))]]) ).
thf(13755,plain,
! [A: $i] :
( ( sk213 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[13428]) ).
thf(35511,plain,
! [A: $i] :
( ( k15_coh_sp @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10744,13755]) ).
thf(1064,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_0) ).
thf(5651,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(3094,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(cnf,[status(esa)],[3093]) ).
thf(737,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( a_2_1_domain_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_domain_1) ).
thf(4425,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( B
= ( a_2_1_domain_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
& ~ ( r2_hidden @ C @ A )
& ~ ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_setwiseo) ).
thf(3714,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
& ~ ( r2_hidden @ C @ A )
& ~ ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(6361,plain,
( ( v1_finset_1 @ sk139 )
!= ( v1_finset_1 @ sk19 ) ),
inference(paramod_ordered,[status(thm)],[1416,2992]) ).
thf(6363,plain,
sk139 != sk19,
inference(simp,[status(thm)],[6361]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( r2_hidden @ B @ A ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(2312,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( r2_hidden @ B @ A ) )
& ( ( r2_hidden @ B @ A )
=> ( m1_subset_1 @ B @ A ) ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( v1_xboole_0 @ B ) )
& ( ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1012,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k7_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_lopclset) ).
thf(5464,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k7_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(4750,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ B )
& ( A = C ) )
=> ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(134,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ~ ( r2_hidden @ k1_xboole_0 @ ( k1_tarski @ A ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( ( r2_hidden @ B @ ( k1_tarski @ A ) )
& ( r2_hidden @ C @ ( k1_tarski @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_tarski @ A ) ) )
& ( ( ( r2_hidden @ B @ ( k1_tarski @ A ) )
& ( r1_tarski @ B @ C ) )
=> ( r2_hidden @ C @ ( k1_tarski @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_card_fil) ).
thf(1842,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
& ~ ( r2_hidden @ k1_xboole_0 @ ( k1_tarski @ A ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( ( r2_hidden @ B @ ( k1_tarski @ A ) )
& ( r2_hidden @ C @ ( k1_tarski @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_tarski @ A ) ) )
& ( ( ( r2_hidden @ B @ ( k1_tarski @ A ) )
& ( r1_tarski @ B @ C ) )
=> ( r2_hidden @ C @ ( k1_tarski @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(26286,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1518,14357]) ).
thf(26287,plain,
( ( v1_relat_1 @ ( sk27 @ sk1 ) )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26286:[bind(A,$thf( sk1 ))]]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(1584,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(99,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r1_tarski @ B @ ( k4_subset_1 @ A @ C @ ( k3_subset_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_rpr_1) ).
thf(1700,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r1_tarski @ B @ ( k4_subset_1 @ A @ C @ ( k3_subset_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C )
& ~ ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(299,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relat_1) ).
thf(2613,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(1937,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(127,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(1810,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(490,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_boolealg @ A @ B @ C )
= ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_boolealg) ).
thf(3428,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_boolealg @ A @ B @ C )
= ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( v1_xboole_0 @ ( k22_gate_1 @ A @ B @ C @ D @ E @ F ) )
<=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_gate_1) ).
thf(5865,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ ( k22_gate_1 @ A @ B @ C @ D @ E @ F ) )
=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F ) ) )
& ( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F ) )
=> ~ ( v1_xboole_0 @ ( k22_gate_1 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(3194,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(2349,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(741,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ D ) @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_boolealg) ).
thf(4444,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ D ) @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(310,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k8_openlatt @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ( ( k1_funct_1 @ B @ C )
= ( a_2_0_openlatt @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_openlatt) ).
thf(2666,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k8_openlatt @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ( ( k1_funct_1 @ B @ C )
= ( a_2_0_openlatt @ A @ C ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ( ( k1_funct_1 @ B @ C )
= ( a_2_0_openlatt @ A @ C ) ) ) )
=> ( B
= ( k8_openlatt @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(511,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_rlvect_1 @ A @ B )
=> ( ( k1_rlvect_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_rlvect_2) ).
thf(3555,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_rlvect_1 @ A @ B )
=> ( ( k1_rlvect_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(746,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ C @ B )
= B ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_rlsub_2) ).
thf(4457,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ C @ B )
= B ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(7445,plain,
! [A: $i] :
( ( v1_realset1 @ ( k1_tarski @ A ) )
!= ( v1_realset1 @ sk75 ) ),
inference(paramod_ordered,[status(thm)],[1488,2139]) ).
thf(7448,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk75 ),
inference(simp,[status(thm)],[7445]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(3573,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(447,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(3242,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(25895,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( v1_struct_0 @ k1_xboole_0 )
| ( A != sk293 ) ),
inference(paramod_ordered,[status(thm)],[1518,5136]) ).
thf(25896,plain,
( ( v1_relat_1 @ ( sk27 @ sk293 ) )
| ( v1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25895:[bind(A,$thf( sk293 ))]]) ).
thf(63,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(1451,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(271,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( v14_lattices @ A )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ ( k17_filter_2 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_filter_2) ).
thf(2487,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( v14_lattices @ A )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ B @ ( k17_filter_2 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(578,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_filter_2 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).
thf(3770,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_filter_2 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( r1_filter_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(292,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r1_lattice4 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lattice4) ).
thf(2581,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r1_lattice4 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) )
=> ( r1_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(439,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) @ ( k16_openlatt @ A ) @ ( k5_lattices @ A ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_openlatt) ).
thf(3222,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) @ ( k16_openlatt @ A ) @ ( k5_lattices @ A ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(402,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_lopclset @ A ) @ ( k4_lattices @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lopclset) ).
thf(3064,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_lopclset @ A ) @ ( k4_lattices @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(2140,plain,
~ ( v1_xboole_0 @ sk75 ),
inference(cnf,[status(esa)],[2138]) ).
thf(1392,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(cnf,[status(esa)],[1391]) ).
thf(1393,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(lifteq,[status(thm)],[1392]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(2370,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(26292,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ( A != k13_nat_lat ) ),
inference(paramod_ordered,[status(thm)],[1518,6107]) ).
thf(26293,plain,
( ( v1_relat_1 @ ( sk27 @ k13_nat_lat ) )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26292:[bind(A,$thf( k13_nat_lat ))]]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(2285,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(117,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(1775,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1776,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1775]) ).
thf(960,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u2_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice2) ).
thf(5273,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(854,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ D @ C ) ) @ ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_filter_1) ).
thf(4846,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ D @ C ) ) @ ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(529,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v14_lattices @ A )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ ( k17_filter_2 @ A ) )
& ( ( k19_filter_2 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_filter_2) ).
thf(3611,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( v14_lattices @ A )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ ( k17_filter_2 @ A ) )
& ( ( k19_filter_2 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1166,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( v1_struct_0 @ ( g1_struct_0 @ A ) )
& ~ ( v3_struct_0 @ ( g1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_tex_1) ).
thf(6134,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( v1_struct_0 @ ( g1_struct_0 @ A ) )
& ~ ( v3_struct_0 @ ( g1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(346,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( B
!= ( k5_lattices @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_0) ).
thf(2836,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( B
!= ( k5_lattices @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_subset_1) ).
thf(3354,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r4_lattice3 @ B @ C @ A )
<=> ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattice3) ).
thf(2387,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r4_lattice3 @ B @ C @ A )
=> ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) )
& ( ( r3_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) )
=> ( r4_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1231,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_realset1 @ A )
| ( v1_tex_2 @ ( sk6 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[1227]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(3743,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k1_filter_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_1) ).
thf(5639,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k1_filter_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(5134,plain,
~ ( v3_realset2 @ sk293 ),
inference(cnf,[status(esa)],[5133]) ).
thf(1180,axiom,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_gate_1) ).
thf(6205,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(6206,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(polarity_switch,[status(thm)],[6205]) ).
thf(6207,plain,
~ ( v1_xboole_0 @ sk338 ),
inference(cnf,[status(esa)],[6206]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k11_openlatt @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_openlatt) ).
thf(2355,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k11_openlatt @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(275,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_tex_2) ).
thf(2505,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(590,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_filter_2) ).
thf(3819,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(626,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(3937,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(812,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k6_lattices @ A )
= ( k6_lattices @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_filter_2) ).
thf(4717,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k6_lattices @ A )
= ( k6_lattices @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(671,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(4120,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1070,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k10_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_filter_2) ).
thf(5683,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k10_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(535,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k6_filter_2 @ A @ ( k5_filter_2 @ A @ B ) )
= B )
& ( ( k5_filter_2 @ A @ ( k6_filter_2 @ A @ C ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_filter_2) ).
thf(3628,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k6_filter_2 @ A @ ( k5_filter_2 @ A @ B ) )
= B )
& ( ( k5_filter_2 @ A @ ( k6_filter_2 @ A @ C ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1107,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_nat_lat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_nat_lat) ).
thf(5823,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_nat_lat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(3115,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(26141,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk149 ) ),
inference(paramod_ordered,[status(thm)],[1518,6410]) ).
thf(26142,plain,
v1_relat_1 @ ( sk27 @ sk149 ),
inference(pattern_uni,[status(thm)],[26141:[bind(A,$thf( sk149 ))]]) ).
thf(636,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( m2_filter_2 @ ( k13_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_filter_2) ).
thf(3967,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( m2_filter_2 @ ( k13_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_fraenkel) ).
thf(3247,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(352,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(2862,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( m1_subset_1 @ ( k11_openlatt @ A @ B @ C ) @ ( k9_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_openlatt) ).
thf(4135,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( m1_subset_1 @ ( k11_openlatt @ A @ B @ C ) @ ( k9_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(2482,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1246,plain,
! [A: $i] :
( ( v1_realset1 @ A )
| ( r2_hidden @ ( sk8 @ A ) @ A ) ),
inference(cnf,[status(esa)],[1244]) ).
thf(163,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relat_1) ).
thf(1979,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(903,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ ( k5_lattices @ A ) )
=> ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_boolealg) ).
thf(5026,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ ( k5_lattices @ A ) )
=> ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(769,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m3_lattice4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_lattice4) ).
thf(4535,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m3_lattice4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) )
=> ( m3_lattice4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m2_filter_2 @ ( k19_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_filter_2) ).
thf(3834,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m2_filter_2 @ ( k19_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(2926,plain,
~ ( v1_xboole_0 @ sk133 ),
inference(cnf,[status(esa)],[2924]) ).
thf(998,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) ) )
& ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_boolealg) ).
thf(5402,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) ) )
& ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(836,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ( v3_realset2 @ A ) )
=> ( v3_realset2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_tex_2) ).
thf(4782,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
& ( v3_realset2 @ A ) )
=> ( v3_realset2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(828,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( v11_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_lattice4) ).
thf(4765,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( v11_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(10621,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk213 @ A ) )
!= ( v1_xboole_0 @ ( k3_sgraph1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4092,5515]) ).
thf(10627,plain,
! [B: $i,A: $i] :
( ( sk213 @ A )
!= ( k3_sgraph1 @ B ) ),
inference(simp,[status(thm)],[10621]) ).
thf(25857,plain,
! [A: $i] :
( ( k3_sgraph1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10627,13755]) ).
thf(257,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k5_lattices @ A ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lopclset) ).
thf(2408,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k5_lattices @ A ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(650,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_tarski @ ( k10_lopclset @ A ) )
= ( k7_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lopclset) ).
thf(4036,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_tarski @ ( k10_lopclset @ A ) )
= ( k7_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(954,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( ( k3_filter_0 @ A @ C )
= ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_filter_0) ).
thf(5249,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( ( k3_filter_0 @ A @ C )
= ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(586,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tex_2) ).
thf(3807,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(941,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_boolealg) ).
thf(5170,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(3454,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(592,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(3824,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(923,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k20_filter_2 @ A @ B @ C )
= ( a_3_0_filter_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_filter_2) ).
thf(5112,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k20_filter_2 @ A @ B @ C )
= ( a_3_0_filter_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(26063,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( v2_lang1 @ k1_xboole_0 )
| ( A != sk145 ) ),
inference(paramod_ordered,[status(thm)],[1518,3043]) ).
thf(26064,plain,
( ( v1_relat_1 @ ( sk27 @ sk145 ) )
| ( v2_lang1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26063:[bind(A,$thf( sk145 ))]]) ).
thf(1039,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(5557,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( v1_xboole_0 @ ( k17_gate_1 @ A @ B @ C @ D ) )
<=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_gate_1) ).
thf(5747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ ( k17_gate_1 @ A @ B @ C @ D ) )
=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D ) ) )
& ( ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D ) )
=> ~ ( v1_xboole_0 @ ( k17_gate_1 @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(724,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k20_filter_2 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k3_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_filter_2) ).
thf(4352,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k20_filter_2 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k3_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(205,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( B = k1_xboole_0 ) )
& ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_wellord2) ).
thf(2203,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( B = k1_xboole_0 ) )
& ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ( ( k1_relat_1 @ B )
= A )
& ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_finset_1 @ ( k8_rlvect_2 @ A @ B @ C ) )
& ( m1_subset_1 @ ( k8_rlvect_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_rlvect_2) ).
thf(3225,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_finset_1 @ ( k8_rlvect_2 @ A @ B @ C ) )
& ( m1_subset_1 @ ( k8_rlvect_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(460,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( r2_hidden @ ( k5_lattices @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_filter_2) ).
thf(3279,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( r2_hidden @ ( k5_lattices @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(868,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice2) ).
thf(4889,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(523,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).
thf(3587,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(433,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_filter_0) ).
thf(3183,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) )
=> ( v1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(431,axiom,
! [A: $i] :
( ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) )
<=> ( v1_finset_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
thf(3173,plain,
! [A: $i] :
( ( ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) )
=> ( v1_finset_1 @ ( k3_tarski @ A ) ) )
& ( ( v1_finset_1 @ ( k3_tarski @ A ) )
=> ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1174,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(6188,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(6189,plain,
~ ! [A: $i] : ( v1_xboole_0 @ A ),
inference(miniscope,[status(thm)],[6188]) ).
thf(6190,plain,
~ ( v1_xboole_0 @ sk336 ),
inference(cnf,[status(esa)],[6189]) ).
thf(6848,plain,
( ( v1_xboole_0 @ sk336 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,6190]) ).
thf(6859,plain,
sk336 != k1_xboole_0,
inference(simp,[status(thm)],[6848]) ).
thf(644,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ B @ C )
<=> ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_boolealg) ).
thf(3999,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_boolealg @ A @ B @ C )
=> ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ C @ B ) ) )
& ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ C @ B ) )
=> ( r1_boolealg @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_lopclset) ).
thf(3321,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( A = C )
& ( v1_filter_0 @ C @ B ) )
=> ( r2_hidden @ A @ ( a_1_1_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(874,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ! [B: $i] :
( ( l3_lattices @ B )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k1_lattice2 @ A )
= ( k1_lattice2 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_filter_2) ).
thf(4906,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ! [B: $i] :
( ( l3_lattices @ B )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ( ( k1_lattice2 @ A )
= ( k1_lattice2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_tex_2 @ B @ A )
<=> ( B
!= ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
thf(2915,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( ( v1_tex_2 @ B @ A )
=> ( B
!= ( k3_tarski @ A ) ) )
& ( ( B
!= ( k3_tarski @ A ) )
=> ( v1_tex_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(306,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k10_lopclset @ A )
= ( k2_relat_1 @ ( k9_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_lopclset) ).
thf(2645,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k10_lopclset @ A )
= ( k2_relat_1 @ ( k9_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ ( k13_gate_1 @ A @ B @ C ) )
<=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_gate_1) ).
thf(6038,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ ( k13_gate_1 @ A @ B @ C ) )
=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C ) ) )
& ( ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C ) )
=> ~ ( v1_xboole_0 @ ( k13_gate_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(1120,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_prelamb @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ? [C: $i] : ( m2_prelamb @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_prelamb) ).
thf(5909,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_prelamb @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ? [C: $i] : ( m2_prelamb @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(598,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( m2_nat_lat @ B @ A )
<=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u2_lattices @ B )
= ( k1_realset1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_lattices @ B )
= ( k1_realset1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_nat_lat) ).
thf(3841,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( m2_nat_lat @ B @ A )
=> ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u2_lattices @ B )
= ( k1_realset1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_lattices @ B )
= ( k1_realset1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ B ) ) ) ) )
& ( ( ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) )
& ( ( u2_lattices @ B )
= ( k1_realset1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_lattices @ B )
= ( k1_realset1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ B ) ) ) )
=> ( m2_nat_lat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(6309,plain,
( ( v1_realset1 @ sk75 )
!= ( v1_realset1 @ sk60 ) ),
inference(paramod_ordered,[status(thm)],[2022,2139]) ).
thf(6311,plain,
sk75 != sk60,
inference(simp,[status(thm)],[6309]) ).
thf(15294,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( ( v12_lattices @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) )
!= ( v12_lattices @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[13600,12892]) ).
thf(15323,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( ( k23_filter_2 @ k1_xboole_0 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[15294]) ).
thf(39234,plain,
( ( ( k23_filter_2 @ k1_xboole_0 @ sk2 )
!= k1_xboole_0 )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,15323]) ).
thf(39322,plain,
( ( ( k23_filter_2 @ k1_xboole_0 @ sk2 )
!= k1_xboole_0 )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[39234]) ).
thf(238,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k6_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k6_lattices @ A ) @ ( k6_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_filter_1) ).
thf(2338,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k6_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k6_lattices @ A ) @ ( k6_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r8_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r8_relat_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_orders_1) ).
thf(1996,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r8_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r8_relat_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(714,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_filter_2 @ C @ A )
=> ( m1_filter_2 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_filter_2) ).
thf(4308,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_filter_2 @ C @ A )
=> ( m1_filter_2 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k7_filter_0 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(5524,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k7_filter_0 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(311,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(2677,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(863,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_filter_0) ).
thf(4872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(1927,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1078,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lopclset) ).
thf(5715,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(951,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k6_lattices @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattices) ).
thf(5241,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k6_lattices @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(879,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattices) ).
thf(4921,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_funct_1 @ A @ ( sk10 @ B @ A ) )
!= ( k1_funct_1 @ B @ ( sk10 @ B @ A ) ) )
| ( v1_relat_1 @ ( sk11 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1268]) ).
thf(1278,plain,
! [B: $i,A: $i] :
( ( ( k1_funct_1 @ A @ ( sk10 @ B @ A ) )
!= ( k1_funct_1 @ B @ ( sk10 @ B @ A ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( v1_relat_1 @ ( sk11 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[1273]) ).
thf(26290,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk236 ) ),
inference(paramod_ordered,[status(thm)],[1518,4344]) ).
thf(26291,plain,
( ( v1_relat_1 @ ( sk27 @ sk236 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26290:[bind(A,$thf( sk236 ))]]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(2001,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1248,plain,
! [A: $i] :
( ( v1_realset1 @ A )
| ( ( sk8 @ A )
!= ( sk9 @ A ) ) ),
inference(cnf,[status(esa)],[1244]) ).
thf(1251,plain,
! [A: $i] :
( ( ( sk9 @ A )
!= ( sk8 @ A ) )
| ( v1_realset1 @ A ) ),
inference(lifteq,[status(thm)],[1248]) ).
thf(1019,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) )
<=> ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ E @ C )
& ( r3_lattices @ A @ E @ D ) )
=> ( r3_lattices @ A @ E @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_boolealg) ).
thf(5483,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) )
=> ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ E @ C )
& ( r3_lattices @ A @ E @ D ) )
=> ( r3_lattices @ A @ E @ B ) ) ) ) )
& ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ E @ C )
& ( r3_lattices @ A @ E @ D ) )
=> ( r3_lattices @ A @ E @ B ) ) ) )
=> ( r1_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(418,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k21_filter_2 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_filter_2) ).
thf(3130,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k21_filter_2 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(1101,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_relat_1 @ ( k9_filter_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(5808,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_relat_1 @ ( k9_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(670,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r2_hidden @ D @ ( k22_filter_2 @ A @ B @ C ) )
<=> ( ( r3_lattices @ A @ B @ D )
& ( r3_lattices @ A @ D @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
thf(4116,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( ( r2_hidden @ D @ ( k22_filter_2 @ A @ B @ C ) )
=> ( ( r3_lattices @ A @ B @ D )
& ( r3_lattices @ A @ D @ C ) ) )
& ( ( ( r3_lattices @ A @ B @ D )
& ( r3_lattices @ A @ D @ C ) )
=> ( r2_hidden @ D @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(4613,plain,
v3_realset2 @ sk250,
inference(cnf,[status(esa)],[4612]) ).
thf(928,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k5_lattices @ A ) )
<=> ( ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) )
& ( r1_boolealg @ A @ C @ ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_boolealg) ).
thf(5138,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k5_lattices @ A ) )
=> ( ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) )
& ( r1_boolealg @ A @ C @ ( k5_lattices @ A ) ) ) )
& ( ( ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) )
& ( r1_boolealg @ A @ C @ ( k5_lattices @ A ) ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc22_trees_3) ).
thf(2149,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_trees_1 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_trees_1 @ B ) )
=> ( ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) )
& ( v1_trees_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_boolealg @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_boolealg) ).
thf(4594,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_boolealg @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(453,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ B ) @ ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_boolealg) ).
thf(3257,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ B ) @ ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(322,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k5_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k5_lattices @ A ) @ ( k5_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_filter_1) ).
thf(2717,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k5_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k5_lattices @ A ) @ ( k5_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1179,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_nat_lat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_nat_lat) ).
thf(6203,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_nat_lat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(864,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(4874,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_filter_2 @ A @ B @ C )
=> ( r1_filter_2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
thf(2570,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_filter_2 @ A @ B @ C )
=> ( r1_filter_2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(901,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_lattice2) ).
thf(5016,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(759,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k18_openlatt @ A )
= ( k8_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k18_openlatt) ).
thf(4503,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k18_openlatt @ A )
= ( k8_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1183,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_domain_1) ).
thf(6228,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(725,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
<=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v15_lattices @ ( k1_lattice2 @ A ) )
& ( v16_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_filter_2) ).
thf(4359,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v15_lattices @ ( k1_lattice2 @ A ) )
& ( v16_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v15_lattices @ ( k1_lattice2 @ A ) )
& ( v16_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1062,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A )
& ( m2_filter_2 @ C @ A ) )
=> ( m2_filter_2 @ ( k21_filter_2 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k21_filter_2) ).
thf(5647,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A )
& ( m2_filter_2 @ C @ A ) )
=> ( m2_filter_2 @ ( k21_filter_2 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(549,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_subset_1) ).
thf(3686,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(2894,plain,
v2_funct_1 @ sk130,
inference(cnf,[status(esa)],[2893]) ).
thf(46,axiom,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(1371,plain,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1372,plain,
~ ? [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
inference(miniscope,[status(thm)],[1371]) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ),
inference(cnf,[status(esa)],[1372]) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ),
inference(lifteq,[status(thm)],[1373]) ).
thf(281,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) )
= ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_filter_1) ).
thf(2524,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) )
= ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ~ ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).
thf(2376,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ~ ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ~ ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(3158,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(24090,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk321 @ B @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,5635]) ).
thf(24105,plain,
! [B: $i,A: $i] :
( ( sk321 @ B @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[24090]) ).
thf(38020,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( sk321 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,24105]) ).
thf(38021,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk27 @ ( sk321 @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[38020:[bind(A,$thf( sk321 @ D @ E )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).
thf(38044,plain,
! [B: $i,A: $i] : ( v1_relat_1 @ ( sk27 @ ( sk321 @ A @ B ) ) ),
inference(simp,[status(thm)],[38021]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_setwiseo) ).
thf(3536,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ B )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(2970,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(577,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k2_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_tops_2) ).
thf(3768,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k2_pre_topc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(333,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k17_filter_2 @ A ) @ ( k18_filter_2 @ A @ ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_2) ).
thf(2789,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k17_filter_2 @ A ) @ ( k18_filter_2 @ A @ ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i] :
~ ( ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ B @ F @ A ) )
& ( v1_xboole_0 @ J ) )
& ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ C @ G @ J ) )
& ( v1_xboole_0 @ K ) )
& ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ D @ H @ K ) )
& ( v1_xboole_0 @ L ) )
& ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ E @ I @ L ) )
& ( v1_xboole_0 @ M ) )
& ~ ( ~ ( v1_xboole_0 @ N )
& ( v1_xboole_0 @ ( k3_gate_1 @ B @ F ) ) )
& ~ ( ~ ( v1_xboole_0 @ O )
& ( v1_xboole_0 @ ( k3_gate_1 @ C @ G ) ) )
& ~ ( ~ ( v1_xboole_0 @ P )
& ( v1_xboole_0 @ ( k3_gate_1 @ D @ H ) ) )
& ~ ( ~ ( v1_xboole_0 @ Q )
& ( v1_xboole_0 @ ( k3_gate_1 @ E @ I ) ) )
& ~ ( ~ ( v1_xboole_0 @ R )
& ( v1_xboole_0 @ ( k18_gate_1 @ A @ N @ O @ P @ Q ) ) )
& ~ ( ~ ( v1_xboole_0 @ S )
& ( v1_xboole_0 @ ( k3_gate_1 @ M @ R ) ) )
& ~ ( ~ ( v1_xboole_0 @ ( k3_gate_1 @ M @ R ) )
& ( v1_xboole_0 @ S ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ M )
& ( v1_xboole_0 @ S ) )
& ~ ( ~ ( v1_xboole_0 @ S )
& ( v1_xboole_0 @ M ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_gate_1) ).
