%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT296+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:47:03 AM UTC 2026
% Result : Theorem 124.41s 30.82s
% Output : Refutation 130.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1065
% Syntax : Number of formulae : 3271 ( 631 unt; 0 typ