thf(4677,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i] :
~ ( ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ B @ F @ A ) )
& ( v1_xboole_0 @ J ) )
& ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ C @ G @ J ) )
& ( v1_xboole_0 @ K ) )
& ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ D @ H @ K ) )
& ( v1_xboole_0 @ L ) )
& ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ E @ I @ L ) )
& ( v1_xboole_0 @ M ) )
& ~ ( ~ ( v1_xboole_0 @ N )
& ( v1_xboole_0 @ ( k3_gate_1 @ B @ F ) ) )
& ~ ( ~ ( v1_xboole_0 @ O )
& ( v1_xboole_0 @ ( k3_gate_1 @ C @ G ) ) )
& ~ ( ~ ( v1_xboole_0 @ P )
& ( v1_xboole_0 @ ( k3_gate_1 @ D @ H ) ) )
& ~ ( ~ ( v1_xboole_0 @ Q )
& ( v1_xboole_0 @ ( k3_gate_1 @ E @ I ) ) )
& ~ ( ~ ( v1_xboole_0 @ R )
& ( v1_xboole_0 @ ( k18_gate_1 @ A @ N @ O @ P @ Q ) ) )
& ~ ( ~ ( v1_xboole_0 @ S )
& ( v1_xboole_0 @ ( k3_gate_1 @ M @ R ) ) )
& ~ ( ~ ( v1_xboole_0 @ ( k3_gate_1 @ M @ R ) )
& ( v1_xboole_0 @ S ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ M )
& ( v1_xboole_0 @ S ) )
& ~ ( ~ ( v1_xboole_0 @ S )
& ( v1_xboole_0 @ M ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( m1_subset_1 @ ( sk16 @ C @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1383]) ).
thf(1388,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( m1_subset_1 @ ( sk16 @ C @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(simp,[status(thm)],[1384]) ).
thf(21949,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,3495]) ).
thf(21962,plain,
! [A: $i] :
( ( k1_funct_2 @ A @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[21949]) ).
thf(37488,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k1_funct_2 @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,21962]) ).
thf(37489,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_funct_2 @ A @ A ) ) ),
inference(pattern_uni,[status(thm)],[37488:[bind(A,$thf( k1_funct_2 @ D @ D )),bind(B,$thf( D ))]]) ).
thf(37519,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_funct_2 @ A @ A ) ) ),
inference(simp,[status(thm)],[37489]) ).
thf(6404,plain,
( ( v1_finset_1 @ sk139 )
!= ( v1_finset_1 @ sk135 ) ),
inference(paramod_ordered,[status(thm)],[2939,2992]) ).
thf(6407,plain,
sk139 != sk135,
inference(simp,[status(thm)],[6404]) ).
thf(13991,plain,
sk139 != k1_xboole_0,
inference(rewrite,[status(thm)],[6407,13144]) ).
thf(14043,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( A != sk139 ) ),
inference(paramod_ordered,[status(thm)],[1284,13991]) ).
thf(14044,plain,
~ ( v1_xboole_0 @ sk139 ),
inference(pattern_uni,[status(thm)],[14043:[bind(A,$thf( sk139 ))]]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_filter_1) ).
thf(4144,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k6_filter_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k5_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_filter_1) ).
thf(3372,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k6_filter_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k5_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1185,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_modal_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_modal_1) ).
thf(6234,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_modal_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(569,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
=> ( r3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice3) ).
thf(3741,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
=> ( r3_lattices @ A @ B @ ( k16_lattice3 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(5386,plain,
v1_relat_1 @ sk305,
inference(cnf,[status(esa)],[5385]) ).
thf(1235,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( B
!= ( k8_lopclset @ A ) )
| ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) ) ),
inference(cnf,[status(esa)],[1232]) ).
thf(1239,plain,
! [B: $i,A: $i] :
( ( B
!= ( k8_lopclset @ A ) )
| ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B ) ),
inference(lifteq,[status(thm)],[1235]) ).
thf(1240,plain,
! [A: $i] :
( ( ( u1_struct_0 @ A )
= ( k1_relat_1 @ ( k8_lopclset @ A ) ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v1_relat_1 @ ( k8_lopclset @ A ) )
| ~ ( v1_funct_1 @ ( k8_lopclset @ A ) ) ),
inference(simp,[status(thm)],[1239]) ).
thf(7210,plain,
! [A: $i] :
( ( ( u1_struct_0 @ A )
= ( k1_relat_1 @ ( k8_lopclset @ A ) ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v17_lattices @ A )
| ( v3_realset2 @ A )
| ~ ( v1_relat_1 @ ( k8_lopclset @ A ) )
| ~ ( v1_funct_1 @ ( k8_lopclset @ A ) )
| ( ( l3_lattices @ sk1 )
!= ( l3_lattices @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1194,1240]) ).
thf(7211,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ( v3_struct_0 @ sk1 )
| ~ ( v10_lattices @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
| ~ ( v1_funct_1 @ ( k8_lopclset @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7210:[bind(A,$thf( sk1 ))]]) ).
thf(7249,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| $false
| ~ $true
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
| ~ ( v1_funct_1 @ ( k8_lopclset @ sk1 ) ) ),
inference(rewrite,[status(thm)],[7211,1197,1198]) ).
thf(7250,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
| ~ ( v1_funct_1 @ ( k8_lopclset @ sk1 ) ) ),
inference(simp,[status(thm)],[7249]) ).
thf(7281,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_funct_1 @ ( k8_lopclset @ sk1 ) )
| ( ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
!= ( v1_relat_1 @ sk305 ) ) ),
inference(paramod_ordered,[status(thm)],[5386,7250]) ).
thf(7287,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ( v3_realset2 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ~ ( v1_funct_1 @ ( k8_lopclset @ sk1 ) )
| ( ( k8_lopclset @ sk1 )
!= sk305 ) ),
inference(simp,[status(thm)],[7281]) ).
thf(4340,plain,
~ ! [A: $i] : ( v2_setfam_1 @ A ),
inference(miniscope,[status(thm)],[4339]) ).
thf(4341,plain,
~ ( v2_setfam_1 @ sk235 ),
inference(cnf,[status(esa)],[4340]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( r1_boolealg @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_boolealg) ).
thf(4268,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( r1_boolealg @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).
thf(2727,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(351,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_filter_0) ).
thf(2859,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ~ ( v1_xboole_0 @ ( k10_openlatt @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_openlatt) ).
thf(5474,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ~ ( v1_xboole_0 @ ( k10_openlatt @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( ~ ( v1_realset1 @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) ) ) )
& ~ ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) )
& ( v1_realset1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_realset1) ).
thf(1884,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( ~ ( v1_realset1 @ B )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) ) ) )
& ~ ( ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( C != D ) ) )
& ( v1_realset1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_filter_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(4283,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_filter_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(120,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_1) ).
thf(1784,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(755,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u1_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattice2) ).
thf(4494,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u1_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( r2_hidden @ ( sk16 @ C @ B @ A ) @ C )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1383]) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ( r2_hidden @ ( sk16 @ C @ B @ A ) @ C )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(simp,[status(thm)],[1385]) ).
thf(3255,plain,
~ ( v3_struct_0 @ sk156 ),
inference(cnf,[status(esa)],[3254]) ).
thf(587,axiom,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(3811,plain,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(6108,plain,
v10_lattices @ k13_nat_lat,
inference(cnf,[status(esa)],[6106]) ).
thf(446,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(3240,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(995,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) )
=> ( m1_subset_1 @ ( k6_filter_2 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_filter_2) ).
thf(5395,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) )
=> ( m1_subset_1 @ ( k6_filter_2 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(2791,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(45757,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk19 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,6913]) ).
thf(45758,plain,
! [A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ sk19 @ A ) ),
inference(pattern_uni,[status(thm)],[45757:[bind(A,$thf( sk19 )),bind(B,$thf( E )),bind(C,$thf( k4_xboole_0 @ sk19 @ E ))]]) ).
thf(45807,plain,
! [A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ sk19 @ A ) ),
inference(simp,[status(thm)],[45758]) ).
thf(13059,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_realset2 @ k1_xboole_0 )
| ( A != sk293 ) ),
inference(paramod_ordered,[status(thm)],[1284,5134]) ).
thf(13060,plain,
( ~ ( v1_xboole_0 @ sk293 )
| ~ ( v3_realset2 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13059:[bind(A,$thf( sk293 ))]]) ).
thf(1125,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r2_boolealg @ A @ B @ C )
& ( r2_boolealg @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_boolealg) ).
thf(5923,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r2_boolealg @ A @ B @ C )
& ( r2_boolealg @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(1752,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(614,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
<=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_2) ).
thf(3900,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(918,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) )
= ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_lattices) ).
thf(5099,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) )
= ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(253,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_relat_1 @ ( k13_lopclset @ A ) )
= ( u1_struct_0 @ ( k12_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lopclset) ).
thf(2398,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_relat_1 @ ( k13_lopclset @ A ) )
= ( u1_struct_0 @ ( k12_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(783,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_lattice4 @ ( k13_lopclset @ A ) @ A @ ( k12_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_lopclset) ).
thf(4590,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_lattice4 @ ( k13_lopclset @ A ) @ A @ ( k12_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(343,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(2817,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(830,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_rlvect_1) ).
thf(4769,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_rlvect_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1256,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_realset1 @ A )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ( v1_xboole_0 @ B )
| ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ),
inference(cnf,[status(esa)],[1254]) ).
thf(1224,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( m1_subset_1 @ B @ A )
| ( A
!= ( k6_domain_1 @ A @ B ) )
| ( v1_realset1 @ A ) ),
inference(cnf,[status(esa)],[1221]) ).
thf(1226,plain,
! [B: $i,A: $i] :
( ( ( k6_domain_1 @ A @ B )
!= A )
| ( v1_xboole_0 @ A )
| ~ ( m1_subset_1 @ B @ A )
| ( v1_realset1 @ A ) ),
inference(lifteq,[status(thm)],[1224]) ).
thf(375,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_tex_2) ).
thf(2959,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lopclset @ B @ C ) )
<=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lopclset) ).
thf(3213,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_lopclset @ B @ C ) )
=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_lopclset @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_struct_0) ).
thf(4526,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(5546,plain,
v5_ringcat1 @ sk318,
inference(cnf,[status(esa)],[5545]) ).
thf(5567,plain,
~ ( v1_xboole_0 @ k4_modal_1 ),
inference(polarity_switch,[status(thm)],[5566]) ).
thf(6660,plain,
( ( v1_xboole_0 @ k4_modal_1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,5567]) ).
thf(6667,plain,
k4_modal_1 != k1_xboole_0,
inference(simp,[status(thm)],[6660]) ).
thf(666,axiom,
! [A: $i] :
( ( v1_struct_0 @ ( g1_struct_0 @ A ) )
& ( l1_struct_0 @ ( g1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_struct_0) ).
thf(4099,plain,
! [A: $i] :
( ( v1_struct_0 @ ( g1_struct_0 @ A ) )
& ( l1_struct_0 @ ( g1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(974,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
<=> ( m1_filter_2 @ B @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).
thf(5314,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( m2_filter_2 @ B @ A )
=> ( m1_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
& ( ( m1_filter_2 @ B @ ( k1_lattice2 @ A ) )
=> ( m2_filter_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( ? [B: $i] :
( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) )
& ( ( k3_tarski @ A )
= k1_xboole_0 ) )
& ~ ( ( ( k3_tarski @ A )
!= k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_orders_1) ).
thf(1765,plain,
! [A: $i] :
( ~ ( ? [B: $i] :
( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) )
& ( ( k3_tarski @ A )
= k1_xboole_0 ) )
& ~ ( ( ( k3_tarski @ A )
!= k1_xboole_0 )
& ! [B: $i] :
~ ( ( B != k1_xboole_0 )
& ( r2_hidden @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(2279,plain,
v1_funct_1 @ sk89,
inference(cnf,[status(esa)],[2276]) ).
thf(13958,plain,
v1_funct_1 @ k1_xboole_0,
inference(rewrite,[status(thm)],[2279,12908]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(3568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(3170,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(505,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(3532,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(906,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v2_filter_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_filter_0) ).
thf(5033,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v2_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) )
=> ( v2_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(2220,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(635,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ C ) @ D )
= ( k4_filter_0 @ A @ B @ ( k4_filter_0 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_filter_1) ).
thf(3964,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ C ) @ D )
= ( k4_filter_0 @ A @ B @ ( k4_filter_0 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k7_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(4096,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k7_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(2293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1015,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_filter_2 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_filter_2) ).
thf(5471,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_filter_2 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(6312,plain,
( ( v1_xboole_0 @ sk75 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,2140]) ).
thf(6313,plain,
sk75 != k1_xboole_0,
inference(simp,[status(thm)],[6312]) ).
thf(26771,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk75 ) ),
inference(paramod_ordered,[status(thm)],[1518,6313]) ).
thf(26772,plain,
v1_relat_1 @ ( sk27 @ sk75 ),
inference(pattern_uni,[status(thm)],[26771:[bind(A,$thf( sk75 ))]]) ).
thf(1271,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( r2_hidden @ ( sk10 @ B @ A ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
| ( v1_relat_1 @ ( sk11 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1268]) ).
thf(2308,plain,
! [A: $i] : ( m1_subset_1 @ ( sk90 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[2306]) ).
thf(980,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( v1_filter_0 @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_filter_0) ).
thf(5331,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( v1_filter_0 @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k6_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(5282,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k6_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k14_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).
thf(4218,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k14_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(777,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_2) ).
thf(4573,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(474,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_tex_2) ).
thf(3340,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(3594,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_finset_1 @ A )
| ~ ( v1_trees_1 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_finset_1 @ B )
| ~ ( v1_trees_1 @ B )
| ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[1329]) ).
thf(6648,plain,
( ( v3_realset2 @ sk293 )
!= ( v3_realset2 @ sk250 ) ),
inference(paramod_ordered,[status(thm)],[4613,5134]) ).
thf(6649,plain,
sk293 != sk250,
inference(simp,[status(thm)],[6648]) ).
thf(553,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k2_pre_topc @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_pre_topc) ).
thf(3700,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k2_pre_topc @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(657,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_lattices @ A @ C @ D )
& ( r2_lattices @ B @ E @ F ) )
<=> ( r2_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_filter_1) ).
thf(4060,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( r2_lattices @ A @ C @ D )
& ( r2_lattices @ B @ E @ F ) )
=> ( r2_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r2_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
=> ( ( r2_lattices @ A @ C @ D )
& ( r2_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(2457,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(857,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
<=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattice3) ).
thf(4854,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) )
& ( ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
=> ( r3_lattice3 @ A @ B @ ( k2_struct_0 @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1162,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( m2_nat_lat @ ( k23_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k23_filter_2) ).
thf(6123,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( m2_nat_lat @ ( k23_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k31_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G )
& ( v1_xboole_0 @ H ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G )
& ( v1_xboole_0 @ H ) )
& ( v1_xboole_0 @ ( k31_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_gate_1) ).
thf(6248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k31_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G )
& ( v1_xboole_0 @ H ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G )
& ( v1_xboole_0 @ H ) )
& ( v1_xboole_0 @ ( k31_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(935,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ E ) ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_lattice4) ).
thf(5158,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ E ) ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(409,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k5_lattices @ A ) @ B ) @ ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_boolealg) ).
thf(3091,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k5_lattices @ A ) @ B ) @ ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(2467,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[2466]) ).
thf(2469,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( r1_tarski @ A @ B ) ),
inference(cnf,[status(esa)],[2467]) ).
thf(2473,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( r1_tarski @ A @ B ) ),
inference(lifteq,[status(thm)],[2469]) ).
thf(2474,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(simp,[status(thm)],[2473]) ).
thf(867,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r4_wellord1 @ A @ B )
& ( r4_wellord1 @ B @ C ) )
=> ( r4_wellord1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_wellord1) ).
thf(4887,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r4_wellord1 @ A @ B )
& ( r4_wellord1 @ B @ C ) )
=> ( r4_wellord1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_filter_0 @ C @ B )
& ( m1_filter_0 @ D @ B ) )
=> ( ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(5432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_filter_0 @ C @ B )
& ( m1_filter_0 @ D @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) )
=> ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ C )
<=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).
thf(2358,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) )
& ( ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) )
=> ( r1_tarski @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(739,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k9_openlatt @ A ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( B
= ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_openlatt) ).
thf(4433,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( r2_hidden @ B @ ( k9_openlatt @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( B
= ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( B
= ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) )
=> ( r2_hidden @ B @ ( k9_openlatt @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(1038,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tex_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tex_1) ).
thf(5554,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tex_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(5555,plain,
~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tex_1 @ A ) ),
inference(miniscope,[status(thm)],[5554]) ).
thf(5556,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tex_1 @ A ) ),
inference(cnf,[status(esa)],[5555]) ).
thf(277,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_xboole_0 @ ( k7_lopclset @ A ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k7_lattices @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lopclset) ).
thf(2510,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_xboole_0 @ ( k7_lopclset @ A ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k7_lattices @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(2361,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_2 @ ( k3_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_filter_2) ).
thf(4790,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_2 @ ( k3_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(950,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_filter_0 @ B @ A )
<=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_filter_0) ).
thf(5212,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m1_filter_0 @ B @ A )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) )
& ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) )
=> ( m1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(589,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( v3_lattice4 @ C @ A @ B )
<=> ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice4) ).
thf(3815,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( v3_lattice4 @ C @ A @ B )
=> ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) ) )
& ( ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) )
=> ( v3_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(5103,plain,
v3_lattices @ sk291,
inference(cnf,[status(esa)],[5102]) ).
thf(10665,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_tex_1 @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,5556]) ).
thf(10675,plain,
! [A: $i] :
( ( k1_tex_1 @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10665]) ).
thf(1177,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_unialg_2 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_unialg_2) ).
thf(6197,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_unialg_2 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(3732,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1020,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattice3 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
thf(5491,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattice3 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(435,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ C ) @ ( k18_filter_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_filter_2) ).
thf(3197,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ C @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ C ) @ ( k18_filter_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(730,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_filter_0) ).
thf(4388,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(13995,plain,
v1_finset_1 @ k1_xboole_0,
inference(rewrite,[status(thm)],[2939,13144]) ).
thf(240,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_filter_0) ).
thf(2346,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relat_1) ).
thf(2721,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(190,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
<=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_grfunc_1) ).
thf(2119,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) ) )
& ( ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( r1_tarski @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(719,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r2_boolealg @ A @ B @ C )
& ( r3_lattices @ A @ D @ C )
& ( r2_boolealg @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_boolealg) ).
thf(4337,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r2_boolealg @ A @ B @ C )
& ( r3_lattices @ A @ D @ C )
& ( r2_boolealg @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(2678,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(cnf,[status(esa)],[2677]) ).
thf(2679,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[2678]) ).
thf(808,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ B @ D ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ B @ D ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lattices) ).
thf(4704,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ B @ D ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ B @ D ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(694,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v15_lattices @ A )
<=> ( ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_lattices) ).
thf(4228,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v15_lattices @ A )
=> ( ( v13_lattices @ A )
& ( v14_lattices @ A ) ) )
& ( ( ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(284,axiom,
? [A: $i] : ( l2_lang1 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lang1) ).
thf(2538,plain,
? [A: $i] : ( l2_lang1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(26366,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( v3_lattices @ k1_xboole_0 )
| ( A != sk334 ) ),
inference(paramod_ordered,[status(thm)],[1518,6128]) ).
thf(26367,plain,
( ( v1_relat_1 @ ( sk27 @ sk334 ) )
| ( v3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26366:[bind(A,$thf( sk334 ))]]) ).
thf(1025,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ C ) @ ( k5_filter_2 @ A @ B ) ) )
& ( ( r3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ C ) @ ( k5_filter_2 @ A @ B ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
=> ( r3_lattices @ A @ ( k6_filter_2 @ A @ E ) @ ( k6_filter_2 @ A @ D ) ) )
& ( ( r3_lattices @ A @ ( k6_filter_2 @ A @ E ) @ ( k6_filter_2 @ A @ D ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_2) ).
thf(5506,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ C ) @ ( k5_filter_2 @ A @ B ) ) )
& ( ( r3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ C ) @ ( k5_filter_2 @ A @ B ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
=> ( r3_lattices @ A @ ( k6_filter_2 @ A @ E ) @ ( k6_filter_2 @ A @ D ) ) )
& ( ( r3_lattices @ A @ ( k6_filter_2 @ A @ E ) @ ( k6_filter_2 @ A @ D ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(445,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(3238,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(303,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k20_filter_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_filter_2) ).
thf(2624,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k20_filter_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(952,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_nat_lat @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_filter_2) ).
thf(5244,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_nat_lat @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(978,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ ( k1_boolealg @ A @ C @ D ) ) @ ( k1_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) )
& ( r1_boolealg @ A @ ( k4_lattices @ A @ ( k1_boolealg @ A @ C @ D ) @ B ) @ ( k1_boolealg @ A @ ( k4_lattices @ A @ C @ B ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_boolealg) ).
thf(5325,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ ( k1_boolealg @ A @ C @ D ) ) @ ( k1_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) )
& ( r1_boolealg @ A @ ( k4_lattices @ A @ ( k1_boolealg @ A @ C @ D ) @ B ) @ ( k1_boolealg @ A @ ( k4_lattices @ A @ C @ B ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(713,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_filter_0) ).
thf(4305,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(795,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k18_filter_2 @ A @ B )
= ( a_2_0_filter_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_2) ).
thf(4620,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k18_filter_2 @ A @ B )
= ( a_2_0_filter_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1805,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(cnf,[status(esa)],[1804]) ).
thf(1806,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(lifteq,[status(thm)],[1805]) ).
thf(41,axiom,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k16_coh_sp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_coh_sp) ).
thf(1348,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k16_coh_sp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1349,plain,
! [A: $i] : ( r2_hidden @ k1_xboole_0 @ ( k16_coh_sp @ A ) ),
inference(cnf,[status(esa)],[1348]) ).
thf(89,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(1603,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(104,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( A
= ( k3_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_grfunc_1) ).
thf(1722,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( A
= ( k3_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(909,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattice2) ).
thf(5054,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(676,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_filter_0) ).
thf(4139,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) ) )
& ( ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(782,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
<=> ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_filter_1) ).
thf(4586,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
=> ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) ) )
& ( ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) )
=> ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(2116,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1049,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_2 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_2) ).
thf(5610,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_2 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(2856,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(3138,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(1100,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
<=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_lattice2) ).
thf(5795,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(2896,plain,
v1_relat_1 @ sk130,
inference(cnf,[status(esa)],[2893]) ).
thf(38142,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,38135]) ).
thf(38143,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[38142:[bind(A,$thf( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ D )),bind(B,$thf( D ))]]) ).
thf(38254,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ A ) ) ),
inference(simp,[status(thm)],[38143]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(3384,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1135,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_nat_lat @ B @ A ) )
=> ( ( k24_filter_2 @ A @ B )
= ( k1_lattice2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k24_filter_2) ).
thf(5972,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_nat_lat @ B @ A ) )
=> ( ( k24_filter_2 @ A @ B )
= ( k1_lattice2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(832,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_filter_0) ).
thf(4773,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(2871,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1376,plain,
! [A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_finset_1 @ ( k1_relat_1 @ A ) )
| ( v1_finset_1 @ A ) ),
inference(cnf,[status(esa)],[1375]) ).
thf(761,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ D ) @ C ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ D @ C ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_filter_1) ).
thf(4509,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ D ) @ C ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ D @ C ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1305,plain,
( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1303]) ).
thf(1307,plain,
( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1305]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k3_filter_2 @ A @ B )
= ( k3_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
thf(4203,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k3_filter_2 @ A @ B )
= ( k3_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(328,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k5_finsub_1 @ A )
= ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(2742,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k5_finsub_1 @ A )
= ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_tex_2) ).
thf(1339,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(132,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relat_1) ).
thf(1838,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(466,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r1_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_filter_0) ).
thf(3298,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r1_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1013,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(5466,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(48,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_partfun1) ).
thf(1378,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1379,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ( ( k2_xboole_0 @ A @ B )
!= C )
| ~ ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
| ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ),
inference(cnf,[status(esa)],[1378]) ).
thf(1380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k2_xboole_0 @ A @ B )
!= C )
| ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ),
inference(lifteq,[status(thm)],[1379]) ).
thf(1381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ~ ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
| ~ ( v1_funct_1 @ ( k2_xboole_0 @ A @ B ) )
| ~ ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ),
inference(simp,[status(thm)],[1380]) ).
thf(986,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(5367,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1026,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m2_filter_2 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v13_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_2) ).
thf(5511,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m2_filter_2 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v13_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1153,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k1_heyting1 @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_heyting1) ).
thf(6087,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k1_heyting1 @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(342,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r3_lattice4 @ A @ B @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice4) ).
thf(2812,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r3_lattice4 @ A @ B @ C )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) ) )
& ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) )
=> ( r3_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( r2_subset_1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_subset_1) ).
thf(5657,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( r2_subset_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(399,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(3055,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(4100,plain,
( ! [A: $i] : ( v1_struct_0 @ ( g1_struct_0 @ A ) )
& ! [A: $i] : ( l1_struct_0 @ ( g1_struct_0 @ A ) ) ),
inference(miniscope,[status(thm)],[4099]) ).
thf(4101,plain,
! [A: $i] : ( l1_struct_0 @ ( g1_struct_0 @ A ) ),
inference(cnf,[status(esa)],[4100]) ).
thf(4103,plain,
! [A: $i] : ( l1_struct_0 @ ( g1_struct_0 @ A ) ),
inference(simp,[status(thm)],[4101]) ).
thf(542,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ ( k20_filter_2 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k20_filter_2 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_filter_2) ).
thf(3668,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( r1_tarski @ B @ ( k20_filter_2 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k20_filter_2 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(849,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattice2) ).
thf(4833,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(747,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ( v3_realset2 @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( ( u1_struct_0 @ A )
= ( k1_struct_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tex_1) ).
thf(4462,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ( ( v3_realset2 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( ( u1_struct_0 @ A )
= ( k1_struct_0 @ A @ B ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( ( u1_struct_0 @ A )
= ( k1_struct_0 @ A @ B ) ) )
=> ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(2111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(10751,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk113 @ A ) )
!= ( v1_xboole_0 @ ( k10_afinsq_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2712,6233]) ).
thf(10764,plain,
! [B: $i,A: $i] :
( ( sk113 @ A )
!= ( k10_afinsq_1 @ B ) ),
inference(simp,[status(thm)],[10751]) ).
thf(37450,plain,
! [A: $i] :
( ( k10_afinsq_1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10764,13812]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(1993,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(845,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] : ( m1_struct_0 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_struct_0) ).
thf(4818,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ? [C: $i] : ( m1_struct_0 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(817,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boolealg) ).
thf(4731,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ~ ( ( ( k7_lopclset @ B )
= ( k3_tarski @ A ) )
& ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k10_lopclset @ B ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ( ( k7_lopclset @ B )
!= ( k3_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lopclset) ).
thf(4028,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ~ ( ( ( k7_lopclset @ B )
= ( k3_tarski @ A ) )
& ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k10_lopclset @ B ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ( ( k7_lopclset @ B )
!= ( k3_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( r2_hidden @ k1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_card_fil) ).
thf(1731,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( r2_hidden @ k1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(6860,plain,
( ( v1_xboole_0 @ sk338 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,6207]) ).
thf(6871,plain,
sk338 != k1_xboole_0,
inference(simp,[status(thm)],[6860]) ).
thf(26943,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk338 ) ),
inference(paramod_ordered,[status(thm)],[1518,6871]) ).
thf(26944,plain,
v1_relat_1 @ ( sk27 @ sk338 ),
inference(pattern_uni,[status(thm)],[26943:[bind(A,$thf( sk338 ))]]) ).
thf(146,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relat_1) ).
thf(1909,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(26041,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk19 ) ),
inference(paramod_ordered,[status(thm)],[1518,6291]) ).
thf(26042,plain,
v1_relat_1 @ ( sk27 @ sk19 ),
inference(pattern_uni,[status(thm)],[26041:[bind(A,$thf( sk19 ))]]) ).
thf(891,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ~ ( v1_xboole_0 @ ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_filter_2) ).
thf(4985,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ~ ( v1_xboole_0 @ ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(744,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_lattices) ).
thf(4452,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(1045,axiom,
? [A: $i] :
( ( l2_quantal1 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_quantal1) ).
thf(5599,plain,
? [A: $i] :
( ( l2_quantal1 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(45648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk133 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1396,15278]) ).
thf(45649,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ sk133 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[45648:[bind(A,$thf( sk133 )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( k4_xboole_0 @ sk133 @ F ))]]) ).
thf(45820,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ sk133 @ B ) @ A ) ),
inference(simp,[status(thm)],[45649]) ).
thf(638,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_filter_1 @ A @ ( k12_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lopclset) ).
thf(3971,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_filter_1 @ A @ ( k12_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(1343,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_relat_1 @ A )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ B )
!= k1_xboole_0 )
| ( A = B ) ),
inference(cnf,[status(esa)],[1342]) ).
thf(1344,plain,
! [B: $i,A: $i] :
( ( ( k1_relat_1 @ A )
!= k1_xboole_0 )
| ( ( k1_relat_1 @ B )
!= k1_xboole_0 )
| ( A = B )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B ) ),
inference(lifteq,[status(thm)],[1343]) ).
thf(286,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k6_lattices @ A )
= ( k5_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_lattice2) ).
thf(2542,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k6_lattices @ A )
= ( k5_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(1460,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( A != C ) )
=> ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(2252,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(602,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_filter_0) ).
thf(3861,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1292,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_relat_1 @ B )
| ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ),
inference(cnf,[status(esa)],[1291]) ).
thf(1293,plain,
! [B: $i,A: $i] :
( ( ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) )
= ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_relat_1 @ B ) ),
inference(lifteq,[status(thm)],[1292]) ).
thf(897,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_lattice4 @ ( k16_openlatt @ A ) @ A @ ( k15_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_openlatt) ).
thf(5007,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_lattice4 @ ( k16_openlatt @ A ) @ A @ ( k15_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1094,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( r2_zfrefle1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_zfrefle1) ).
thf(5780,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( r2_zfrefle1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1084,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( k3_filter_0 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_0) ).
thf(5742,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( k3_filter_0 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(695,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v14_lattices @ A )
=> ( v14_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_filter_0) ).
thf(4232,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v14_lattices @ A )
=> ( v14_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(26430,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk336 ) ),
inference(paramod_ordered,[status(thm)],[1518,6859]) ).
thf(26431,plain,
v1_relat_1 @ ( sk27 @ sk336 ),
inference(pattern_uni,[status(thm)],[26430:[bind(A,$thf( sk336 ))]]) ).
thf(7531,plain,
! [A: $i] :
( ( ( k6_domain_1 @ A @ ( sk5 @ A ) )
= A )
| ( v1_xboole_0 @ A )
| ( ( v1_realset1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( v1_realset1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7442,1225]) ).
thf(7532,plain,
( ( ( k6_domain_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
= ( k1_zfmisc_1 @ k1_xboole_0 ) )
| ( v1_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) ),
inference(pattern_uni,[status(thm)],[7531:[bind(A,$thf( k1_zfmisc_1 @ k1_xboole_0 ))]]) ).
thf(22066,plain,
( ( ( k6_domain_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
= ( k1_zfmisc_1 @ k1_xboole_0 ) )
| $false ),
inference(rewrite,[status(thm)],[7532,4239]) ).
thf(22067,plain,
( ( k6_domain_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( sk5 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ) )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(simp,[status(thm)],[22066]) ).
thf(283,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_grfunc_1) ).
thf(2535,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_boolealg @ A @ B @ C )
=> ( r3_boolealg @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r3_boolealg) ).
thf(4720,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_boolealg @ A @ B @ C )
=> ( r3_boolealg @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(325,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ ( k1_boolealg @ A @ C @ D ) ) @ ( k1_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_boolealg) ).
thf(2725,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ ( k1_boolealg @ A @ C @ D ) ) @ ( k1_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(254,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_pre_topc) ).
thf(2401,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1213,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( sk3 @ A )
| ~ ( v1_xboole_0 @ ( k3_tarski @ A ) ) ),
inference(cnf,[status(esa)],[1209]) ).
thf(1370,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(cnf,[status(esa)],[1369]) ).
thf(37698,plain,
! [B: $i,A: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(rewrite,[status(thm)],[1370,1201]) ).
thf(574,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k10_openlatt @ A @ B ) @ ( k10_openlatt @ A @ C ) ) )
=> ( ( m1_filter_0 @ D @ A )
& ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_openlatt) ).
thf(3759,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k10_openlatt @ A @ B ) @ ( k10_openlatt @ A @ C ) ) )
=> ( ( m1_filter_0 @ D @ A )
& ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(597,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( ( r2_boolealg @ A @ B @ C )
& ( r2_boolealg @ A @ B @ D ) )
& ( r2_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_boolealg) ).
thf(3838,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( ( r2_boolealg @ A @ B @ C )
& ( r2_boolealg @ A @ B @ D ) )
& ( r2_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(2620,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(1060,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
<=> ? [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
& ( v3_lattice4 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_lattice4) ).
thf(5641,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r1_filter_1 @ A @ B )
=> ? [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
& ( v3_lattice4 @ C @ A @ B ) ) )
& ( ? [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
& ( v3_lattice4 @ C @ A @ B ) )
=> ( r1_filter_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(6959,plain,
! [A: $i] :
( ( ( k6_domain_1 @ A @ ( sk5 @ A ) )
= A )
| ( v1_xboole_0 @ A )
| ( ( v1_realset1 @ sk72 )
!= ( v1_realset1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2114,1225]) ).
thf(6960,plain,
( ( ( k6_domain_1 @ sk72 @ ( sk5 @ sk72 ) )
= sk72 )
| ( v1_xboole_0 @ sk72 ) ),
inference(pattern_uni,[status(thm)],[6959:[bind(A,$thf( sk72 ))]]) ).
thf(10781,plain,
( ( ( k6_domain_1 @ sk72 @ ( sk5 @ sk72 ) )
= sk72 )
| $false ),
inference(rewrite,[status(thm)],[6960,2115]) ).
thf(10782,plain,
( ( k6_domain_1 @ sk72 @ ( sk5 @ sk72 ) )
= sk72 ),
inference(simp,[status(thm)],[10781]) ).
thf(6280,plain,
( ( v1_xboole_0 @ sk44 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,1735]) ).
thf(6288,plain,
sk44 != k1_xboole_0,
inference(simp,[status(thm)],[6280]) ).
thf(618,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(3917,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1028,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v14_lattices @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_filter_0) ).
thf(5516,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v14_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(633,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) @ ( k5_filter_2 @ A @ C ) ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) @ ( k5_filter_2 @ A @ C ) ) )
& ( ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E )
= ( k3_lattices @ A @ ( k6_filter_2 @ A @ D ) @ ( k6_filter_2 @ A @ E ) ) )
& ( ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
= ( k4_lattices @ A @ ( k6_filter_2 @ A @ D ) @ ( k6_filter_2 @ A @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_filter_2) ).
thf(3953,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) @ ( k5_filter_2 @ A @ C ) ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) @ ( k5_filter_2 @ A @ C ) ) )
& ( ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E )
= ( k3_lattices @ A @ ( k6_filter_2 @ A @ D ) @ ( k6_filter_2 @ A @ E ) ) )
& ( ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
= ( k4_lattices @ A @ ( k6_filter_2 @ A @ D ) @ ( k6_filter_2 @ A @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k8_rlvect_2 @ A @ B @ C )
= ( k8_rlvect_2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k8_rlvect_2) ).
thf(4918,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k8_rlvect_2 @ A @ B @ C )
= ( k8_rlvect_2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).
thf(1364,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(2390,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(72,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tex_2) ).
thf(1496,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(969,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r4_wellord1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_wellord1) ).
thf(5299,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r4_wellord1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1143,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k7_real_lat @ A ) )
& ( v3_lattices @ ( k7_real_lat @ A ) )
& ( v10_lattices @ ( k7_real_lat @ A ) )
& ( l3_lattices @ ( k7_real_lat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_real_lat) ).
thf(6027,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k7_real_lat @ A ) )
& ( v3_lattices @ ( k7_real_lat @ A ) )
& ( v10_lattices @ ( k7_real_lat @ A ) )
& ( l3_lattices @ ( k7_real_lat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(26157,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( v12_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1518,14500]) ).
thf(26158,plain,
( ( v1_relat_1 @ ( sk27 @ sk1 ) )
| ( v12_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26157:[bind(A,$thf( sk1 ))]]) ).
thf(658,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lattice2) ).
thf(4067,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r6_binop_1 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(43234,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( k2_xboole_0 @ ( k1_tarski @ B ) @ A ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,38119]) ).
thf(43284,plain,
! [B: $i,A: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[43234]) ).
thf(40494,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk72 )
| ( ( r2_hidden @ A @ ( k1_tarski @ A ) )
!= ( r2_hidden @ sk2 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[3667,40469]) ).
thf(40575,plain,
! [A: $i] :
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk72 )
| ( A != sk2 )
| ( ( k1_tarski @ A )
!= sk72 ) ),
inference(simp,[status(thm)],[40494]) ).
thf(40603,plain,
( ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk72 )
| ( ( k1_tarski @ sk2 )
!= sk72 ) ),
inference(simp,[status(thm)],[40575]) ).
thf(615,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boolealg) ).
thf(3908,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(317,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
& ( C = D ) )
=> ( ( ( k3_filter_2 @ A @ C )
= ( k3_filter_2 @ B @ D ) )
& ( ( k19_filter_2 @ A @ C )
= ( k19_filter_2 @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l48_filter_2) ).
thf(2693,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
& ( C = D ) )
=> ( ( ( k3_filter_2 @ A @ C )
= ( k3_filter_2 @ B @ D ) )
& ( ( k19_filter_2 @ A @ C )
= ( k19_filter_2 @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(687,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_filter_1 @ A @ ( k15_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_openlatt) ).
thf(4209,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_filter_1 @ A @ ( k15_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(161,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_relat_1 @ ( k8_lopclset @ A ) )
& ( v1_funct_1 @ ( k8_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_lopclset) ).
thf(1973,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_relat_1 @ ( k8_lopclset @ A ) )
& ( v1_funct_1 @ ( k8_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(751,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( v2_lang1 @ ( k13_lang1 @ A ) )
& ( l2_lang1 @ ( k13_lang1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_lang1) ).
thf(4481,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( v2_lang1 @ ( k13_lang1 @ A ) )
& ( l2_lang1 @ ( k13_lang1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(1530,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1529]) ).
thf(1531,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1530]) ).
thf(17809,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[1531,1201]) ).
thf(1053,axiom,
! [A: $i] :
( ~ ( v2_setfam_1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(5619,plain,
! [A: $i] :
( ~ ( v2_setfam_1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(661,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
= ( k6_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( ( k4_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
= ( k6_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_1) ).
thf(4084,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
= ( k6_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( ( k4_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
= ( k6_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1413,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( v1_funct_1 @ ( k4_xboole_0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1411]) ).
thf(1036,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
<=> ( r4_wellord1 @ ( k9_filter_1 @ A ) @ ( k9_filter_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_1) ).
thf(5548,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r1_filter_1 @ A @ B )
=> ( r4_wellord1 @ ( k9_filter_1 @ A ) @ ( k9_filter_1 @ B ) ) )
& ( ( r4_wellord1 @ ( k9_filter_1 @ A ) @ ( k9_filter_1 @ B ) )
=> ( r1_filter_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(1088,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k17_filter_2 @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_2) ).
thf(5757,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k17_filter_2 @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(423,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(3146,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(712,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ~ ( ( r2_filter_2 @ A @ D )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_filter_2) ).
thf(4292,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ~ ( ( r2_filter_2 @ A @ D )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(366,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( v14_lattices @ A )
& ( B
!= ( k6_lattices @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( r2_filter_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_filter_2) ).
thf(2927,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ( v14_lattices @ A )
& ( B
!= ( k6_lattices @ A ) )
& ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( r2_filter_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1090,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ~ ( v3_struct_0 @ ( k14_lattice3 @ A ) )
& ( v3_lattices @ ( k14_lattice3 @ A ) )
& ( v10_lattices @ ( k14_lattice3 @ A ) )
& ( l3_lattices @ ( k14_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_lattice3) ).
thf(5763,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ( ~ ( v3_struct_0 @ ( k14_lattice3 @ A ) )
& ( v3_lattices @ ( k14_lattice3 @ A ) )
& ( v10_lattices @ ( k14_lattice3 @ A ) )
& ( l3_lattices @ ( k14_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_subset_1) ).
thf(2899,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(3571,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A )
& ( m2_filter_2 @ C @ A ) )
=> ( ( k21_filter_2 @ A @ B @ C )
= ( k20_filter_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k21_filter_2) ).
thf(3849,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A )
& ( m2_filter_2 @ C @ A ) )
=> ( ( k21_filter_2 @ A @ B @ C )
= ( k20_filter_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(501,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k7_lattices @ A @ ( k3_boolealg @ A @ B @ C ) ) @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_boolealg) ).
thf(3522,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k7_lattices @ A @ ( k3_boolealg @ A @ B @ C ) ) @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(387,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( v1_filter_0 @ C @ A )
& ~ ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
& ( r2_hidden @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_lopclset) ).
thf(3009,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( v1_filter_0 @ C @ A )
& ~ ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
& ( r2_hidden @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(732,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k4_lattices @ A @ B @ C ) ) @ ( k1_boolealg @ A @ B @ C ) )
& ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k4_lattices @ A @ C @ B ) ) @ ( k1_boolealg @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_boolealg) ).
thf(4394,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k4_lattices @ A @ B @ C ) ) @ ( k1_boolealg @ A @ B @ C ) )
& ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k4_lattices @ A @ C @ B ) ) @ ( k1_boolealg @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(740,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
thf(4441,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(2096,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( C
= ( k2_xboole_0 @ B @ D ) ) )
=> ( ( k1_funct_1 @ C @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_grfunc_1) ).
thf(1758,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( C
= ( k2_xboole_0 @ B @ D ) ) )
=> ( ( k1_funct_1 @ C @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(872,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( v1_funcsdom @ ( k13_funcsdom @ A ) )
& ( l1_funcsdom @ ( k13_funcsdom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_funcsdom) ).
thf(4901,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( v1_funcsdom @ ( k13_funcsdom @ A ) )
& ( l1_funcsdom @ ( k13_funcsdom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1203,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_trees_1 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_finset_1 @ B )
| ~ ( v1_trees_1 @ B )
| ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[1202]) ).
thf(1117,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k16_gate_1 @ A @ B @ C @ D ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
& ( v1_xboole_0 @ ( k16_gate_1 @ A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_gate_1) ).
thf(5881,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k16_gate_1 @ A @ B @ C @ D ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D ) )
& ( v1_xboole_0 @ ( k16_gate_1 @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(1191,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( k17_filter_2 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_filter_2) ).
thf(6276,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( k17_filter_2 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(1182,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ ( k12_filter_2 @ A @ B ) )
& ( m2_lattice4 @ ( k12_filter_2 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_filter_2) ).
thf(6225,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ ( k12_filter_2 @ A @ B ) )
& ( m2_lattice4 @ ( k12_filter_2 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(2271,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(10707,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk113 @ A ) )
!= ( v1_xboole_0 @ ( k16_coh_sp @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2712,5787]) ).
thf(10723,plain,
! [B: $i,A: $i] :
( ( sk113 @ A )
!= ( k16_coh_sp @ B ) ),
inference(simp,[status(thm)],[10707]) ).
thf(35476,plain,
! [A: $i] :
( ( k16_coh_sp @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10723,13812]) ).
thf(787,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( k3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) @ ( k3_lattices @ B @ E @ F ) ) )
& ( ( k4_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) @ ( k4_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_filter_1) ).
thf(4598,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( k3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) @ ( k3_lattices @ B @ E @ F ) ) )
& ( ( k4_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) @ ( k4_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(427,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(3161,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(819,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ C @ B )
= B ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_rlsub_2) ).
thf(4735,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ C @ B )
= B ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_funct_1 @ A @ ( sk10 @ B @ A ) )
!= ( k1_funct_1 @ B @ ( sk10 @ B @ A ) ) )
| ( v1_funct_1 @ ( sk11 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1268]) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( ( k1_funct_1 @ A @ ( sk10 @ B @ A ) )
!= ( k1_funct_1 @ B @ ( sk10 @ B @ A ) ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( v1_funct_1 @ ( sk11 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[1270]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k11_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_filter_2) ).
thf(6191,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k11_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(775,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
<=> ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_lattices) ).
thf(4566,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
=> ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(859,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_filter_0 @ A @ D ) @ B ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ E @ B )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ E ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice4) ).
thf(4859,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_filter_0 @ A @ D ) @ B ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ E @ B )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ E ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(204,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(2202,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(2846,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
<=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( D = A )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_lopclset) ).
thf(2256,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( D = A )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( D = A )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_nat_lat @ B @ A ) )
=> ( ( v3_lattices @ ( k24_filter_2 @ A @ B ) )
& ( m2_nat_lat @ ( k24_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k24_filter_2) ).
thf(4581,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_nat_lat @ B @ A ) )
=> ( ( v3_lattices @ ( k24_filter_2 @ A @ B ) )
& ( m2_nat_lat @ ( k24_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(26053,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k15_coh_sp @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,15229]) ).
thf(26054,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k15_coh_sp @ A ) ) ),
inference(pattern_uni,[status(thm)],[26053:[bind(A,$thf( k15_coh_sp @ C )),bind(B,$thf( C ))]]) ).
thf(27189,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k15_coh_sp @ A ) ) ),
inference(simp,[status(thm)],[26054]) ).
thf(5710,plain,
v10_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[5707]) ).
thf(814,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc8_tex_2) ).
thf(4722,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).
thf(2942,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(10592,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
!= ( v1_xboole_0 @ sk135 ) ),
inference(paramod_ordered,[status(thm)],[2941,4239]) ).
thf(10604,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= sk135 ),
inference(simp,[status(thm)],[10592]) ).
thf(14289,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10604,13144]) ).
thf(26941,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,14289]) ).
thf(26942,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_zfmisc_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26941:[bind(A,$thf( k1_zfmisc_1 @ C )),bind(B,$thf( C ))]]) ).
thf(27152,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_zfmisc_1 @ A ) ) ),
inference(simp,[status(thm)],[26942]) ).
thf(25945,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk250 ) ),
inference(paramod_ordered,[status(thm)],[1518,4614]) ).
thf(25946,plain,
( ( v1_relat_1 @ ( sk27 @ sk250 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[25945:[bind(A,$thf( sk250 ))]]) ).
thf(6396,plain,
( ( v1_finset_1 @ sk139 )
!= ( v1_finset_1 @ sk133 ) ),
inference(paramod_ordered,[status(thm)],[2925,2992]) ).
thf(6399,plain,
sk139 != sk133,
inference(simp,[status(thm)],[6396]) ).
thf(992,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) @ B )
=> ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_boolealg) ).
thf(5388,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) @ B )
=> ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(631,axiom,
? [A: $i] : ( l1_funcsdom @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_funcsdom) ).
thf(3949,plain,
? [A: $i] : ( l1_funcsdom @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(2713,plain,
! [A: $i] : ( m1_subset_1 @ ( sk113 @ A ) @ ( k5_finsub_1 @ A ) ),
inference(cnf,[status(esa)],[2710]) ).
thf(39851,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k5_finsub_1 @ A ) ),
inference(rewrite,[status(thm)],[2713,13812]) ).
thf(798,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( C
= ( k19_filter_2 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_filter_2) ).
thf(4630,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m2_filter_2 @ C @ A )
=> ( ( ( C
= ( k19_filter_2 @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m2_filter_2 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) )
=> ( C
= ( k19_filter_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1098,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
thf(5790,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(1007,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_lattice2 @ A )
<=> ( ( v3_filter_0 @ A )
& ( v13_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lattice2) ).
thf(5446,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v1_lattice2 @ A )
=> ( ( v3_filter_0 @ A )
& ( v13_lattices @ A ) ) )
& ( ( ( v3_filter_0 @ A )
& ( v13_lattices @ A ) )
=> ( v1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(642,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ ( k4_lattices @ A @ B @ C ) ) @ ( k3_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_boolealg) ).
thf(3988,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ ( k3_boolealg @ A @ B @ C ) @ ( k4_lattices @ A @ B @ C ) ) @ ( k3_lattices @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(2513,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(567,axiom,
! [A: $i] :
( ~ ( v1_finset_1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_card_5) ).
thf(3737,plain,
! [A: $i] :
( ~ ( v1_finset_1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(483,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) )
& ( r2_hidden @ E @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ C @ E ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ E ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_filter_1) ).
thf(3376,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) )
& ( r2_hidden @ E @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ C @ E ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ E ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(1161,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A ) )
=> ( ( k15_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
thf(6120,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ A ) )
=> ( ( k15_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(3640,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(10663,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk113 @ A ) )
!= ( v1_xboole_0 @ ( k1_tex_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2712,5556]) ).
thf(10681,plain,
! [B: $i,A: $i] :
( ( sk113 @ A )
!= ( k1_tex_1 @ B ) ),
inference(simp,[status(thm)],[10663]) ).
thf(33617,plain,
! [A: $i] :
( ( k1_tex_1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10681,13812]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k10_filter_2 @ A @ B ) )
& ( m2_lattice4 @ ( k10_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_2) ).
thf(5607,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k10_filter_2 @ A @ B ) )
& ( m2_lattice4 @ ( k10_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(159,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(1961,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(45767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k4_xboole_0 @ sk149 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,15123]) ).
thf(45768,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k4_xboole_0 @ sk149 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[45767:[bind(A,$thf( k4_xboole_0 @ sk149 @ J )),bind(B,$thf( H )),bind(C,$thf( k4_xboole_0 @ ( k4_xboole_0 @ sk149 @ J ) @ H )),bind(D,$thf( J ))]]) ).
thf(45812,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k4_xboole_0 @ sk149 @ B ) @ A ) ),
inference(simp,[status(thm)],[45768]) ).
thf(1046,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k12_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_filter_2) ).
thf(5602,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k12_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(309,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k7_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k7_lattices @ A @ B ) )
& ( ( k7_lattices @ A @ ( k6_filter_2 @ A @ C ) )
= ( k7_lattices @ ( k1_lattice2 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_filter_2) ).
thf(2661,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( k7_lattices @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k7_lattices @ A @ B ) )
& ( ( k7_lattices @ A @ ( k6_filter_2 @ A @ C ) )
= ( k7_lattices @ ( k1_lattice2 @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( v1_xboole_0 @ ( k21_gate_1 @ A @ B @ C @ D @ E ) )
<=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_gate_1) ).
thf(6051,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ ( k21_gate_1 @ A @ B @ C @ D @ E ) )
=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E ) ) )
& ( ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E ) )
=> ~ ( v1_xboole_0 @ ( k21_gate_1 @ A @ B @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1018,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ( v3_realset2 @ A )
<=> ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_group_6) ).
thf(5478,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ( ( v3_realset2 @ A )
=> ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) ) )
& ( ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) )
=> ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(997,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) )
= ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattices) ).
thf(5399,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) )
= ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( B
= ( k2_xboole_0 @ C @ D ) )
& ( ( k1_funct_1 @ B @ A )
!= ( k1_funct_1 @ C @ A ) )
& ( ( k1_funct_1 @ B @ A )
!= ( k1_funct_1 @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_grfunc_1) ).
thf(2143,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ( B
= ( k2_xboole_0 @ C @ D ) )
& ( ( k1_funct_1 @ B @ A )
!= ( k1_funct_1 @ C @ A ) )
& ( ( k1_funct_1 @ B @ A )
!= ( k1_funct_1 @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(173,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ( ( k6_lattices @ A )
= ( k15_lattice3 @ A @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_lattice3) ).
thf(2012,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ( ( k6_lattices @ A )
= ( k15_lattice3 @ A @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(293,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( r2_filter_2 @ A @ B )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_filter_2) ).
thf(2588,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( r2_filter_2 @ A @ B )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) )
=> ( r2_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(5499,plain,
v1_struct_0 @ sk316,
inference(cnf,[status(esa)],[5496]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_boolealg @ A @ B @ C )
= ( k2_boolealg @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_boolealg) ).
thf(3754,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_boolealg @ A @ B @ C )
= ( k2_boolealg @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(883,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(4950,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(327,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattice4) ).
thf(2732,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) )
=> ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(155,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(1940,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1941,plain,
v1_relat_1 @ k1_xboole_0,
inference(cnf,[status(esa)],[1940]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(1252,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(5074,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(1366,plain,
! [B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ( B = k1_xboole_0 )
| ( m1_subset_1 @ ( sk15 @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[1364]) ).
thf(1368,plain,
! [B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ( m1_subset_1 @ ( sk15 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[1366]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_filter_1) ).
thf(4517,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(3228,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(1081,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k15_gate_1 @ A @ B @ C @ D ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D ) )
& ( v1_xboole_0 @ ( k15_gate_1 @ A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_gate_1) ).
thf(5721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k15_gate_1 @ A @ B @ C @ D ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D ) )
& ( v1_xboole_0 @ ( k15_gate_1 @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(4961,plain,
l1_funcsdom @ sk280,
inference(cnf,[status(esa)],[4959]) ).
thf(581,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_xboole_0 @ B )
=> ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tex_2) ).
thf(3786,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_xboole_0 @ B )
=> ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1266,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(miniscope,[status(thm)],[1265]) ).
thf(1267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ A @ B )
| ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[1266]) ).
thf(605,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
& ( ( u2_lattices @ A )
= ( u1_lattices @ ( k1_lattice2 @ A ) ) )
& ( ( u1_lattices @ A )
= ( u2_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_lattice2) ).
thf(3872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
& ( ( u2_lattices @ A )
= ( u1_lattices @ ( k1_lattice2 @ A ) ) )
& ( ( u1_lattices @ A )
= ( u2_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(727,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k23_filter_2 @ A @ ( k17_filter_2 @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) )
& ( ( k23_filter_2 @ A @ ( k1_filter_2 @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_filter_2) ).
thf(4377,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k23_filter_2 @ A @ ( k17_filter_2 @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) )
& ( ( k23_filter_2 @ A @ ( k1_filter_2 @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(528,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_boolealg @ A @ B @ C )
= ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_boolealg) ).
thf(3608,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_boolealg @ A @ B @ C )
= ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1230,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_realset1 @ A )
| ( v1_realset1 @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[1227]) ).
thf(44795,plain,
! [B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ ( k4_xboole_0 @ sk133 @ B ) @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[15278,2992]) ).
thf(44831,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ sk133 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[44795]) ).
thf(7254,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
| ( ( v1_funct_1 @ ( k8_lopclset @ sk1 ) )
!= ( v1_funct_1 @ sk149 ) ) ),
inference(paramod_ordered,[status(thm)],[3121,7250]) ).
thf(7286,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ( v3_realset2 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ~ ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
| ( ( k8_lopclset @ sk1 )
!= sk149 ) ),
inference(simp,[status(thm)],[7254]) ).
thf(7549,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ( v3_realset2 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( ( k8_lopclset @ sk1 )
!= sk149 )
| ( ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
!= ( v1_relat_1 @ sk149 ) ) ),
inference(paramod_ordered,[status(thm)],[3122,7286]) ).
thf(7575,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ( v3_realset2 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( ( k8_lopclset @ sk1 )
!= sk149 )
| ( ( k8_lopclset @ sk1 )
!= sk149 ) ),
inference(simp,[status(thm)],[7549]) ).
thf(7586,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ( v3_realset2 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ( ( k8_lopclset @ sk1 )
!= sk149 ) ),
inference(simp,[status(thm)],[7575]) ).
thf(4593,plain,
l1_struct_0 @ sk249,
inference(cnf,[status(esa)],[4592]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
& ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_realset1) ).
thf(2888,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
& ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(10024,plain,
( ( v1_finset_1 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[9822,2992]) ).
thf(10027,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk139 ),
inference(simp,[status(thm)],[10024]) ).
thf(10696,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk213 @ A ) )
!= ( v1_xboole_0 @ ( k1_heyting1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4092,5633]) ).
thf(10701,plain,
! [B: $i,A: $i] :
( ( sk213 @ A )
!= ( k1_heyting1 @ B ) ),
inference(simp,[status(thm)],[10696]) ).
thf(33649,plain,
! [A: $i] :
( ( k1_heyting1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10701,13755]) ).
thf(699,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_realset2 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_realset2) ).
thf(4240,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v3_realset2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B = C ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B = C ) ) )
=> ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(561,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(3722,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(510,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(3552,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(3554,plain,
v1_relat_1 @ sk179,
inference(cnf,[status(esa)],[3552]) ).
thf(6283,plain,
( ( v1_xboole_0 @ sk60 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,2023]) ).
thf(6290,plain,
sk60 != k1_xboole_0,
inference(simp,[status(thm)],[6283]) ).
thf(26935,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk60 ) ),
inference(paramod_ordered,[status(thm)],[1518,6290]) ).
thf(26936,plain,
v1_relat_1 @ ( sk27 @ sk60 ),
inference(pattern_uni,[status(thm)],[26935:[bind(A,$thf( sk60 ))]]) ).
thf(1261,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ! [C: $i] : ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(miniscope,[status(thm)],[1260]) ).
thf(1262,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ A @ B )
| ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(cnf,[status(esa)],[1261]) ).
thf(13171,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v2_setfam_1 @ k1_xboole_0 )
| ( A != sk235 ) ),
inference(paramod_ordered,[status(thm)],[1284,4341]) ).
thf(13172,plain,
( ~ ( v1_xboole_0 @ sk235 )
| ~ ( v2_setfam_1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13171:[bind(A,$thf( sk235 ))]]) ).
thf(101,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).
thf(1711,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(3019,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(493,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v16_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattices @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d19_lattices) ).
thf(3448,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v16_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattices @ A @ C @ B ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattices @ A @ C @ B ) ) )
=> ( v16_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(716,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( ( ( k20_filter_2 @ A @ B @ C )
= ( k5_filter_0 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) @ ( k7_filter_2 @ A @ C ) ) )
& ( ( k20_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) @ ( k7_filter_2 @ A @ C ) )
= ( k5_filter_0 @ A @ B @ C ) )
& ( ( k20_filter_2 @ ( k1_lattice2 @ A ) @ D @ E )
= ( k5_filter_0 @ A @ ( k8_filter_2 @ A @ D ) @ ( k8_filter_2 @ A @ E ) ) )
& ( ( k20_filter_2 @ A @ ( k8_filter_2 @ A @ D ) @ ( k8_filter_2 @ A @ E ) )
= ( k5_filter_0 @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_filter_2) ).
thf(4314,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) ) ) )
=> ( ( ( k20_filter_2 @ A @ B @ C )
= ( k5_filter_0 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) @ ( k7_filter_2 @ A @ C ) ) )
& ( ( k20_filter_2 @ ( k1_lattice2 @ A ) @ ( k7_filter_2 @ A @ B ) @ ( k7_filter_2 @ A @ C ) )
= ( k5_filter_0 @ A @ B @ C ) )
& ( ( k20_filter_2 @ ( k1_lattice2 @ A ) @ D @ E )
= ( k5_filter_0 @ A @ ( k8_filter_2 @ A @ D ) @ ( k8_filter_2 @ A @ E ) ) )
& ( ( k20_filter_2 @ A @ ( k8_filter_2 @ A @ D ) @ ( k8_filter_2 @ A @ E ) )
= ( k5_filter_0 @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(958,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_filter_2 @ C @ A )
=> ! [D: $i] :
( ( m1_filter_2 @ D @ B )
=> ( ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
& ( C = D ) )
=> ( ( k8_filter_0 @ A @ C )
= ( k8_filter_0 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_filter_2) ).
thf(5262,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_filter_2 @ C @ A )
=> ! [D: $i] :
( ( m1_filter_2 @ D @ B )
=> ( ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
& ( C = D ) )
=> ( ( k8_filter_0 @ A @ C )
= ( k8_filter_0 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(165,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_realset1) ).
thf(1987,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(262,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v6_group_1 @ A )
<=> ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_group_1) ).
thf(2454,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( u1_struct_0 @ A ) ) )
& ( ( v1_finset_1 @ ( u1_struct_0 @ A ) )
=> ( v6_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( v1_realset1 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( D
= ( k4_subset_1 @ A @ B @ C ) )
& ~ ( ( B = D )
& ( C = D ) )
& ~ ( ( B = D )
& ( C = k1_xboole_0 ) )
& ~ ( ( B = k1_xboole_0 )
& ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_rpr_1) ).
thf(1432,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( v1_realset1 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( D
= ( k4_subset_1 @ A @ B @ C ) )
& ~ ( ( B = D )
& ( C = D ) )
& ~ ( ( B = D )
& ( C = k1_xboole_0 ) )
& ~ ( ( B = k1_xboole_0 )
& ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(682,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( u1_struct_0 @ ( k15_openlatt @ A ) )
= ( k9_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_openlatt) ).
thf(4190,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( u1_struct_0 @ ( k15_openlatt @ A ) )
= ( k9_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k9_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(3885,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k9_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(128,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( v1_realset1 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( D
= ( k4_subset_1 @ A @ B @ C ) )
& ( B != C )
& ~ ( ( B = k1_xboole_0 )
& ( C = D ) )
& ~ ( ( B = D )
& ( C = k1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_rpr_1) ).
thf(1813,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( v1_realset1 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( D
= ( k4_subset_1 @ A @ B @ C ) )
& ( B != C )
& ~ ( ( B = k1_xboole_0 )
& ( C = D ) )
& ~ ( ( B = D )
& ( C = k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1297,plain,
! [A: $i] :
( ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ~ ( l3_lattices @ A )
| ( ( k5_lattices @ A )
= ( k15_lattice3 @ A @ k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1294]) ).
thf(1300,plain,
! [A: $i] :
( ( ( k15_lattice3 @ A @ k1_xboole_0 )
= ( k5_lattices @ A ) )
| ( v3_struct_0 @ A )
| ~ ( v10_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ~ ( l3_lattices @ A ) ),
inference(lifteq,[status(thm)],[1297]) ).
thf(315,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_grcat_1 @ A ) )
=> ? [B: $i] : ( m3_grcat_1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_grcat_1) ).
thf(2688,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_grcat_1 @ A ) )
=> ? [B: $i] : ( m3_grcat_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(472,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k19_filter_2 @ A @ C ) @ ( k19_filter_2 @ A @ D ) ) )
& ( r1_tarski @ ( k19_filter_2 @ A @ ( k19_filter_2 @ A @ B ) ) @ ( k19_filter_2 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_2) ).
thf(3334,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k19_filter_2 @ A @ C ) @ ( k19_filter_2 @ A @ D ) ) )
& ( r1_tarski @ ( k19_filter_2 @ A @ ( k19_filter_2 @ A @ B ) ) @ ( k19_filter_2 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(45728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ A @ B )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k4_xboole_0 @ sk133 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,44831]) ).
thf(45729,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ ( k4_xboole_0 @ sk133 @ B ) @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45728:[bind(A,$thf( k4_xboole_0 @ sk133 @ J )),bind(B,$thf( H )),bind(C,$thf( k4_xboole_0 @ ( k4_xboole_0 @ sk133 @ J ) @ H )),bind(D,$thf( J ))]]) ).
thf(45793,plain,
! [B: $i,A: $i] :
( ( k3_xboole_0 @ ( k4_xboole_0 @ sk133 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[45729]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(2700,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(645,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ( l3_lattices @ A ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_lattice2) ).
thf(4003,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ( l3_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(26005,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l2_lang1 @ k1_xboole_0 )
| ( A != sk145 ) ),
inference(paramod_ordered,[status(thm)],[1518,3044]) ).
thf(26006,plain,
( ( v1_relat_1 @ ( sk27 @ sk145 ) )
| ( l2_lang1 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26005:[bind(A,$thf( sk145 ))]]) ).
thf(26354,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l1_struct_0 @ k1_xboole_0 )
| ( A != sk244 ) ),
inference(paramod_ordered,[status(thm)],[1518,4525]) ).
thf(26355,plain,
( ( v1_relat_1 @ ( sk27 @ sk244 ) )
| ( l1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26354:[bind(A,$thf( sk244 ))]]) ).
thf(437,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ~ ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).
thf(3202,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ~ ( r2_hidden @ D @ C ) )
& ( ~ ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(905,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ ( k9_filter_0 @ A @ B @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_filter_1) ).
thf(5030,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ ( k9_filter_0 @ A @ B @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1163,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_openlatt) ).
thf(6125,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(45680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,14961]) ).
thf(45681,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[45680:[bind(A,$thf( k4_xboole_0 @ sk19 @ J )),bind(B,$thf( H )),bind(C,$thf( k4_xboole_0 @ ( k4_xboole_0 @ sk19 @ J ) @ H )),bind(D,$thf( J ))]]) ).
thf(45835,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k4_xboole_0 @ sk19 @ B ) @ A ) ),
inference(simp,[status(thm)],[45681]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k10_filter_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_1) ).
thf(5154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k10_filter_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(949,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v17_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_filter_0) ).
thf(5203,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v17_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(972,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_filter_0) ).
thf(5309,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(1317,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(130,axiom,
! [A: $i] :
~ ( ( A
= ( k1_tarski @ k1_xboole_0 ) )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_gate_1) ).
thf(1830,plain,
! [A: $i] :
~ ( ( A
= ( k1_tarski @ k1_xboole_0 ) )
& ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1034,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_2) ).
thf(5543,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(932,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattice4) ).
thf(5152,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(287,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k12_lopclset @ A )
= ( k6_lopclset @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lopclset) ).
thf(2545,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k12_lopclset @ A )
= ( k6_lopclset @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(2599,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(3329,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(2044,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1169,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_2) ).
thf(6159,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_filter_2 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(1008,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k4_lattice4 @ A @ B )
= ( a_2_0_lattice4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice4) ).
thf(5450,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k4_lattice4 @ A @ B )
= ( a_2_0_lattice4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(411,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_boolealg @ A @ B @ ( k1_boolealg @ A @ C @ D ) )
=> ( r3_boolealg @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_boolealg) ).
thf(3095,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_boolealg @ A @ B @ ( k1_boolealg @ A @ C @ D ) )
=> ( r3_boolealg @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(3853,plain,
! [A: $i] : ( m1_subset_1 @ ( sk195 @ A ) @ A ),
inference(cnf,[status(esa)],[3852]) ).
thf(26687,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk44 ) ),
inference(paramod_ordered,[status(thm)],[1518,6288]) ).
thf(26688,plain,
v1_relat_1 @ ( sk27 @ sk44 ),
inference(pattern_uni,[status(thm)],[26687:[bind(A,$thf( sk44 ))]]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(5277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A )
& ( m1_subset_1 @ C @ A )
& ( m1_subset_1 @ D @ A )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ A )
& ( m1_subset_1 @ G @ A )
& ( m1_subset_1 @ H @ A )
& ( m1_subset_1 @ I @ A ) )
=> ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(100,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( r3_lattice3 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice3) ).
thf(1702,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r3_lattice3 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
=> ( r1_lattices @ A @ B @ D ) ) )
=> ( r3_lattice3 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(982,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ C ) ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_boolealg) ).
thf(5347,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ C ) ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(1050,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m2_card_fil @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_card_fil) ).
thf(5613,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m2_card_fil @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(1797,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(348,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_tex_2) ).
thf(2848,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_filter_2) ).
thf(5319,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(1356,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk13 @ A ) )
| ( r4_lattice3 @ A @ ( sk14 @ B @ A ) @ ( sk13 @ A ) )
| ( v4_lattice3 @ A ) ),
inference(cnf,[status(esa)],[1350]) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk13 @ A ) )
| ( r4_lattice3 @ A @ ( sk14 @ B @ A ) @ ( sk13 @ A ) )
| ( v4_lattice3 @ A ) ),
inference(simp,[status(thm)],[1356]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(1934,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( v1_xboole_0 @ ( k18_gate_1 @ A @ B @ C @ D @ E ) )
<=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_gate_1) ).
thf(5949,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( v1_xboole_0 @ ( k18_gate_1 @ A @ B @ C @ D @ E ) )
=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) ) )
& ( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E ) )
=> ~ ( v1_xboole_0 @ ( k18_gate_1 @ A @ B @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(2411,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(656,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_struct_0 @ A )
<=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
thf(4057,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v3_struct_0 @ A )
=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) )
& ( ( v1_xboole_0 @ ( u1_struct_0 @ A ) )
=> ( v3_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(5675,plain,
l1_funcsdom @ sk324,
inference(cnf,[status(esa)],[5673]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( B = C )
<=> ( ( k3_subset_1 @ A @ B )
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_fin_topo) ).
thf(3415,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( B = C )
=> ( ( k3_subset_1 @ A @ B )
= ( k3_subset_1 @ A @ C ) ) )
& ( ( ( k3_subset_1 @ A @ B )
= ( k3_subset_1 @ A @ C ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(1055,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k9_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_filter_2) ).
thf(5628,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k9_filter_2 @ A @ B )
= ( k7_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C )
<=> ( ( r2_hidden @ B @ C )
& ( r1_tarski @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_setwiseo) ).
thf(3124,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C )
=> ( ( r2_hidden @ B @ C )
& ( r1_tarski @ A @ C ) ) )
& ( ( ( r2_hidden @ B @ C )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(2975,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1353,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( v4_lattice3 @ A )
| ~ ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ C @ B )
| ( r1_lattices @ A @ ( sk12 @ B @ A ) @ C ) ),
inference(cnf,[status(esa)],[1350]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_boolealg @ A @ B @ C )
=> ( r1_boolealg @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_boolealg) ).
thf(5504,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_boolealg @ A @ B @ C )
=> ( r1_boolealg @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(668,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ B @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_filter_1) ).
thf(4106,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ B @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(894,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v16_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_filter_0) ).
thf(4991,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v16_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relat_1) ).
thf(2579,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1009,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_boolealg) ).
thf(5453,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_boolealg @ A @ ( k1_boolealg @ A @ B @ C ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relat_1) ).
thf(1427,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(697,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r1_boolealg @ A @ C @ ( k3_lattices @ A @ B @ ( k1_boolealg @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_boolealg) ).
thf(4235,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r1_boolealg @ A @ C @ ( k3_lattices @ A @ B @ ( k1_boolealg @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(14838,plain,
( ( sk1 != k1_xboole_0 )
| ( ( v12_lattices @ ( k23_filter_2 @ sk1 @ sk2 ) )
!= ( v12_lattices @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[14500,1199]) ).
thf(14853,plain,
( ( sk1 != k1_xboole_0 )
| ( ( k23_filter_2 @ sk1 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[14838]) ).
thf(4200,plain,
! [B: $i,A: $i] :
( ( ( g1_struct_0 @ A )
!= ( g1_struct_0 @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[4199]) ).
thf(4201,plain,
! [B: $i,A: $i] :
( ( ( g1_struct_0 @ A )
!= ( g1_struct_0 @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[4200]) ).
thf(4202,plain,
! [A: $i] :
( ( sk223 @ ( g1_struct_0 @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(g1_struct_0),[sk223])]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(3117,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(985,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) @ ( k3_lattices @ A @ B @ C ) )
=> ( ( r2_boolealg @ A @ C @ ( k7_lattices @ A @ B ) )
| ( r2_boolealg @ A @ B @ ( k7_lattices @ A @ C ) )
| ( ( r1_boolealg @ A @ B @ ( k7_lattices @ A @ B ) )
& ( r1_boolealg @ A @ C @ ( k7_lattices @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_boolealg) ).
thf(5364,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) @ ( k3_lattices @ A @ B @ C ) )
=> ( ( r2_boolealg @ A @ C @ ( k7_lattices @ A @ B ) )
| ( r2_boolealg @ A @ B @ ( k7_lattices @ A @ C ) )
| ( ( r1_boolealg @ A @ B @ ( k7_lattices @ A @ B ) )
& ( r1_boolealg @ A @ C @ ( k7_lattices @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(371,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( v2_funct_1 @ ( k9_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lopclset) ).
thf(2949,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( v2_funct_1 @ ( k9_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(26945,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk139 ) ),
inference(paramod_ordered,[status(thm)],[1518,13991]) ).
thf(26946,plain,
v1_relat_1 @ ( sk27 @ sk139 ),
inference(pattern_uni,[status(thm)],[26945:[bind(A,$thf( sk139 ))]]) ).
thf(103,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( r2_hidden @ C @ A )
& ( B
= ( k6_domain_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_rpr_1) ).
thf(1717,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ A )
& ( r2_hidden @ C @ A )
& ( B
= ( k6_domain_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(178,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( v1_realset1 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( r1_tarski @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_rpr_1) ).
thf(2030,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( v1_realset1 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( r1_tarski @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(693,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_filter_0) ).
thf(4225,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1079,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k9_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_openlatt) ).
thf(5717,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k9_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(851,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k5_lattices @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattices) ).
thf(4838,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k5_lattices @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(3256,plain,
l2_lang1 @ sk156,
inference(cnf,[status(esa)],[3254]) ).
thf(6356,plain,
( ( v1_xboole_0 @ sk133 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,2926]) ).
thf(6358,plain,
sk133 != k1_xboole_0,
inference(simp,[status(thm)],[6356]) ).
thf(143,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_pre_topc) ).
thf(1881,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1170,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k6_gate_1 @ A @ B ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
& ( v1_xboole_0 @ ( k6_gate_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_gate_1) ).
thf(6161,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k6_gate_1 @ A @ B ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
& ( v1_xboole_0 @ ( k6_gate_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1272,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( r2_hidden @ ( sk10 @ B @ A ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
| ( v1_funct_1 @ ( sk11 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1268]) ).
thf(841,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v1_filter_2 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_filter_2) ).
thf(4795,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( v1_filter_2 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) ) )
=> ( v1_filter_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(386,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( m1_subset_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_setwiseo) ).
thf(3007,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( m1_subset_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(679,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k16_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k16_filter_2) ).
thf(4150,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
=> ( ( k16_filter_2 @ A @ B )
= ( k8_filter_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finset_1) ).
thf(3684,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(464,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k5_lattices @ A )
= ( k6_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_lattice2) ).
thf(3288,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k5_lattices @ A )
= ( k6_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(4217,plain,
l1_orders_2 @ sk225,
inference(cnf,[status(esa)],[4216]) ).
thf(514,axiom,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( ( v5_orders_2 @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( ( v5_orders_2 @ C @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_orders_2) ).
thf(3565,plain,
! [A: $i] :
( ( l1_orders_2 @ A )
=> ! [B: $i] :
( ( ( v5_orders_2 @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( ( v5_orders_2 @ C @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(1458,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1457]) ).
thf(1459,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1458]) ).
thf(827,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_quantal1 @ B @ A )
& ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_quantal1) ).
thf(4763,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v1_quantal1 @ B @ A )
& ( v1_xboole_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(1133,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( r1_filter_1 @ A @ B )
& ( r1_filter_1 @ B @ C ) )
=> ( r1_filter_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_filter_1) ).
thf(5966,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( r1_filter_1 @ A @ B )
& ( r1_filter_1 @ B @ C ) )
=> ( r1_filter_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(1167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k32_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G )
& ~ ( v1_xboole_0 @ H ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G )
& ~ ( v1_xboole_0 @ H ) )
& ( v1_xboole_0 @ ( k32_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_gate_1) ).
thf(6137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k32_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
& ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G )
& ~ ( v1_xboole_0 @ H ) )
& ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G )
& ~ ( v1_xboole_0 @ H ) )
& ( v1_xboole_0 @ ( k32_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(623,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_filter_0) ).
thf(3928,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(305,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_filter_2) ).
thf(2643,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(1998,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1092,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_0) ).
thf(5771,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(462,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ B @ ( k5_lattices @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_boolealg) ).
thf(3284,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ B @ ( k5_lattices @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( B
= ( k3_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(2760,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k3_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(6282,plain,
( ( v1_xboole_0 @ sk72 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,2115]) ).
thf(6286,plain,
sk72 != k1_xboole_0,
inference(simp,[status(thm)],[6282]) ).
thf(45652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k1_tarski @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,9850]) ).
thf(45653,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[45652:[bind(A,$thf( k1_tarski @ H )),bind(B,$thf( G )),bind(C,$thf( k4_xboole_0 @ ( k1_tarski @ H ) @ G )),bind(D,$thf( H ))]]) ).
thf(45823,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k1_tarski @ B ) @ A ) ),
inference(simp,[status(thm)],[45653]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k12_openlatt @ A @ B @ C )
= ( k12_openlatt @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k12_openlatt) ).
thf(3946,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k12_openlatt @ A @ B @ C )
= ( k12_openlatt @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(772,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m3_lattice4 @ C @ A )
=> ( ( C
= ( k3_lattice4 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_lattice4) ).
thf(4548,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m3_lattice4 @ C @ A )
=> ( ( ( C
= ( k3_lattice4 @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) )
=> ( C
= ( k3_lattice4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(707,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_2) ).
thf(4278,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(802,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k6_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_filter_0) ).
thf(4651,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k6_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(532,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_pre_topc) ).
thf(3620,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(304,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( B
= ( k16_lattice3 @ A @ C ) )
<=> ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice3) ).
thf(2626,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( B
= ( k16_lattice3 @ A @ C ) )
=> ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) ) )
& ( ( ( r3_lattice3 @ A @ B @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattice3 @ A @ D @ C )
=> ( r3_lattices @ A @ D @ B ) ) ) )
=> ( B
= ( k16_lattice3 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(3457,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(1314,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1315,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = B ) ),
inference(cnf,[status(esa)],[1314]) ).
thf(1316,plain,
! [B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
!= k1_xboole_0 )
| ( A = B ) ),
inference(lifteq,[status(thm)],[1315]) ).
thf(26312,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( l3_lattices @ k1_xboole_0 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1518,14338]) ).
thf(26313,plain,
( ( v1_relat_1 @ ( sk27 @ sk1 ) )
| ( l3_lattices @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26312:[bind(A,$thf( sk1 ))]]) ).
thf(242,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_0) ).
thf(2352,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_subset_1) ).
thf(3757,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(268,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_tex_2) ).
thf(2479,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_realset1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(856,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lopclset @ A )
= ( a_1_1_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_lopclset) ).
thf(4851,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lopclset @ A )
= ( a_1_1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(789,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice2) ).
thf(4606,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r1_lattice2 @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(881,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( k1_lattice2 @ A )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice2) ).
thf(4945,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( k1_lattice2 @ A )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u1_lattices @ A ) @ ( u2_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(2818,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[2817]) ).
thf(403,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
<=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).
thf(3067,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(1065,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(5653,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(7078,plain,
! [A: $i] :
( ( ( k1_relat_1 @ A )
!= ( u1_struct_0 @ sk1 ) )
| ( ( a_2_0_lopclset @ sk1 @ ( sk7 @ A @ sk1 ) )
!= ( k1_funct_1 @ A @ ( sk7 @ A @ sk1 ) ) )
| ( A
= ( k8_lopclset @ sk1 ) )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_relat_1 @ A )
| ( ( v1_funct_1 @ sk149 )
!= ( v1_funct_1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3121,7075]) ).
thf(7079,plain,
( ( ( u1_struct_0 @ sk1 )
!= ( k1_relat_1 @ sk149 ) )
| ( ( a_2_0_lopclset @ sk1 @ ( sk7 @ sk149 @ sk1 ) )
!= ( k1_funct_1 @ sk149 @ ( sk7 @ sk149 @ sk1 ) ) )
| ( ( k8_lopclset @ sk1 )
= sk149 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_relat_1 @ sk149 ) ),
inference(pattern_uni,[status(thm)],[7078:[bind(A,$thf( sk149 ))]]) ).
thf(7176,plain,
( ( ( u1_struct_0 @ sk1 )
!= ( k1_relat_1 @ sk149 ) )
| ( ( a_2_0_lopclset @ sk1 @ ( sk7 @ sk149 @ sk1 ) )
!= ( k1_funct_1 @ sk149 @ ( sk7 @ sk149 @ sk1 ) ) )
| ( ( k8_lopclset @ sk1 )
= sk149 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[7079,3122]) ).
thf(7177,plain,
( ( ( u1_struct_0 @ sk1 )
!= ( k1_relat_1 @ sk149 ) )
| ( ( a_2_0_lopclset @ sk1 @ ( sk7 @ sk149 @ sk1 ) )
!= ( k1_funct_1 @ sk149 @ ( sk7 @ sk149 @ sk1 ) ) )
| ( ( k8_lopclset @ sk1 )
= sk149 )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 ) ),
inference(simp,[status(thm)],[7176]) ).
thf(1067,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
<=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v17_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_filter_2) ).
thf(5660,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v17_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v17_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(3553,plain,
v1_funct_1 @ sk179,
inference(cnf,[status(esa)],[3552]) ).
thf(7283,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
| ( ( v1_funct_1 @ ( k8_lopclset @ sk1 ) )
!= ( v1_funct_1 @ sk179 ) ) ),
inference(paramod_ordered,[status(thm)],[3553,7250]) ).
thf(7288,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ( v3_realset2 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ~ ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
| ( ( k8_lopclset @ sk1 )
!= sk179 ) ),
inference(simp,[status(thm)],[7283]) ).
thf(1412,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1411]) ).
thf(207,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(2215,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1000,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m1_filter_2 @ ( k16_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_filter_2) ).
thf(5421,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_filter_2 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m1_filter_2 @ ( k16_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(924,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ C ) @ B )
= ( k4_filter_0 @ A @ C @ B ) )
& ( ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ B @ C ) )
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_filter_1) ).
thf(5115,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ C ) @ B )
= ( k4_filter_0 @ A @ C @ B ) )
& ( ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ B @ C ) )
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(835,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k1_boolealg @ A @ B @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_boolealg) ).
thf(4780,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k1_boolealg @ A @ B @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(1781,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_funct_2 @ C @ A ) @ ( k1_funct_2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_5) ).
thf(3625,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_funct_2 @ C @ A ) @ ( k1_funct_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(800,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_filter_0) ).
thf(4646,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(562,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tex_2) ).
thf(3725,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( v1_xboole_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1119,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m2_lattice4 @ ( k11_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_filter_2) ).
thf(5907,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m2_lattice4 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m2_lattice4 @ ( k11_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(2997,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(4102,plain,
! [A: $i] : ( v1_struct_0 @ ( g1_struct_0 @ A ) ),
inference(cnf,[status(esa)],[4100]) ).
thf(13177,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk156 ) ),
inference(paramod_ordered,[status(thm)],[1284,3255]) ).
thf(13178,plain,
( ~ ( v1_xboole_0 @ sk156 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13177:[bind(A,$thf( sk156 ))]]) ).
thf(1386,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r1_lattices @ A @ ( sk16 @ C @ B @ A ) @ B )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[1383]) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r1_lattices @ A @ ( sk16 @ C @ B @ A ) @ B )
| ( r4_lattice3 @ A @ B @ C ) ),
inference(simp,[status(thm)],[1386]) ).
thf(239,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_filter_0) ).
thf(2342,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(84,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( B
!= ( k2_pre_topc @ A ) )
& ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
!= k1_xboole_0 )
& ( B
= ( k2_pre_topc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_pre_topc) ).
thf(1575,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( B
!= ( k2_pre_topc @ A ) )
& ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
!= k1_xboole_0 )
& ( B
= ( k2_pre_topc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1734,plain,
v1_trees_1 @ sk44,
inference(cnf,[status(esa)],[1733]) ).
thf(21970,plain,
! [A: $i] :
( ~ ( r2_hidden @ k1_xboole_0 @ sk72 )
| ( ( r2_hidden @ A @ ( k1_tarski @ A ) )
!= ( r2_hidden @ sk2 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[3667,13961]) ).
thf(21989,plain,
! [A: $i] :
( ~ ( r2_hidden @ k1_xboole_0 @ sk72 )
| ( A != sk2 )
| ( ( k1_tarski @ A )
!= sk72 ) ),
inference(simp,[status(thm)],[21970]) ).
thf(21996,plain,
( ~ ( r2_hidden @ k1_xboole_0 @ sk72 )
| ( ( k1_tarski @ sk2 )
!= sk72 ) ),
inference(simp,[status(thm)],[21989]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_subset_1) ).
thf(1807,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1274,plain,
! [B: $i,A: $i] :
( ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B )
| ( ( k1_funct_1 @ A @ ( sk10 @ B @ A ) )
!= ( k1_funct_1 @ B @ ( sk10 @ B @ A ) ) )
| ( ( k2_xboole_0 @ A @ B )
= ( sk11 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1268]) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ( ( k1_funct_1 @ A @ ( sk10 @ B @ A ) )
!= ( k1_funct_1 @ B @ ( sk10 @ B @ A ) ) )
| ( ( sk11 @ B @ A )
= ( k2_xboole_0 @ A @ B ) )
| ~ ( v1_relat_1 @ A )
| ~ ( v1_funct_1 @ A )
| ~ ( v1_relat_1 @ B )
| ~ ( v1_funct_1 @ B ) ),
inference(lifteq,[status(thm)],[1274]) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
| ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(cnf,[status(esa)],[1252]) ).
thf(219,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k5_filter_0 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_filter_0) ).
thf(2273,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k5_filter_0 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1340,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_realset1 @ B )
| ~ ( r1_tarski @ A @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[1339]) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( v1_xboole_0 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_realset1 @ B )
| ~ ( r1_tarski @ A @ B ) ),
inference(lifteq,[status(thm)],[1340]) ).
thf(1142,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v13_lattices @ A )
& ( v13_lattices @ B ) )
<=> ( v13_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_filter_1) ).
thf(6023,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v13_lattices @ A )
& ( v13_lattices @ B ) )
=> ( v13_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v13_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v13_lattices @ A )
& ( v13_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(3561,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(75,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relat_1) ).
thf(1523,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(13251,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ( sk250 != k1_xboole_0 )
| ( A != sk293 ) ),
inference(paramod_ordered,[status(thm)],[1284,6649]) ).
thf(13252,plain,
( ~ ( v1_xboole_0 @ sk293 )
| ( sk250 != k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[13251:[bind(A,$thf( sk293 ))]]) ).
thf(810,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_unialg_2 @ B @ A ) )
=> ! [C: $i] :
( ( m2_unialg_2 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_unialg_2) ).
thf(4710,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_unialg_2 @ B @ A ) )
=> ! [C: $i] :
( ( ( m2_unialg_2 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m2_unialg_2 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(382,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k2_boolealg @ A @ B @ C ) @ ( k2_boolealg @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_boolealg) ).
thf(2988,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k2_boolealg @ A @ B @ C ) @ ( k2_boolealg @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(603,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_lattice2) ).
thf(3864,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(2283,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(842,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k1_boolealg @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_boolealg) ).
thf(4806,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k1_boolealg @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(2853,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(225,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( k3_lattice3 @ A )
= ( k3_lattice3 @ B ) )
=> ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice3) ).
thf(2290,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( k3_lattice3 @ A )
= ( k3_lattice3 @ B ) )
=> ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(793,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_group_2) ).
thf(4615,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(12697,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
| ~ ( v3_struct_0 @ k1_xboole_0 )
| ( A != sk236 ) ),
inference(paramod_ordered,[status(thm)],[1284,4343]) ).
thf(12698,plain,
( ~ ( v1_xboole_0 @ sk236 )
| ~ ( v3_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[12697:[bind(A,$thf( sk236 ))]]) ).
thf(256,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ ( k3_filter_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_filter_0) ).
thf(2406,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ ( k3_filter_0 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(662,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_boolealg @ A @ B @ C )
=> ( r2_boolealg @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_boolealg) ).
thf(4089,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_boolealg @ A @ B @ C )
=> ( r2_boolealg @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(990,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) ) @ ( k7_lattices @ A @ B ) )
& ( r3_lattices @ A @ ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_boolealg) ).
thf(5382,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) ) @ ( k7_lattices @ A @ B ) )
& ( r3_lattices @ A @ ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(748,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
<=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_tops_3) ).
thf(4468,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( l1_struct_0 @ B )
=> ( ( ( u1_struct_0 @ A )
= ( u1_struct_0 @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( C = D )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) ) )
& ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C )
= ( k3_subset_1 @ ( u1_struct_0 @ B ) @ D ) )
=> ( C = D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(3369,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(652,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( a_2_0_lopclset @ A @ B ) @ ( k7_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lopclset) ).
thf(4042,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( a_2_0_lopclset @ A @ B ) @ ( k7_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m2_filter_2 @ ( k18_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_filter_2) ).
thf(4715,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m2_filter_2 @ ( k18_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).
thf(2004,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(471,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lopclset) ).
thf(3331,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k12_openlatt @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k12_openlatt) ).
thf(4881,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k9_openlatt @ A ) )
& ( m1_subset_1 @ C @ ( k9_openlatt @ A ) ) )
=> ( ( k12_openlatt @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(5104,plain,
l3_lattices @ sk291,
inference(cnf,[status(esa)],[5102]) ).
thf(451,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tex_2) ).
thf(3252,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ~ ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v1_tex_2 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(847,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ ( k3_boolealg @ A @ B @ C ) @ ( k4_lattices @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_boolealg) ).
thf(4823,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ ( k3_boolealg @ A @ B @ C ) @ ( k4_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_boolealg @ A @ B @ C )
<=> ( r2_boolealg @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_boolealg) ).
thf(4969,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r3_boolealg @ A @ B @ C )
=> ( r2_boolealg @ A @ B @ C ) )
& ( ( r2_boolealg @ A @ B @ C )
=> ( r3_boolealg @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(79,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(1558,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(367,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k2_boolealg @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_boolealg) ).
thf(2934,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k2_boolealg @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( B
= ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(2152,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( B
= ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(5600,plain,
~ ( v3_struct_0 @ sk319 ),
inference(cnf,[status(esa)],[5599]) ).
thf(407,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k18_filter_2 @ A @ B ) )
& ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k18_filter_2 @ A @ B ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k18_filter_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_2) ).
thf(3085,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k18_filter_2 @ A @ B ) )
& ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k18_filter_2 @ A @ B ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k18_filter_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1132,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_filter_1 @ A )
= ( a_1_0_filter_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
thf(5963,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_filter_1 @ A )
= ( a_1_0_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(640,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
<=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_2) ).
thf(3978,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(801,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_domain_1) ).
thf(4649,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(2912,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(750,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_filter_0) ).
thf(4478,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(742,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v14_lattices @ A )
=> ( ( k6_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_filter_0) ).
thf(4446,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v14_lattices @ A )
=> ( ( k6_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(145,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( C
= ( k15_lattice3 @ A @ B ) )
<=> ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattice3) ).
thf(1893,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( C
= ( k15_lattice3 @ A @ B ) )
=> ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) ) )
& ( ( ( r4_lattice3 @ A @ C @ B )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r4_lattice3 @ A @ D @ B )
=> ( r1_lattices @ A @ C @ D ) ) ) )
=> ( C
= ( k15_lattice3 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(862,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k16_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(4869,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k16_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(174,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ~ ( v1_xboole_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_prvect_1) ).
thf(2019,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ~ ( v1_xboole_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(26829,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk133 ) ),
inference(paramod_ordered,[status(thm)],[1518,6358]) ).
thf(26830,plain,
v1_relat_1 @ ( sk27 @ sk133 ),
inference(pattern_uni,[status(thm)],[26829:[bind(A,$thf( sk133 ))]]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k23_gate_1 @ A @ B @ C @ D @ E @ F ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F ) )
& ( v1_xboole_0 @ ( k23_gate_1 @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_gate_1) ).
thf(5828,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k23_gate_1 @ A @ B @ C @ D @ E @ F ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F ) )
& ( v1_xboole_0 @ ( k23_gate_1 @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(139,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(1861,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_subset_1) ).
thf(3181,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(332,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v13_lattices @ A )
& ( r3_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattice4) ).
thf(2786,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v13_lattices @ A )
& ( r3_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_0 @ ( k2_filter_0 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(5164,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_0 @ ( k2_filter_0 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(937,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_funct_1 @ ( k8_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_openlatt) ).
thf(5162,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_funct_1 @ ( k8_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(45646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ ( k4_xboole_0 @ sk133 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,15278]) ).
thf(45647,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k4_xboole_0 @ sk133 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[45646:[bind(A,$thf( k4_xboole_0 @ sk133 @ J )),bind(B,$thf( H )),bind(C,$thf( k4_xboole_0 @ ( k4_xboole_0 @ sk133 @ J ) @ H )),bind(D,$thf( J ))]]) ).
thf(45817,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ ( k4_xboole_0 @ sk133 @ B ) @ A ) ),
inference(simp,[status(thm)],[45647]) ).
thf(680,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
<=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) )
=> ( m2_filter_2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_2) ).
thf(4153,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m2_filter_2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(606,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( a_3_0_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_0) ).
thf(3879,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( a_3_0_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_prelamb @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_prelamb @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_prelamb) ).
thf(4214,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_prelamb @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k3_prelamb @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(2648,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(522,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k6_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k2_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice4) ).
thf(3585,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k6_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k2_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(1160,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(6118,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(118,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= C )
=> ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_pre_topc) ).
thf(1777,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= C )
=> ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1073,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k9_gate_1 @ A @ B @ C ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C ) )
& ( v1_xboole_0 @ ( k9_gate_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_gate_1) ).
thf(5692,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k9_gate_1 @ A @ B @ C ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C ) )
& ( v1_xboole_0 @ ( k9_gate_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k4_lattice4 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(4759,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k4_lattice4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(6018,plain,
v5_grcat_1 @ sk330,
inference(cnf,[status(esa)],[6017]) ).
thf(1147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k6_filter_0 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(6045,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k6_filter_0 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(922,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( v1_filter_2 @ B @ A )
<=> ( v2_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_filter_2) ).
thf(5109,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( v1_filter_2 @ B @ A )
=> ( v2_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) ) )
& ( ( v2_filter_0 @ ( k15_filter_2 @ A @ B ) @ ( k1_lattice2 @ A ) )
=> ( v1_filter_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(902,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_filter_0) ).
thf(5023,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(424,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(3149,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(3896,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(203,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tex_2) ).
thf(2198,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(25937,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k16_coh_sp @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,15045]) ).
thf(25938,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k16_coh_sp @ A ) ) ),
inference(pattern_uni,[status(thm)],[25937:[bind(A,$thf( k16_coh_sp @ C )),bind(B,$thf( C ))]]) ).
thf(27160,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k16_coh_sp @ A ) ) ),
inference(simp,[status(thm)],[25938]) ).
thf(504,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_tex_2) ).
thf(3529,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_realset2 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(2162,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1042,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_filter_1) ).
thf(5568,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( v1_xboole_0 @ ( k30_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
<=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G )
& ~ ( v1_xboole_0 @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_gate_1) ).
thf(6062,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ ( k30_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G )
& ~ ( v1_xboole_0 @ H ) ) )
& ( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G )
& ~ ( v1_xboole_0 @ H ) )
=> ~ ( v1_xboole_0 @ ( k30_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(312,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ~ ( r3_lattices @ A @ B @ C )
=> ( r2_hidden @ ( k2_filter_0 @ A @ B ) @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k10_openlatt @ A @ B ) @ ( k10_openlatt @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_openlatt) ).
thf(2680,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ~ ( r3_lattices @ A @ B @ C )
=> ( r2_hidden @ ( k2_filter_0 @ A @ B ) @ ( k6_subset_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k10_openlatt @ A @ B ) @ ( k10_openlatt @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1212,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( sk3 @ A )
| ( v1_trees_1 @ ( k3_tarski @ A ) ) ),
inference(cnf,[status(esa)],[1209]) ).
thf(912,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m3_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice4) ).
thf(5072,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m3_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).
thf(3351,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1083,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k23_filter_2 @ A @ B )
= ( k24_filter_2 @ ( k1_lattice2 @ A ) @ ( k23_filter_2 @ ( k1_lattice2 @ A ) @ ( k10_filter_2 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_filter_2) ).
thf(5739,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( k23_filter_2 @ A @ B )
= ( k24_filter_2 @ ( k1_lattice2 @ A ) @ ( k23_filter_2 @ ( k1_lattice2 @ A ) @ ( k10_filter_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(93,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_finset_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_rpr_1) ).
thf(1661,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( v1_finset_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1075,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( r3_zfrefle1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_zfrefle1) ).
thf(5704,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ( r3_zfrefle1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(224,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v14_lattices @ A )
& ( r2_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_lattice4) ).
thf(2287,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v14_lattices @ A )
& ( r2_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).
thf(1678,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(3291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(844,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_filter_0) ).
thf(4811,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1229,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( v1_realset1 @ A )
| ~ ( v1_xboole_0 @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[1227]) ).
thf(607,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(3882,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(456,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(3264,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(853,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_filter_2) ).
thf(4843,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(21967,plain,
! [A: $i] :
( ~ ( r2_hidden @ sk2 @ sk60 )
| ( ( r2_hidden @ A @ ( k1_tarski @ A ) )
!= ( r2_hidden @ k1_xboole_0 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[3667,13933]) ).
thf(21992,plain,
! [A: $i] :
( ~ ( r2_hidden @ sk2 @ sk60 )
| ( A != k1_xboole_0 )
| ( ( k1_tarski @ A )
!= sk60 ) ),
inference(simp,[status(thm)],[21967]) ).
thf(21999,plain,
( ~ ( r2_hidden @ sk2 @ sk60 )
| ( ( k1_tarski @ k1_xboole_0 )
!= sk60 ) ),
inference(simp,[status(thm)],[21992]) ).
thf(42657,plain,
( ~ ( r2_hidden @ sk2 @ sk60 )
| ( ( k1_zfmisc_1 @ k1_xboole_0 )
!= sk60 ) ),
inference(rewrite,[status(thm)],[21999,1201]) ).
thf(1089,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_lattice3 @ A )
= ( k9_filter_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
thf(5760,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_lattice3 @ A )
= ( k9_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(745,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( ( r2_boolealg @ A @ C @ D )
| ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_boolealg) ).
thf(4455,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( ( r2_boolealg @ A @ C @ D )
| ( r1_boolealg @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(428,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
<=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_filter_1) ).
thf(3164,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ B )
=> ( r3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(484,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k18_filter_2 @ A @ B )
= ( k2_filter_2 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) ) )
& ( ( k18_filter_2 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k2_filter_2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_filter_2) ).
thf(3379,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( k18_filter_2 @ A @ B )
= ( k2_filter_2 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) ) )
& ( ( k18_filter_2 @ ( k1_lattice2 @ A ) @ ( k5_filter_2 @ A @ B ) )
= ( k2_filter_2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(26558,plain,
! [B: $i,A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A
!= ( k1_tex_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1518,10675]) ).
thf(26559,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_tex_1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26558:[bind(A,$thf( k1_tex_1 @ C )),bind(B,$thf( C ))]]) ).
thf(27294,plain,
! [A: $i] : ( v1_relat_1 @ ( sk27 @ ( k1_tex_1 @ A ) ) ),
inference(simp,[status(thm)],[26559]) ).
thf(945,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k10_openlatt @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_openlatt) ).
thf(5187,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k10_openlatt @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(208,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tex_2) ).
thf(2218,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) )
<=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(4125,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) )
=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) ) )
& ( ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(908,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_openlatt @ A )
= ( k2_relat_1 @ ( k8_openlatt @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_openlatt) ).
thf(5051,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_openlatt @ A )
= ( k2_relat_1 @ ( k8_openlatt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(26051,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( v1_struct_0 @ k1_xboole_0 )
| ( A != sk244 ) ),
inference(paramod_ordered,[status(thm)],[1518,4524]) ).
thf(26052,plain,
( ( v1_relat_1 @ ( sk27 @ sk244 ) )
| ( v1_struct_0 @ k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[26051:[bind(A,$thf( sk244 ))]]) ).
thf(651,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k5_lattices @ A ) @ B )
= ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattices) ).
thf(4039,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k5_lattices @ A ) @ B )
= ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(230,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) )
<=> ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lopclset) ).
thf(2302,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) )
=> ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) )
=> ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(898,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_boolealg @ A @ B @ C )
=> ( ~ ( r2_boolealg @ A @ ( k4_lattices @ A @ D @ B ) @ ( k4_lattices @ A @ D @ C ) )
& ~ ( r2_boolealg @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_boolealg) ).
thf(5009,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_boolealg @ A @ B @ C )
=> ( ~ ( r2_boolealg @ A @ ( k4_lattices @ A @ D @ B ) @ ( k4_lattices @ A @ D @ C ) )
& ~ ( r2_boolealg @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(280,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_0) ).
thf(2517,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(555,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k5_lattices @ A ) )
= ( k6_lattices @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice4) ).
thf(3705,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k5_lattices @ A ) )
= ( k6_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(1280,plain,
! [A: $i] :
( ~ ( l1_struct_0 @ A )
| ~ ( v3_realset2 @ A )
| ( v1_realset1 @ ( u1_struct_0 @ A ) ) ),
inference(cnf,[status(esa)],[1279]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( B
= ( k3_xboole_0 @ C @ D ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( ( k1_funct_1 @ B @ A )
= ( k1_funct_1 @ C @ A ) )
& ( ( k1_funct_1 @ B @ A )
= ( k1_funct_1 @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_grfunc_1) ).
thf(2155,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( B
= ( k3_xboole_0 @ C @ D ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( ( k1_funct_1 @ B @ A )
= ( k1_funct_1 @ C @ A ) )
& ( ( k1_funct_1 @ B @ A )
= ( k1_funct_1 @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(14484,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( ( v12_lattices @ ( k23_filter_2 @ sk1 @ sk2 ) )
!= ( v12_lattices @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[13600,1199]) ).
thf(14499,plain,
( ~ ( v1_xboole_0 @ sk1 )
| ( ( k23_filter_2 @ sk1 @ sk2 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[14484]) ).
thf(786,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_prelamb @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_prelamb @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_prelamb) ).
thf(4596,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_prelamb @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_prelamb @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1165,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k6_metric_1 @ A ) )
& ( v1_metric_1 @ ( k6_metric_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_metric_1) ).
thf(6131,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v3_struct_0 @ ( k6_metric_1 @ A ) )
& ( v1_metric_1 @ ( k6_metric_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ A @ B @ C ) )
& ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
& ~ ( ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ A ) ) )
& ~ ( ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
& ~ ( ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ A ) ) )
& ( v1_xboole_0 @ ( k11_gate_1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_gate_1) ).
thf(3100,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k11_gate_1 @ A @ B @ C ) )
& ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
& ~ ( ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ A ) ) )
& ~ ( ~ ( ~ ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
& ~ ( ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C ) )
& ~ ( ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ A ) ) )
& ( v1_xboole_0 @ ( k11_gate_1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1004,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
& ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ D ) @ ( k5_lattices @ A ) ) )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_boolealg) ).
thf(5430,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
& ( r1_boolealg @ A @ ( k4_lattices @ A @ B @ D ) @ ( k5_lattices @ A ) ) )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r3_lattice3 @ B @ C @ A )
<=> ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_lattice3) ).
thf(2951,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r3_lattice3 @ B @ C @ A )
=> ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) ) )
& ( ( r4_lattice3 @ B @ ( k7_lattices @ B @ C ) @ ( a_2_0_lattice3 @ A @ B ) )
=> ( r3_lattice3 @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(838,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k6_lattices @ A ) @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattices) ).
thf(4787,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k6_lattices @ A ) @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(852,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_0) ).
thf(4841,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(583,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_quantal1 @ B @ A )
<=> ! [C: $i] :
( ( ( v1_finset_1 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k15_lattice3 @ A @ C ) @ D )
& ( r2_hidden @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_quantal1) ).
thf(3790,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_quantal1 @ B @ A )
=> ! [C: $i] :
( ( ( v1_finset_1 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k15_lattice3 @ A @ C ) @ D )
& ( r2_hidden @ D @ B ) ) ) )
& ( ! [C: $i] :
( ( ( v1_finset_1 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k15_lattice3 @ A @ C ) @ D )
& ( r2_hidden @ D @ B ) ) )
=> ( v1_quantal1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(3337,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(6670,plain,
( ( v3_realset2 @ sk316 )
!= ( v3_realset2 @ sk293 ) ),
inference(paramod_ordered,[status(thm)],[5497,5134]) ).
thf(6671,plain,
sk316 != sk293,
inference(simp,[status(thm)],[6670]) ).
thf(419,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r4_lattice4 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice4) ).
thf(3132,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r4_lattice4 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) )
=> ( r4_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(987,axiom,
! [A: $i] :
( ( l1_prelamb @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_prelamb) ).
thf(5371,plain,
! [A: $i] :
( ( l1_prelamb @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k1_funct_2 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_2) ).
thf(2050,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k1_funct_2 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
& ( ? [E: $i] :
( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( D = E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k1_funct_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(5601,plain,
l2_quantal1 @ sk319,
inference(cnf,[status(esa)],[5599]) ).
thf(754,axiom,
! [A: $i] :
( ~ ( v2_setfam_1 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_setfam_1) ).
thf(4491,plain,
! [A: $i] :
( ~ ( v2_setfam_1 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k3_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(3496,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k3_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(866,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_lattice4 @ ( k16_openlatt @ A ) @ A @ ( k15_openlatt @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_openlatt) ).
thf(4885,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_lattice4 @ ( k16_openlatt @ A ) @ A @ ( k15_openlatt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_2 @ ( k2_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_filter_2) ).
thf(5014,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_2 @ ( k2_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v17_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice3) ).
thf(3690,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v17_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
& ( A
= ( k7_lattices @ C @ D ) )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( a_2_0_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(166,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_rpr_1) ).
thf(1989,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(6281,plain,
( ( v1_xboole_0 @ sk2 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,1196]) ).
thf(6287,plain,
sk2 != k1_xboole_0,
inference(simp,[status(thm)],[6281]) ).
thf(26959,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[1518,6287]) ).
thf(26960,plain,
v1_relat_1 @ ( sk27 @ sk2 ),
inference(pattern_uni,[status(thm)],[26959:[bind(A,$thf( sk2 ))]]) ).
thf(512,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(3558,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(3804,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(749,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( C = D )
=> ( ( k7_lattices @ A @ C )
= ( k7_lattices @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_2) ).
thf(4474,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
= ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ( ( C = D )
=> ( ( k7_lattices @ A @ C )
= ( k7_lattices @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(2714,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(576,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tops_1) ).
thf(3765,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(1040,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) ) )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( r3_lattices @ A @ C @ D )
<=> ( r3_lattices @ ( k23_filter_2 @ A @ B ) @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_filter_2) ).
thf(5559,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k23_filter_2 @ A @ B ) ) )
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ ( k23_filter_2 @ A @ B ) @ E @ F ) )
& ( ( r3_lattices @ ( k23_filter_2 @ A @ B ) @ E @ F )
=> ( r3_lattices @ A @ C @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(3822,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_setwiseo) ).
thf(2751,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ A @ B )
| ( A = C ) ) )
& ( ( ( r2_hidden @ A @ B )
| ( A = C ) )
=> ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(337,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r3_lattice3 @ A @ B @ C ) )
=> ( ( k16_lattice3 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_lattice3) ).
thf(2800,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v4_lattice3 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ B @ C )
& ( r3_lattice3 @ A @ B @ C ) )
=> ( ( k16_lattice3 @ A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(45678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk19 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1396,14961]) ).
thf(45679,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ sk19 @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[45678:[bind(A,$thf( sk19 )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( k4_xboole_0 @ sk19 @ F ))]]) ).
thf(45834,plain,
! [B: $i,A: $i] : ( v1_finset_1 @ ( k4_xboole_0 @ ( k3_xboole_0 @ sk19 @ B ) @ A ) ),
inference(simp,[status(thm)],[45679]) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
| ( ( k1_relat_1 @ C )
= A ) ),
inference(cnf,[status(esa)],[1360]) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_relat_1 @ C )
= A )
| ~ ( v1_relat_1 @ C )
| ~ ( v1_funct_1 @ C )
| ~ ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ),
inference(lifteq,[status(thm)],[1362]) ).
thf(5709,plain,
v13_lattices @ k6_nat_lat,
inference(cnf,[status(esa)],[5707]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(4281,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(476,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_relat_1 @ ( k10_filter_0 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_filter_0) ).
thf(3347,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_relat_1 @ ( k10_filter_0 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(920,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ E ) @ ( k1_boolealg @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_boolealg) ).
thf(5105,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( r3_lattices @ A @ ( k1_boolealg @ A @ B @ E ) @ ( k1_boolealg @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(45689,plain,
! [C: $i,B: $i,A: $i] :
( ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk149 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1396,6916]) ).
thf(45690,plain,
! [A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ sk149 @ A ) ),
inference(pattern_uni,[status(thm)],[45689:[bind(A,$thf( sk149 )),bind(B,$thf( E )),bind(C,$thf( k4_xboole_0 @ sk149 @ E ))]]) ).
thf(45839,plain,
! [A: $i] : ( v1_finset_1 @ ( k3_xboole_0 @ sk149 @ A ) ),
inference(simp,[status(thm)],[45690]) ).
thf(290,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v14_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( ( k6_lattices @ ( k5_filter_1 @ A @ B ) )
= ( k6_filter_1 @ A @ B @ ( k6_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_filter_1) ).
thf(2572,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v14_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( ( k6_lattices @ ( k5_filter_1 @ A @ B ) )
= ( k6_filter_1 @ A @ B @ ( k6_lattices @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1011,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m2_filter_2 @ ( k14_filter_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_filter_2) ).
thf(5462,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ ( k1_lattice2 @ A ) ) )
=> ( m2_filter_2 @ ( k14_filter_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(80,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( A
= ( k2_xboole_0 @ B @ C ) )
=> ( ( ( k1_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) )
& ( ( k2_relat_1 @ A )
= ( k2_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_grfunc_1) ).
thf(1561,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( A
= ( k2_xboole_0 @ B @ C ) )
=> ( ( ( k1_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) )
& ( ( k2_relat_1 @ A )
= ( k2_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(3479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(255,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k3_boolealg @ A @ C @ D ) ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_boolealg) ).
thf(2404,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k3_boolealg @ A @ C @ D ) ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ ( k3_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(45695,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k3_xboole_0 @ B @ C )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ k1_xboole_0 @ A )
!= ( k4_xboole_0 @ B @ ( k4_xboole_0 @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[2197,1396]) ).
thf(45696,plain,
! [A: $i] :
( ( k3_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[45695:[bind(A,$thf( k4_xboole_0 @ k1_xboole_0 @ E )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( E ))]]) ).
thf(45778,plain,
! [A: $i] :
( ( k3_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(simp,[status(thm)],[45696]) ).
thf(210,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
<=> ! [C: $i] :
( ( r1_tarski @ C @ B )
<=> ( ( C = k1_xboole_0 )
| ( C = B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_rpr_1) ).
thf(2223,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( ( r1_tarski @ C @ B )
=> ( ( C = k1_xboole_0 )
| ( C = B ) ) )
& ( ( ( C = k1_xboole_0 )
| ( C = B ) )
=> ( r1_tarski @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r1_tarski @ C @ B )
=> ( ( C = k1_xboole_0 )
| ( C = B ) ) )
& ( ( ( C = k1_xboole_0 )
| ( C = B ) )
=> ( r1_tarski @ C @ B ) ) )
=> ( ~ ( v1_xboole_0 @ B )
& ( v1_realset1 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(536,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ B @ ( k4_lattices @ A @ B @ C ) ) @ ( k1_boolealg @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_boolealg) ).
thf(3633,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k3_boolealg @ A @ B @ ( k4_lattices @ A @ B @ C ) ) @ ( k1_boolealg @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_boolealg @ A @ B @ C )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_boolealg) ).
thf(4193,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_boolealg @ A @ B @ C )
=> ( B = C ) )
& ( ( B = C )
=> ( r1_boolealg @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(876,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_filter_0) ).
thf(4912,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_finset_1 @ A )
=> ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(3045,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_finset_1 @ A )
=> ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(948,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k10_openlatt @ A @ B )
= ( a_2_1_openlatt @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_openlatt) ).
thf(5200,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k10_openlatt @ A @ B )
= ( a_2_1_openlatt @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(3673,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1335,plain,
~ ( v1_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1333]) ).
thf(9967,plain,
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) ),
inference(rewrite,[status(thm)],[1335,1201]) ).
thf(9969,plain,
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) )
!= ( v1_xboole_0 @ k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1922,9967]) ).
thf(9987,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[9969]) ).
thf(45730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
!= sk139 )
| ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
!= ( k4_xboole_0 @ sk133 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1396,44831]) ).
thf(45731,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ sk133 @ B ) @ A )
!= sk139 ),
inference(pattern_uni,[status(thm)],[45730:[bind(A,$thf( sk133 )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( k4_xboole_0 @ sk133 @ F ))]]) ).
thf(45794,plain,
! [B: $i,A: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ sk133 @ B ) @ A )
!= sk139 ),
inference(simp,[status(thm)],[45731]) ).
thf(308,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattice4) ).
thf(2651,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(1742,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(961,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_filter_0) ).
thf(5275,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(2810,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(3025,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(26840,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != sk72 ) ),
inference(paramod_ordered,[status(thm)],[1518,6286]) ).
thf(26841,plain,
v1_relat_1 @ ( sk27 @ sk72 ),
inference(pattern_uni,[status(thm)],[26840:[bind(A,$thf( sk72 ))]]) ).
thf(752,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_openlatt @ A ) @ ( k3_lattices @ A @ B @ C ) )
= ( k2_xboole_0 @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ B ) @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_openlatt) ).
thf(4484,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_openlatt @ A ) @ ( k3_lattices @ A @ B @ C ) )
= ( k2_xboole_0 @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ B ) @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(3245,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(6109,plain,
~ ( v3_struct_0 @ k13_nat_lat ),
inference(cnf,[status(esa)],[6106]) ).
thf(1128,axiom,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_nat_lat) ).
thf(5945,plain,
( ~ ( v3_struct_0 @ k6_nat_lat )
& ( v10_lattices @ k6_nat_lat )
& ( l3_lattices @ k6_nat_lat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(5500,plain,
l1_struct_0 @ sk316,
inference(cnf,[status(esa)],[5496]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_boolealg @ A @ B @ C )
= ( k3_boolealg @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_boolealg) ).
thf(4848,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_boolealg @ A @ B @ C )
= ( k3_boolealg @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(3057,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(338,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_ringcat1 @ A ) )
=> ? [B: $i] : ( m3_ringcat1 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_ringcat1) ).
thf(2803,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v5_ringcat1 @ A ) )
=> ? [B: $i] : ( m3_ringcat1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(78,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(1532,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(728,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) )
=> ( ( r3_lattices @ ( k15_openlatt @ A ) @ B @ C )
<=> ( r1_tarski @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_openlatt) ).
thf(4382,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) )
=> ( ( ( r3_lattices @ ( k15_openlatt @ A ) @ B @ C )
=> ( r1_tarski @ B @ C ) )
& ( ( r1_tarski @ B @ C )
=> ( r3_lattices @ ( k15_openlatt @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(527,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_pre_topc) ).
thf(3605,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(889,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_filter_0 @ A @ B ) @ C ) ) )
& ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_filter_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_filter_0) ).
thf(4972,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_filter_0 @ A @ B ) @ C ) ) )
& ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_filter_0 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(15292,plain,
( ~ ( v12_lattices @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) )
| ( ( v1_xboole_0 @ sk1 )
!= ( v1_xboole_0 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1922,12892]) ).
thf(15324,plain,
( ~ ( v12_lattices @ ( k23_filter_2 @ k1_xboole_0 @ sk2 ) )
| ( sk1 != k1_xboole_0 ) ),
inference(simp,[status(thm)],[15292]) ).
thf(1058,axiom,
! [A: $i,B: $i] :
( ( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k17_grcat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_grcat_1) ).
thf(5637,plain,
! [A: $i,B: $i] :
( ( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k17_grcat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_subset_1) ).
thf(2265,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(604,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
<=> ( v13_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_lattice2) ).
thf(3869,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v14_lattices @ A )
=> ( v13_lattices @ ( k1_lattice2 @ A ) ) )
& ( ( v13_lattices @ ( k1_lattice2 @ A ) )
=> ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_subset_1) ).
thf(1976,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(1136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( v1_xboole_0 @ ( k26_gate_1 @ A @ B @ C @ D @ E @ F @ G ) )
<=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_gate_1) ).
thf(5975,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ~ ( v1_xboole_0 @ ( k26_gate_1 @ A @ B @ C @ D @ E @ F @ G ) )
=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G ) ) )
& ( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ~ ( v1_xboole_0 @ C )
& ~ ( v1_xboole_0 @ D )
& ~ ( v1_xboole_0 @ E )
& ~ ( v1_xboole_0 @ F )
& ~ ( v1_xboole_0 @ G ) )
=> ~ ( v1_xboole_0 @ ( k26_gate_1 @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk13 @ A ) )
| ( m1_subset_1 @ ( sk14 @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( v4_lattice3 @ A ) ),
inference(cnf,[status(esa)],[1350]) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( v3_struct_0 @ A )
| ~ ( l3_lattices @ A )
| ~ ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
| ~ ( r4_lattice3 @ A @ B @ ( sk13 @ A ) )
| ( m1_subset_1 @ ( sk14 @ B @ A ) @ ( u1_struct_0 @ A ) )
| ( v4_lattice3 @ A ) ),
inference(simp,[status(thm)],[1351]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k15_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(4506,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k15_lattice3 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(6922,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( m1_subset_1 @ ( sk5 @ A ) @ A )
| ( ( v1_realset1 @ sk72 )
!= ( v1_realset1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2114,1223]) ).
thf(6923,plain,
( ( v1_xboole_0 @ sk72 )
| ( m1_subset_1 @ ( sk5 @ sk72 ) @ sk72 ) ),
inference(pattern_uni,[status(thm)],[6922:[bind(A,$thf( sk72 ))]]) ).
thf(7070,plain,
( $false
| ( m1_subset_1 @ ( sk5 @ sk72 ) @ sk72 ) ),
inference(rewrite,[status(thm)],[6923,2115]) ).
thf(7071,plain,
m1_subset_1 @ ( sk5 @ sk72 ) @ sk72,
inference(simp,[status(thm)],[7070]) ).
thf(454,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( m1_subset_1 @ ( k3_tarski @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_borsuk_1) ).
thf(3259,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( m1_subset_1 @ ( k3_tarski @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_1) ).
thf(5958,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1091,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ C )
= ( k1_filter_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_filter_1) ).
thf(5768,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ C )
= ( k1_filter_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(686,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(4206,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(508,axiom,
! [A: $i] :
( ( v2_setfam_1 @ A )
<=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( r2_hidden @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_setfam_1) ).
thf(3538,plain,
! [A: $i] :
( ( ( v2_setfam_1 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( r2_hidden @ B @ A ) ) )
& ( ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( r2_hidden @ B @ A ) )
=> ( v2_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(627,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k3_boolealg @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_boolealg) ).
thf(3939,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_boolealg @ A @ ( k4_lattices @ A @ B @ C ) @ ( k3_boolealg @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(2539,plain,
l2_lang1 @ sk101,
inference(cnf,[status(esa)],[2538]) ).
thf(353,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( C
= ( k7_lattices @ A @ B ) )
<=> ( r2_lattices @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattices) ).
thf(2864,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( C
= ( k7_lattices @ A @ B ) )
=> ( r2_lattices @ A @ C @ B ) )
& ( ( r2_lattices @ A @ C @ B )
=> ( C
= ( k7_lattices @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(270,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( ( v1_relat_1 @ ( k2_xboole_0 @ A @ C ) )
& ( v1_funct_1 @ ( k2_xboole_0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_grfunc_1) ).
thf(2484,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( ( v1_relat_1 @ ( k2_xboole_0 @ A @ C ) )
& ( v1_funct_1 @ ( k2_xboole_0 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(9839,plain,
! [A: $i] :
( ( v1_finset_1 @ ( k1_tarski @ A ) )
!= ( v1_finset_1 @ sk139 ) ),
inference(paramod_ordered,[status(thm)],[1699,2992]) ).
thf(9842,plain,
! [A: $i] :
( ( k1_tarski @ A )
!= sk139 ),
inference(simp,[status(thm)],[9839]) ).
thf(3812,plain,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(cnf,[status(esa)],[3811]) ).
thf(1061,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_filter_0) ).
thf(5645,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(722,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( v1_filter_0 @ D @ A )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
<=> ( ( r2_hidden @ B @ D )
| ( r2_hidden @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lopclset) ).
thf(4345,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( v1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
=> ( ( r2_hidden @ B @ D )
| ( r2_hidden @ C @ D ) ) )
& ( ( ( r2_hidden @ B @ D )
| ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(758,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( v3_lattice4 @ ( k13_lopclset @ A ) @ A @ ( k12_lopclset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_lopclset) ).
thf(4501,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( v3_lattice4 @ ( k13_lopclset @ A ) @ A @ ( k12_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(1399,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
| ( m1_subset_1 @ ( sk17 @ A ) @ A )
| ~ ( v1_realset1 @ A ) ),
inference(cnf,[status(esa)],[1397]) ).
thf(705,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) )
<=> ( ( r2_hidden @ B @ ( k7_openlatt @ A ) )
& ( r2_hidden @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_openlatt) ).
thf(4271,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ B @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) )
=> ( ( r2_hidden @ B @ ( k7_openlatt @ A ) )
& ( r2_hidden @ C @ B ) ) )
& ( ( ( r2_hidden @ B @ ( k7_openlatt @ A ) )
& ( r2_hidden @ C @ B ) )
=> ( r2_hidden @ B @ ( k1_funct_1 @ ( k8_openlatt @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(692,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k12_lopclset @ A ) )
& ( v10_lattices @ ( k12_lopclset @ A ) )
& ( l3_lattices @ ( k12_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_lopclset) ).
thf(4221,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k12_lopclset @ A ) )
& ( v10_lattices @ ( k12_lopclset @ A ) )
& ( l3_lattices @ ( k12_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(981,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) )
<=> ( r3_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
thf(5344,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ A @ B @ C )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1331,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ A )
| ~ ( v1_finset_1 @ A )
| ~ ( v1_trees_1 @ A )
| ( v1_xboole_0 @ B )
| ~ ( v1_finset_1 @ B )
| ~ ( v1_trees_1 @ B )
| ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(cnf,[status(esa)],[1329]) ).
thf(942,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) )
=> ( ( ( k3_lattices @ ( k15_openlatt @ A ) @ B @ C )
= ( k2_xboole_0 @ B @ C ) )
& ( ( k4_lattices @ ( k15_openlatt @ A ) @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_openlatt) ).
thf(5172,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k15_openlatt @ A ) ) )
=> ( ( ( k3_lattices @ ( k15_openlatt @ A ) @ B @ C )
= ( k2_xboole_0 @ B @ C ) )
& ( ( k4_lattices @ ( k15_openlatt @ A ) @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(3950,plain,
l1_funcsdom @ sk201,
inference(cnf,[status(esa)],[3949]) ).
thf(601,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( B
!= ( k17_filter_2 @ A ) )
& ( v1_filter_2 @ B @ A ) )
<=> ( r2_filter_2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_filter_2) ).
thf(3854,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_filter_2 @ B @ A )
=> ( ( ( ( B
!= ( k17_filter_2 @ A ) )
& ( v1_filter_2 @ B @ A ) )
=> ( r2_filter_2 @ A @ B ) )
& ( ( r2_filter_2 @ A @ B )
=> ( ( B
!= ( k17_filter_2 @ A ) )
& ( v1_filter_2 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(829,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_boolealg) ).
thf(4767,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r1_boolealg @ A @ ( k1_boolealg @ A @ B @ ( k4_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ ( k1_boolealg @ A @ B @ C ) @ ( k1_boolealg @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(316,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_filter_0) ).
thf(2690,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1097,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v12_lattices @ A )
=> ( v12_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_filter_0) ).
thf(5788,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v12_lattices @ A )
=> ( v12_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(384,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lopclset) ).
thf(2993,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(3047,plain,
! [A: $i,B: $i] :
( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(3580,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1318,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
inference(miniscope,[status(thm)],[1317]) ).
thf(1319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_tarski @ A )
!= ( k2_xboole_0 @ B @ C ) )
| ( B = C )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1318]) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_tarski @ A )
!= ( k2_xboole_0 @ B @ C ) )
| ( B = C )
| ( B = k1_xboole_0 )
| ( C = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1319]) ).
thf(1116,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) )
<=> ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_filter_1) ).
thf(5877,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) )
=> ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) )
=> ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1172,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_lattice4 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(6173,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_lattice4 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(764,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_filter_0) ).
thf(4520,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(234,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( a_2_1_lattice4 @ A @ B )
= ( k3_lattice4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice4) ).
thf(2321,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( a_2_1_lattice4 @ A @ B )
= ( k3_lattice4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1639,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_funct_1 @ ( sk38 @ B @ A ) ) ),
inference(cnf,[status(esa)],[1635]) ).
thf(1652,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( v1_funct_1 @ ( sk38 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[1639]) ).
thf(1653,plain,
! [A: $i] : ( v1_funct_1 @ ( sk38 @ k1_xboole_0 @ A ) ),
inference(simp,[status(thm)],[1652]) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ( B = k1_xboole_0 )
| ( r2_hidden @ ( sk15 @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[1364]) ).
thf(1367,plain,
! [B: $i,A: $i] :
( ( B = k1_xboole_0 )
| ~ ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
| ( r2_hidden @ ( sk15 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[1365]) ).
thf(797,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_filter_0 @ A @ ( k1_filter_0 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_filter_0) ).
thf(4627,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_filter_0 @ A @ ( k1_filter_0 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(4584,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_struct_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(621,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_filter_0) ).
thf(3924,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(973,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_0) ).
thf(5312,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k20_filter_2 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_filter_2) ).
thf(5494,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k20_filter_2 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(869,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r1_filter_0 @ A @ D @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_filter_0) ).
thf(4891,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r1_filter_0 @ A @ D @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(49468,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk18 @ B @ A )
= C )
| ( ( k4_xboole_0 @ A @ k1_xboole_0 )
!= ( k4_xboole_0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1313,1410]) ).
thf(49469,plain,
! [A: $i] :
( ( sk18 @ k1_xboole_0 @ A )
= A ),
inference(pattern_uni,[status(thm)],[49468:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(1063,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_filter_2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_2) ).
thf(5649,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_filter_2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(681,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m2_filter_2 @ B @ A )
<=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_2) ).
thf(4161,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m2_filter_2 @ B @ A )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) )
& ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ D @ C ) )
=> ( r2_hidden @ D @ B ) ) ) ) )
=> ( m2_filter_2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(7272,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ~ ( v17_lattices @ sk1 )
| ( v3_realset2 @ sk1 )
| ~ ( v1_funct_1 @ ( k8_lopclset @ sk1 ) )
| ( ( v1_relat_1 @ ( k8_lopclset @ sk1 ) )
!= ( v1_relat_1 @ k1_xboole_0 ) ) ),
inference(paramod_ordered,[status(thm)],[1941,7250]) ).
thf(7284,plain,
( ( ( u1_struct_0 @ sk1 )
= ( k1_relat_1 @ ( k8_lopclset @ sk1 ) ) )
| ( v3_realset2 @ sk1 )
| ~ ( v17_lattices @ sk1 )
| ~ ( v1_funct_1 @ ( k8_lopclset @ sk1 ) )
| ( ( k8_lopclset @ sk1 )
!= k1_xboole_0 ) ),
inference(simp,[status(thm)],[7272]) ).
thf(135,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k1_pre_topc @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(1848,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k1_pre_topc @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(69,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relat_1) ).
thf(1490,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(821,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_struct_0 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_struct_0) ).
thf(4742,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ( m1_struct_0 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m1_struct_0 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(228,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ C ) ) )
& ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k19_filter_2 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_filter_2) ).
thf(2297,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ B ) @ C ) ) )
& ( r1_filter_2 @ ( u1_struct_0 @ A ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k19_filter_2 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k19_filter_2 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(5445,plain,
l2_quantal1 @ sk310,
inference(cnf,[status(esa)],[5444]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_openlatt @ B @ C ) )
<=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_openlatt) ).
thf(4977,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_openlatt @ B @ C ) )
=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( A = D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_1_openlatt @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(736,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(4423,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(398,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_filter_0) ).
thf(3052,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(860,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ D )
=> ( ( r3_lattices @ A @ B @ D )
& ( r3_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boolealg) ).
thf(4863,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ D )
=> ( ( r3_lattices @ A @ B @ D )
& ( r3_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(10599,plain,
! [B: $i,A: $i] :
( ( v1_xboole_0 @ ( sk213 @ A ) )
!= ( v1_xboole_0 @ ( k1_zfmisc_1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4092,4239]) ).
thf(10601,plain,
! [B: $i,A: $i] :
( ( sk213 @ A )
!= ( k1_zfmisc_1 @ B ) ),
inference(simp,[status(thm)],[10599]) ).
thf(25831,plain,
! [A: $i] :
( ( k1_zfmisc_1 @ A )
!= k1_xboole_0 ),
inference(rewrite,[status(thm)],[10601,13755]) ).
thf(1082,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k3_gate_1 @ A @ B ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ( v1_xboole_0 @ ( k3_gate_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_gate_1) ).
thf(5732,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( v1_xboole_0 @ ( k3_gate_1 @ A @ B ) )
& ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ~ ( ~ ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B ) )
& ( v1_xboole_0 @ ( k3_gate_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( v1_xboole_0 @ ( k33_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
<=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G )
& ( v1_xboole_0 @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_gate_1) ).
thf(6094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ~ ( v1_xboole_0 @ ( k33_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
=> ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G )
& ( v1_xboole_0 @ H ) ) )
& ( ( ( v1_xboole_0 @ A )
& ( v1_xboole_0 @ B )
& ( v1_xboole_0 @ C )
& ( v1_xboole_0 @ D )
& ( v1_xboole_0 @ E )
& ( v1_xboole_0 @ F )
& ( v1_xboole_0 @ G )
& ( v1_xboole_0 @ H ) )
=> ~ ( v1_xboole_0 @ ( k33_gate_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(1121,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k3_zf_model @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zf_model) ).
thf(5911,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k3_zf_model @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(26528,plain,
! [A: $i] :
( ( v1_relat_1 @ ( sk27 @ A ) )
| ( A != k4_modal_1 ) ),
inference(paramod_ordered,[status(thm)],[1518,6667]) ).
thf(26529,plain,
v1_relat_1 @ ( sk27 @ k4_modal_1 ),
inference(pattern_uni,[status(thm)],[26528:[bind(A,$thf( k4_modal_1 ))]]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(3575,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(1870,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(53733,plain,
$false,
inference(e,[status(thm)],[3962,13955,4909,4262,5390,5676,6074,4904,5385,5810,1322,1665,5686,2822,2094,5469,3944,1411,25928,4094,26016,5918,1469,5088,1369,4835,2295,2306,4571,15278,3345,5136,6231,4899,3798,4022,1729,3434,3167,45837,1237,2921,4290,3477,3698,1840,13933,3969,1982,5028,4728,2309,1406,1290,5297,4960,4603,45811,4623,6194,1855,1200,5444,3534,1750,49475,6022,3681,1211,3990,3072,1924,3317,5168,5820,4339,14625,2622,7008,4311,2808,6106,14996,3813,3230,6199,13062,4391,3153,1422,1569,2248,42640,15045,3910,5793,2114,5405,1793,4614,18284,6017,45832,25970,15153,4747,4487,6480,4592,26066,5501,5120,1608,1655,3120,4528,2448,5257,5701,4564,5674,1354,3717,4762,3276,2195,3017,4543,5425,5814,4234,1310,26004,6246,3367,5755,3648,4026,3044,5288,1735,6127,1275,2141,38135,1260,1342,3121,6680,4247,5005,6117,5708,1954,3577,2042,45801,2046,1914,13098,5476,3898,1529,2819,2957,1196,4047,6236,4792,1835,3836,4343,3236,3545,2723,5393,3915,2548,2491,1243,2985,4496,1391,5123,5518,3249,4079,5745,5195,1650,5825,1645,3730,26186,2886,11024,1359,1601,3281,5301,3140,4137,6291,1518,1265,4610,25940,9850,4948,1228,3597,26996,1254,3688,5621,4249,5352,3891,1409,10286,6274,3495,4761,5064,1323,38131,4778,5160,5712,2745,1287,4546,5585,2603,4524,5306,4866,3644,2039,6034,4070,15229,4654,1330,1264,4334,2682,1826,5150,1313,4349,1279,4275,5182,3089,2897,5989,2466,2126,4428,6208,3043,5279,45800,6130,2703,15182,1922,5605,1479,5925,4675,3951,4265,5076,5617,37686,3788,1800,26970,13961,3374,2169,3638,4617,5521,27028,1247,6310,4664,40410,5397,2373,5323,1347,3919,1398,7075,1931,1568,5942,3014,4952,2024,3708,1494,13102,3602,4400,4771,5077,4514,26403,2533,1232,4967,2007,5787,4857,1911,2893,4733,45833,6176,2254,2540,5259,27087,4988,1415,2616,1946,3524,3431,1302,5892,2794,3887,2324,1714,2027,3199,5526,3934,4578,3075,5597,4820,5856,1418,2451,3527,6410,3702,1858,4147,4050,2925,3973,26012,5914,12794,5156,5135,3093,1581,2335,14500,3986,1215,3421,12670,1796,2979,1394,4825,6021,21972,45838,9822,3389,2508,2964,5059,2367,2437,5773,4033,3739,2281,6110,5375,3712,13072,5246,1526,5321,3676,13600,1345,2799,2103,1405,4643,1943,1201,5137,6156,4707,38246,1697,1242,4285,5328,4211,12892,2982,2884,2954,3582,6020,1691,3720,6047,45808,5291,21998,6092,3679,1863,26567,5961,3097,1206,3011,7533,5012,4199,5875,4216,5783,4893,4323,3301,4962,3852,1306,4531,1199,3635,2364,5968,5545,1338,13104,5142,1311,5862,4576,2307,1736,2496,3735,4915,1387,2805,4375,5719,3233,4449,6107,5102,4661,3261,1223,2601,3827,6247,6000,27054,14357,4397,5002,1355,6032,1570,4989,5044,5349,2133,2147,5266,3022,5455,4344,4091,2606,4785,4499,3778,13250,1238,4044,3286,5843,3271,4725,5690,4385,1296,2609,1291,5285,6090,6926,2464,14789,45840,2873,3269,3618,4608,41593,24111,2477,2332,26283,4757,5177,27188,3750,1457,4776,5534,5988,3894,5551,14338,4402,4942,1210,1656,5566,6060,2213,4740,6168,3028,3926,1195,1407,6267,5858,3763,4104,3727,1281,1634,40469,3667,3931,1740,1573,5515,2895,4525,3386,3078,6919,2268,4808,2245,1350,4123,1360,5189,2300,3784,2498,3615,3831,2115,3482,5145,1762,2515,3254,1851,1259,3122,2946,2990,10295,5673,2685,5423,1804,5615,1328,1375,27139,7173,5635,1970,1227,26980,1498,1587,5428,1672,3119,5373,1755,3941,6128,4109,38119,5497,3060,1397,2460,1329,45789,1361,5915,5107,45829,5253,3671,27178,5387,2023,5166,3143,45836,5818,3922,5080,5496,3622,35511,5651,6116,3094,4425,3714,6363,2312,5464,4750,1414,1842,26287,1584,5547,1700,2613,1937,1810,3428,1214,5865,3194,2349,4444,2666,3555,4457,12724,7448,3573,3242,25896,1451,2487,3770,2581,3222,3064,2140,1393,2370,26293,2285,6752,1776,5273,1263,4846,3611,6134,2836,1382,3354,2387,1231,3743,5639,5134,6207,6129,1192,2355,5498,2505,3819,4237,3937,4717,4120,5683,3628,5823,3115,26142,1429,3967,3247,2862,4135,2482,1246,1979,5026,1333,4535,3834,2926,5711,5402,4782,4765,6279,25857,2408,4036,5249,3807,5170,3454,3824,5112,26064,5557,5747,1202,4352,2203,44671,14961,3225,3279,4889,3587,3183,3173,6859,3999,3321,4906,2915,2645,5513,6038,5909,3841,6311,39322,2338,1996,4308,2936,5524,2677,4872,3042,1927,1301,5715,5241,4921,1278,26291,2001,1251,5483,3130,5808,4116,4613,5138,2149,4594,3257,2717,1219,6203,4874,2570,44512,5016,4503,6228,4359,18682,5647,3686,2894,1374,2524,2376,3158,38044,3536,2970,3768,2789,4677,1388,37519,1403,6019,14044,4144,3372,6234,3741,7287,4341,4268,2727,6916,2859,5474,1884,4283,1784,4494,1389,3255,3811,6108,3240,5395,2791,45807,13060,5923,1752,13755,3900,5099,5876,1795,2398,4590,4612,2817,4769,1256,1226,1488,2959,3213,4526,5546,6667,4099,1733,5314,1765,13958,3568,3170,3532,5033,2220,3964,5567,4096,2293,5471,26772,1271,2308,1371,5331,5282,4218,4573,3340,3594,1332,6649,3123,3700,4060,2457,4854,6123,14957,6248,5158,3091,2474,4887,5432,2358,4433,5634,5556,2510,2361,4790,5212,3815,5103,10675,6197,3732,5491,3197,4388,1194,13995,2346,1209,2721,2119,4337,2679,4704,4228,2538,1282,26367,5506,3238,2624,5244,5325,4305,4620,1806,1349,5631,1492,1603,1722,5054,4139,4586,2116,5610,6289,2856,3138,5795,2896,38254,3384,5972,4773,2871,1376,4509,2197,1307,4203,2742,1339,1838,3298,5466,1381,5367,5511,6087,5816,2812,5657,3055,4103,3668,4833,4462,2111,37450,1993,4818,4731,4028,1731,26944,1909,26042,4985,4452,5599,45820,3971,1344,2542,1460,2252,3861,7250,1293,5007,5780,2710,5742,4232,26431,22067,2139,1775,2535,1198,4720,1396,2725,2401,1699,1213,37698,3759,3838,2620,5641,10782,6288,3917,5516,3953,2797,4918,2022,1364,2390,1250,1496,5299,6027,26158,4067,12890,43284,40603,3908,2693,4209,1973,4481,17809,5619,4084,1413,5548,1873,5757,3146,4292,2927,5763,2899,3571,3849,3522,3009,13144,4394,4441,2096,1758,4901,1203,15276,5881,6276,6225,13310,2271,35476,5785,4598,3161,4735,1277,6191,14438,4566,4859,2202,2846,2256,4581,27189,5710,5133,4722,2942,27152,25946,6399,5388,3949,39851,4630,5790,5446,3988,2513,3737,3376,6120,3640,33617,5607,1961,45812,5602,2661,6051,1225,5478,1400,5399,2143,2012,2588,5499,3754,4950,2732,1941,1252,5074,1368,4517,3228,5721,4961,3786,1267,3872,4377,3608,1230,44831,7586,15323,4593,2888,10027,33649,4561,4240,3722,3554,26936,1262,1336,13172,1711,3019,3448,4314,5262,1987,2454,1432,4190,3885,1813,1300,2688,3334,45793,2700,4003,26006,26355,3202,2276,5030,6125,45835,5154,5203,5309,1317,1830,6313,5543,5152,2545,2599,3329,2044,6159,1285,1218,5450,3095,3853,26688,5277,3493,1702,5347,5613,1797,2848,13256,1404,5319,1358,1934,5949,6188,2411,4057,1257,5675,4959,2113,3415,5628,3124,2992,1221,1284,2975,1353,5504,4106,4991,2579,10028,5633,5453,1427,4235,14853,4202,3117,5364,2949,26946,1717,2030,4225,4342,6917,5717,4838,3256,6358,1881,6161,1272,4795,3007,13342,4150,3684,3288,1240,4217,3565,1459,4763,5966,6137,3928,2643,1998,5771,1940,3284,2760,6286,45823,2924,3946,4548,4278,4651,3620,2626,3457,1316,26313,2352,3757,2479,4851,4606,4945,2818,3067,5653,13812,7177,24105,5660,5386,1321,7288,1412,2215,5421,5115,4780,1781,1216,3625,4646,3725,5907,2997,4102,13178,1390,2342,1575,1734,21996,1807,1276,1326,1253,2273,1341,1508,1481,6023,6913,3561,1523,13252,4710,2988,10697,3864,2283,4806,2853,2290,4615,12698,2406,4089,5382,4468,3369,4042,4715,2004,3331,4881,5104,3252,4823,4969,1558,2934,2152,5600,3085,5963,3978,4649,2912,4478,4446,1893,6871,4869,2019,26830,5828,1861,3181,2786,5164,5162,21962,45817,4153,3879,6290,4214,2648,3585,6118,1777,5692,4759,6018,6045,1294,5109,5023,3149,1308,3896,2198,27160,3529,1193,14289,2162,5568,6062,2680,1212,5072,3351,5739,1661,5704,3552,2287,13991,1678,3291,4811,1229,5554,3882,3264,4843,42657,5760,4455,3164,3379,15425,27294,5187,2218,4125,5051,26052,4039,1348,2302,5009,2517,3705,1280,2155,14499,4596,6131,15108,3100,5430,2951,4523,4787,1303,4841,3790,3337,6671,3132,5371,2050,5601,4491,3496,4885,5014,3690,1989,15123,26960,3558,3804,4474,6287,2714,3765,5559,3822,2751,2800,45834,1363,1314,5709,4281,3347,5105,45839,1693,2572,5462,1561,3479,1410,6765,1288,1197,2404,45778,2223,12944,3633,4193,4912,6612,3045,5200,3673,2021,9987,45794,2651,1742,13646,5275,2810,3025,1268,26841,4484,3245,6109,5945,6190,5500,4848,3057,2803,1532,4382,3605,4972,15324,1378,5637,2265,3869,1976,5975,6205,4987,1357,4506,7071,3259,4239,6233,5958,5768,4206,3538,3939,2539,2864,1880,1431,2484,9842,3812,5645,4345,4501,1399,4271,4221,6658,5344,2138,1331,5172,3950,3854,4767,2690,5788,1416,2993,3047,3580,1320,5877,5913,6173,12908,4520,2321,1653,1367,4627,4584,3924,5986,5312,5494,4891,5707,49469,6842,5649,10763,4161,7284,1848,1490,4742,2297,5445,1917,4977,4423,3052,4863,25831,5732,6739,3553,6094,5911,26529,3575,1417,1870,7442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT334+4 : TPTP v8.2.0. Released v3.4.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 21:12:14 EDT 2024
% 0.14/0.36 % CPUTime :
% 1.16/1.17 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 11.09/5.22 % [INFO] Parsing done (4047ms).
% 11.09/5.25 % [INFO] Running in sequential loop mode.
% 11.74/5.71 % [INFO] eprover registered as external prover.
% 11.74/5.71 % [INFO] cvc4 registered as external prover.
% 11.98/5.72 % [INFO] Scanning for conjecture ...
% 19.79/8.42 % [INFO] Found a conjecture (or negated_conjecture) and 34749 axioms. Running axiom selection ...
% 32.29/16.76 % [INFO] Axiom selection finished. Selected 1189 axioms (removed 33560 axioms).
% 35.14/17.69 % [INFO] Problem is first-order (TPTP FOF).
% 35.25/17.75 % [INFO] Type checking passed.
% 35.25/17.76 % [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 ...
% 296.99/68.02 % External prover 'e' found a proof!
% 296.99/68.02 % [INFO] Killing All external provers ...
% 296.99/68.02 % Time passed: 67482ms (effective reasoning time: 62764ms)
% 296.99/68.02 % 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)>
% 296.99/68.03 % Axioms used in derivation (1189): rc2_setfam_1, t10_rpr_1, t7_filter_0, rc2_lopclset, dt_k4_filter_2, t14_realset1, fraenkel_a_1_0_domain_1, d16_lattice3, dt_k7_filter_0, dt_l1_prelamb, t15_finset_1, d14_filter_2, t51_filter_1, t42_xboole_1, t30_lopclset, t37_orders_2, t2_filter_0, t31_boolealg, dt_k9_filter_2, dt_k5_filter_1, t50_lattice4, t2_quantal1, t21_zfmisc_1, t20_filter_1, t44_xboole_1, t11_filter_2, t13_zfmisc_1, t24_filter_0, d13_filter_0, t38_filter_2, t30_coh_sp, t39_lattices, t31_filter_0, t36_lopclset, d5_lopclset, t35_subset_1, d1_tarski, fc11_finseq_1, rc2_funcsdom, t19_xboole_1, dt_g1_struct_0, t26_lopclset, t17_xboole_1, t17_gate_1, t37_lattice2, dt_k1_filter_1, t78_filter_0, t42_subset_1, cc2_finset_1, t20_zfmisc_1, t3_rlvect_2, t62_filter_0, t68_boolealg, t14_finset_1, cc2_tex_2, t36_grfunc_1, dt_k1_filter_2, dt_k2_trees_3, t56_filter_1, t53_subset_1, t44_filter_2, fraenkel_a_1_0_filter_1, rc3_lang1, t30_lattice2, t29_filter_0, t48_filter_1, t24_lattice4, rc2_tex_1, d6_filter_0, t23_gate_1, t54_filter_1, rc6_grcat_1, t140_zfmisc_1, t109_xboole_1, idempotence_k3_xboole_0, redefinition_k16_filter_2, rc4_finset_1, t35_filter_1, t50_boolealg, t1_boole, d6_lattice2, t7_subset_1, t10_filter_2, dt_k3_prelamb, t23_xboole_1, t36_lattice4, t19_filter_2, fc2_pre_topc, t15_filter_1, t9_boolealg, symmetry_r1_filter_1, t34_filter_2, t34_gate_1, redefinition_k5_subset_1, t2_collsp, t81_filter_0, t3_boolealg, t3_xboole_1, d4_lattice4, t58_boolealg, dt_k6_filter_1, t35_trees_2, t8_grfunc_1, t29_boolealg, t52_trees_1, t34_xboole_1, t113_xboole_1, rc7_finseq_1, t64_funct_5, t24_boolealg, t9_filter_2, t6_grfunc_1, t63_filter_2, t43_lattices, t13_openlatt, fc1_xboole_0, t53_filter_1, t28_filter_2, t42_filter_0, cc6_lattices, t51_lattice3, fc3_funcsdom, t7_boolealg, t67_lattice2, t48_domain_1, t59_filter_2, t34_grfunc_1, t8_subset_1, t80_lattice2, t15_funct_1, dt_k11_domain_1, fc4_relat_1, t19_lattices, t4_ordinal1, t1_subset, t25_boolealg, dt_k1_lattice4, t10_partfun1, existence_l1_funcsdom, commutativity_k11_openlatt, t52_zfmisc_1, rc2_rlvect_2, t21_boolealg, fc3_realset1, t43_xboole_1, t81_zfmisc_1, t16_fraenkel, t9_measure1, t18_xboole_1, t4_funcop_1, dt_k15_filter_2, t45_boolealg, t6_xboole_1, d5_xboole_0, t38_filter_1, t70_filter_2, t29_subset_1, t35_gate_1, t4_lattice4, cc9_tex_2, t12_openlatt, t12_filter_2, existence_l3_lattices, dt_k6_nat_lat, t39_filter_2, t53_lattices, d2_group_6, t23_lopclset, t87_filter_0, t16_setwiseo, t6_lattice3, fc3_relat_1, t96_zfmisc_1, t45_filter_1, t43_lattice3, t21_lattice2, fc4_openlatt, d8_funct_1, t19_relat_1, dt_k16_filter_2, dt_k13_domain_1, fc1_lattice2, t69_filter_0, redefinition_k13_lopclset, fc22_trees_3, t86_boolealg, t57_filter_2, existence_m1_rfunct_3, t14_gate_1, t2_boole, dt_k1_lattice2, t2_card_fil, t29_openlatt, t83_filter_0, dt_k1_struct_0, t35_lattice4, t85_filter_0, t23_pre_topc, t23_filter_0, t41_boolealg, dt_m2_nat_lat, existence_m3_lattice4, t25_xboole_1, existence_m1_struct_0, t18_filter_0, dt_k3_lattice4, t29_lopclset, fraenkel_a_2_0_lattice4, dt_k4_subset_1, rc1_tex_1, t27_xboole_1, t55_filter_2, t1_gate_1, t12_pre_topc, t43_zfmisc_1, redefinition_k12_filter_2, t22_lattice3, rc4_lang1, dt_k19_filter_2, t95_zfmisc_1, t14_filter_0, t28_openlatt, t18_relat_1, fc1_filter_0, t48_filter_0, d9_lattice4, fc1_tex_1, cc1_sgraph1, t64_filter_2, t35_openlatt, t68_filter_2, fraenkel_a_2_0_filter_0, t99_zfmisc_1, t20_gate_1, t50_wellord1, cc4_lattices, redefinition_k11_filter_0, fc2_filter_2, t13_pre_topc, rc3_funct_1, t14_boolealg, t41_lattice2, t45_zfmisc_1, l70_filter_2, t34_lattice3, dt_k5_filter_0, dt_k3_filter_0, t1_rpr_1, t69_zfmisc_1, d1_struct_0, dt_k1_boolealg, t37_xboole_1, t41_zfmisc_1, cc1_relat_1, t43_filter_2, idempotence_k5_subset_1, t36_subset_1, t83_boolealg, commutativity_k3_xboole_0, t32_filter_0, dt_k10_filter_1, t26_filter_0, t47_filter_1, t17_funct_1, t9_xboole_1, t21_filter_2, existence_m3_grcat_1, t18_finset_1, dt_k5_filter_2, fc2_modal_1, abstractness_v1_struct_0, t49_zfmisc_1, dt_k1_pre_topc, reflexivity_r1_filter_1, t33_lattice4, existence_l2_lang1, t30_gate_1, t95_orders_1, dt_k8_lopclset, d3_pre_topc, t19_funct_1, dt_k15_openlatt, t2_partfun1, rc1_funct_1, fc2_xboole_0, t31_relat_1, t55_boolealg, existence_l2_quantal1, t32_subset_1, d5_realset2, dt_m1_filter_2, redefinition_k6_filter_0, dt_k1_filter_0, dt_k6_filter_2, existence_m2_card_fil, t36_boolealg, dt_m2_lattice4, d8_openlatt, t41_filter_2, d11_filter_0, fc11_finset_1, t5_tex_2, t26_filter_2, t31_lattices, t71_filter_2, redefinition_r1_boolealg, dt_k4_lattice3, t29_finset_1, involutiveness_k3_subset_1, t40_boolealg, t13_relat_1, existence_m3_ringcat1, t53_filter_0, redefinition_k13_filter_2, dt_k7_real_lat, d18_lattice3, t27_relat_1, d1_xboole_0, existence_m2_unialg_2, t56_filter_0, commutativity_k8_rlvect_2, t61_boolealg, rc6_finseq_1, t36_filter_1, dt_m1_unialg_2, cc1_tex_2, cc10_tex_2, t57_filter_0, dt_k13_funcsdom, t15_relat_1, d16_lattice4, t70_filter_0, dt_k12_lopclset, t20_filter_2, cc7_tex_2, t108_xboole_1, t72_filter_0, t48_filter_2, t24_lopclset, d2_tex_2, t46_filter_0, t40_lattice2, t64_relat_1, t37_boolealg, t37_filter_0, t66_filter_2, fraenkel_a_3_0_filter_0, rc3_lattices, t52_filter_0, rc10_tex_2, t51_xboole_1, redefinition_k1_filter_1, t52_domain_1, dt_k12_filter_2, t45_filter_2, fc10_finset_1, t3_tops_2, t26_finset_1, dt_k7_lattices, t50_xboole_1, redefinition_m3_grcat_1, t85_boolealg, dt_k4_lattice4, t19_lopclset, t26_boolealg, t76_nat_lat, dt_m2_card_fil, t39_lattice4, t38_lattice4, dt_k11_filter_2, t28_lopclset, t46_zfmisc_1, t74_filter_2, d15_lattice4, fc2_funct_2, t6_boole, t12_funct_1, t42_gate_1, rc2_subset_1, fc9_finset_1, dt_k6_subset_1, t10_relat_1, t33_openlatt, existence_l1_prelamb, t2_filter_1, t59_filter_0, t24_finsub_1, l59_filter_2, t28_grfunc_1, t75_filter_2, t50_filter_2, t32_gate_1, t28_wellord2, t74_boolealg, t29_grfunc_1, commutativity_k2_xboole_0, redefinition_m3_ringcat1, t5_subset, t44_filter_1, t30_grfunc_1, t1_xboole_1, t17_filter_2, t16_openlatt, t29_relat_1, d14_lattice4, cc1_finseq_5, t6_rpr_1, t4_tex_2, t16_pre_topc, t78_boolealg, dt_k4_card_fil, d5_filter_2, t32_lattices, t57_boolealg, idempotence_k1_filter_1, rc3_funcsdom, t34_filter_0, d4_filter_2, t5_lattice4, t3_partfun1, t54_filter_2, t25_rpr_1, t19_filter_0, t52_xboole_1, t44_lattice4, d4_boolealg, t49_filter_0, t34_relat_1, d9_filter_2, fc4_lang1, t43_boolealg, fc17_finseq_1, commutativity_k5_subset_1, t50_lattices, rc3_setfam_1, t51_filter_2, fc2_subset_1, t17_filter_1, t79_zfmisc_1, t94_zfmisc_1, redefinition_k4_filter_2, t8_lattice4, t8_tops_1, dt_k13_lopclset, t63_funct_5, t1_zfmisc_1, dt_m2_filter_2, t47_filter_2, t30_filter_2, d16_nat_lat, t18_pre_topc, t21_filter_1, t2_tops_1, t18_setwiseo, t16_filter_2, rc6_tex_2, t97_zfmisc_1, t65_filter_2, rc1_rpr_1, existence_m2_rfunct_3, t8_tex_2, t9_relat_1, t84_lattice2, t67_filter_2, t39_filter_1, t50_lattice3, fc1_zf_model, t24_finset_1, dt_m1_struct_0, t40_filter_0, d3_filter_2, d12_filter_2, t2_tarski, t16_funct_1, t14_relat_1, t33_relat_1, dt_k4_filter_0, t33_xboole_1, fc4_prvect_1, t47_lattices, t25_borsuk_1, d7_filter_2, d20_lattices, t4_filter_0, t2_zfmisc_1, rc4_quantal1, t89_filter_0, t1_filter_1, t67_zfmisc_1, t38_filter_0, t22_lopclset, d2_funct_2, d21_lattice3, d2_pre_topc, rc3_orders_2, t34_lopclset, cc1_abian, d8_filter_0, t32_xboole_1, t4_boolealg, t52_subset_1, t60_filter_0, dt_k9_filter_1, t5_ordinal1, t4_boole, t53_xboole_1, fc5_trees_2, t21_xboole_1, t34_lattice4, t11_rpr_1, cc5_lattices, rc5_tex_2, t26_grfunc_1, t4_subset, t31_gate_1, t71_boolealg, fraenkel_a_1_1_lopclset, fc3_xboole_0, t169_funct_2, t3_quantal1, t48_boolealg, fraenkel_a_2_1_openlatt, t44_lattices, d2_xboole_0, t30_xboole_1, fraenkel_a_2_0_openlatt, t18_lopclset, t15_realset1, dt_k17_filter_2, fc3_filter_2, fc6_coh_sp, t88_boolealg, dt_k8_filter_0, t14_funct_1, d4_tarski, dt_k8_openlatt, t24_gate_1, t42_filter_1, reflexivity_r2_zfrefle1, t12_boolealg, t44_lattice3, t85_lattice2, t38_lattice2, redefinition_k12_openlatt, redefinition_k14_filter_2, fc1_realset1, t141_zfmisc_1, t38_gate_1, t45_lattices, rc2_realset1, d2_trees_3, t25_finset_1, t3_rlvect_1, reflexivity_r3_zfrefle1, t52_filter_1, t63_boolealg, fraenkel_a_2_0_lopclset, d7_realset2, d3_boolealg, d3_lattice3, dt_k8_rlvect_2, d7_lopclset, t30_boolealg, t33_gate_1, t33_boolealg, t29_xboole_1, t75_filter_0, t7_realset1, fc2_tex_1, t25_filter_2, d9_lopclset, t11_card_fil, existence_l1_orders_2, cc1_funct_1, cc1_rpr_1, dt_k16_openlatt, dt_k13_lang1, rc3_struct_0, t19_openlatt, fc1_subset_1, t3_ordinal1, d6_filter_2, dt_k10_openlatt, t32_lopclset, t6_realset1, t7_boole, dt_k14_filter_2, redefinition_k1_filter_2, t27_pre_topc, rc1_matrix_2, d10_lattice4, d17_lattice3, t27_boolealg, t15_gate_1, dt_m1_modal_1, t55_filter_0, t50_filter_1, d2_subset_1, redefinition_k9_filter_2, t66_zfmisc_1, t53_trees_1, fc1_metric_1, t13_finset_1, symmetry_r1_boolealg, fc2_trees_3, commutativity_k2_struct_0, t7_filter_2, t36_gate_1, rc3_tex_2, free_g1_struct_0, t23_filter_2, t48_xboole_1, dt_k6_domain_1, t21_lattice3, t84_boolealg, t19_gate_1, t33_filter_1, d1_rlvect_1, t16_subset_1, t72_boolealg, t7_ordinal1, t37_filter_1, t90_filter_0, t4_subset_1, t68_filter_0, existence_m1_modal_1, t67_boolealg, t49_trees_1, d6_lopclset, t91_orders_1, t34_filter_1, t31_lattice4, t82_boolealg, t5_setwiseo, t6_filter_2, t29_fin_topo, dt_k8_filter_1, t41_lopclset, rc2_funct_1, fc5_openlatt, dt_k10_filter_2, dt_k14_lattice3, cc2_setfam_1, rc1_subset_1, t37_gate_1, dt_k9_filter_0, redefinition_k15_filter_2, commutativity_k3_boolealg, t31_xboole_1, d26_grcat_1, fc3_lopclset, t43_gate_1, t24_xboole_1, l48_filter_2, t5_filter_0, t64_zfmisc_1, existence_m1_filter_0, t49_filter_1, t30_filter_0, t27_lopclset, t6_tex_2, cc11_tex_2, t6_setwiseo, t48_trees_1, t54_xboole_1, d21_lattices, d4_realset1, t41_lattices, t4_realset1, t42_boolealg, t33_grfunc_1, fc5_relat_1, t40_lattice4, t75_boolealg, t58_filter_1, redefinition_m1_filter_2, t25_openlatt, t16_gate_1, t13_filter_2, d7_openlatt, d5_openlatt, d1_tex_2, dt_k2_struct_0, t49_lattices, t14_funct_2, t48_lattices, t20_xboole_1, dt_k2_lattice4, t9_filter_0, fc17_abian, t40_lattices, t84_rlsub_2, t81_boolealg, t40_filter_2, dt_k3_boolealg, t32_openlatt, t46_filter_1, t7_lattice4, t36_filter_2, cc2_funct_1, t40_lattice3, t55_xboole_1, fc1_filter_2, d6_lattice4, commutativity_k12_openlatt, t55_subset_1, t41_lattice4, d9_filter_1, dt_k7_filter_2, t3_relat_1, t22_filter_0, dt_k16_lattice3, dt_k15_lattice3, fraenkel_a_2_1_lattice4, t26_lattice2, dt_k24_filter_2, t2_gate_1, t18_funct_1, t5_realset1, t1_toler_1, t10_filter_0, t31_subset_1, t3_subset, t12_filter_0, s1_domain_1, t12_gate_1, t18_filter_1, fraenkel_a_2_1_domain_1, d13_filter_2, existence_m1_filter_2, existence_m1_subset_1, t73_boolealg, t6_boolealg, t35_xboole_1, dt_k2_filter_0, t44_zfmisc_1, rc6_ringcat1, idempotence_k11_openlatt, dt_k20_filter_2, fc10_afinsq_1, d1_boolealg, t19_lattice2, t71_tops_3, dt_k1_prelamb, t42_lattice3, t30_subset_1, t8_setwiseo, t38_lattice3, t73_filter_0, t12_rpr_1, redefinition_k4_subset_1, rc4_tex_2, t14_xboole_1, t44_setfam_1, t22_openlatt, d2_filter_0, rc1_struct_0, t46_grfunc_1, redefinition_k9_lopclset, t47_xboole_1, t27_filter_2, d2_card_fil, fc1_finset_1, t15_subset_1, t44_filter_0, t73_filter_2, d1_quantal1, cc3_lattices, d5_subset_1, t92_zfmisc_1, t9_zfrefle1, t48_lattice3, t100_zfmisc_1, t15_xboole_1, rc2_relat_1, t36_lattice2, t2_tex_2, t64_filter_0, cc5_tex_2, t31_zfmisc_1, cc4_tex_2, t10_boolealg, dt_k23_filter_2, cc8_tex_2, redefinition_m3_matrix_2, d1_zfmisc_1, t16_xboole_1, dt_k1_tex_1, t35_grfunc_1, t75_nat_lat, t14_filter_2, d1_filter_0, t27_filter_0, t26_xboole_1, t7_tex_2, t32_boolealg, t15_filter_2, redefinition_k7_filter_0, t76_filter_2, t1_filter_0, commutativity_k4_subset_1, t39_filter_0, t50_trees_1, dt_k7_lopclset, rc9_tex_2, t11_lattice4, t85_rlsub_2, t11_filter_0, rc2_realset2, dt_k5_subset_1, t8_boolealg, t30_openlatt, t29_filter_2, existence_m2_lattice4, d6_openlatt, t24_openlatt, t69_filter_2, dt_k12_openlatt, t22_gate_1, t51_filter_0, t37_lattice4, t21_openlatt, t84_zfmisc_1, commutativity_k1_filter_1, t66_boolealg, t41_subset_1, cc3_finsub_1, t56_filter_2, t17_pre_topc, rc2_trees_1, t74_filter_0, t65_lattice2, t42_filter_2, existence_m2_filter_1, t51_subset_1, existence_m1_lattice4, t111_xboole_1, d5_filter_0, d10_filter_2, t60_nat_lat, t22_xboole_1, t9_tex_2, t60_filter_1, t51_boolealg, redefinition_m2_rfunct_3, redefinition_k24_filter_2, t41_gate_1, t29_gate_1, t32_filter_2, dt_l1_orders_2, redefinition_r3_boolealg, t58_filter_2, t21_gate_1, d4_filter_0, reflexivity_r1_filter_2, t21_lopclset, t48_wellord1, t8_xboole_1, dt_m3_lattice4, d3_tarski, fraenkel_a_1_0_openlatt, redefinition_k1_struct_0, t25_lattice4, rc1_relat_1, t24_filter_2, rc1_lattice4, t17_subset_1, symmetry_r2_subset_1, t47_afinsq_1, t14_setwiseo, t32_grfunc_1, t28_xboole_1, t34_openlatt, redefinition_k11_filter_2, fc1_struct_0, t62_filter_1, d8_filter_1, t52_lattice2, t76_boolealg, t78_lattice2, t26_gate_1, t69_boolealg, t37_filter_2, fraenkel_a_3_1_filter_0, t39_zfmisc_1, d15_lattices, t22_boolealg, dt_k22_filter_2, t49_boolealg, t17_openlatt, t34_boolealg, d2_heyting1, t13_xboole_1, t60_relat_1, t40_subset_1, d1_trees_3, t83_zfmisc_1, t24_lattice2, t19_lattice4, reflexivity_r1_tarski, t9_funct_1, t6_zfmisc_1, t52_boolealg, t52_wellord1, t56_setfam_1, t24_lattice3, t3_group_2, t52_lattices, t2_xboole_1, t35_lattice2, t4_xboole_1, t25_lopclset, fc6_relat_1, t5_rpr_1, t52_filter_2, symmetry_r1_filter_2, t27_finsub_1, redefinition_m1_struct_0, dt_k1_rlvect_2, t81_card_2, t18_filter_2, t10_subset_1, t21_fin_topo, t41_filter_0, existence_m2_nat_lat, rc2_setwiseo, existence_m3_matrix_2, t38_lopclset, t41_xboole_1, t87_boolealg, d1_tex_1, rc6_lattices, dt_k1_heyting1, t67_filter_0, t77_filter_0, t77_boolealg, dt_k10_filter_0, t54_lattice2, rc1_realset1, rc3_finset_1, t46_boolealg, dt_k3_filter_2, redefinition_k2_filter_2, d4_xboole_0, t18_zfmisc_1, t7_gate_1, t47_filter_0, t39_lattice2, t36_xboole_1, t51_zfmisc_1, t15_openlatt, d7_lattice4, d8_filter_2, fc2_filter_1, t58_filter_0, dt_k12_domain_1, t53_filter_2, t18_lattice4, t1_tops_2, t22_pre_topc, t17_boolealg, t40_filter_1, fc1_relat_1, t33_filter_2, d6_relat_1, redefinition_k2_lattice3, t80_zfmisc_1, dt_k2_filter_2, t59_filter_1, t24_zfmisc_1, dt_k2_boolealg, rc1_trees_1, t54_subset_1, rc1_finset_1, t20_filter_0, t28_finsub_1, t16_boolealg, t60_boolealg, t72_filter_2, t49_xboole_1, cc1_finset_1, t3_hahnban, t29_lattices, t16_filter_1, t88_filter_0, fc12_finset_1, abstractness_v3_lattices, t26_finsub_1, t8_boole, rc1_xboole_0, fc2_sgraph1, t54_filter_0, t11_xboole_1, fc1_trees_3, fc3_openlatt, t35_filter_2, t23_openlatt, t31_openlatt, d9_card_fil, t15_filter_0, t68_zfmisc_1, rc2_tex_2, rc1_card_5, redefinition_k16_openlatt, t12_xboole_1, t16_finset_1, t40_gate_1, fc7_relat_1, t46_filter_2, t65_relat_1, dt_k6_filter_0, t23_finsub_1, t30_finsub_1, redefinition_k3_boolealg, dt_m1_filter_0, d6_lattice3, t13_filter_1, t37_lopclset, t19_filter_1, rc8_tex_2, fraenkel_a_1_1_openlatt, rc5_struct_0, rc7_tex_2, t2_subset, fc7_grcat_1, redefinition_k21_filter_2, d9_filter_0, t38_boolealg, t34_finsub_1, fc1_tex_2, t37_zfmisc_1, fc2_relat_1, t49_filter_2, existence_m1_unialg_2, dt_k21_filter_2, t18_openlatt, t25_finsub_1, fc8_relat_1, t54_boolealg, t40_lopclset, idempotence_k12_openlatt, idempotence_k2_xboole_0, symmetry_r3_boolealg, rc1_setwiseo, d2_boolealg, t35_lopclset, t15_pre_topc, t34_lattices, t51_lattices, t46_xboole_1, t7_xboole_1, t59_boolealg, redefinition_k10_filter_2, t23_lattice3, t27_gate_1, t32_finsub_1, t48_subset_1, d1_filter_2, t27_openlatt, t28_relat_1, cc1_card_5, redefinition_k18_openlatt, t57_filter_1, t32_filter_1, t62_boolealg, d12_filter_0, t42_lattice4, t50_subset_1, t65_filter_0, d10_xboole_0, d2_lattice2, t1_tex_2, d11_setfam_1, fc2_realset1, d11_filter_2, t41_lattice3, t39_gate_1, t34_lattice2, d19_lattices, t79_lattice2, t20_lopclset, cc1_realset1, d1_rlvect_2, t14_filter_1, fraenkel_a_2_0_lattice3, fc1_lattice4, t7_rpr_1, t25_gate_1, t53_lattice2, existence_l1_struct_0, t27_grfunc_1, t5_xboole_1, t45_filter_0, t49_subset_1, t7_tarski, t70_boolealg, t44_boolealg, rc1_partfun1, t71_filter_0, redefinition_r1_filter_2, t79_boolealg, t11_boolealg, rc1_rfunct_3, t3_boole, t9_grfunc_1, d5_funct_1, t6_ordinal1, dt_k18_filter_2, redefinition_k6_subset_1, t28_boolealg, t43_filter_1, t25_relat_1, dt_k8_filter_2, t38_grfunc_1, dt_k13_nat_lat, t43_lattice4, idempotence_k4_subset_1, d14_group_1, redefinition_k11_openlatt, t22_filter_2, d3_filter_0, t40_zfmisc_1, rc2_xboole_0, t45_xboole_1, t93_orders_1, t41_filter_1, t50_filter_0, rc1_tex_2, t28_gate_1, t31_filter_2, t66_filter_0, t55_filter_1, dt_k2_prelamb, t6_filter_0, redefinition_k3_filter_2, dt_k11_openlatt, existence_m2_prelamb, t47_real_lat, reflexivity_r1_boolealg, fc5_coh_sp, t80_boolealg, t15_boolealg, t24_pre_topc, t63_filter_0, t63_lattice2, t35_boolealg, symmetry_r2_zfrefle1, t18_lattice2, t73_lattice2, t42_lopclset, t40_xboole_1, existence_m2_filter_2, t10_xboole_1, t60_filter_2, t6_lattice4, t53_boolealg, t65_zfmisc_1, t63_subset_1, t38_xboole_1, t14_openlatt, t46_lattice3, t26_relat_1, irreflexivity_r2_subset_1, dt_k2_pre_topc, dt_k3_subset_1, fc1_funct_2, t33_subset_1, t56_boolealg, redefinition_m2_unialg_2, dt_k13_filter_2, fc3_topreal1, cc6_tex_2, t14_pre_topc, fc2_lopclset, t13_filter_0, d3_xboole_0, t39_xboole_1, t3_filter_0, t10_lattice4, antisymmetry_r2_hidden, t26_rpr_1, t43_lopclset, t39_boolealg, t47_boolealg, d5_lattice4, t21_tops_1, d8_lattice4, redefinition_k6_domain_1, t64_lattice2
% 296.99/68.03 % No. of inferences in proof: 3264
% 296.99/68.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 67482 ms resp. 62764 ms w/o parsing
% 299.15/68.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 299.24/68.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------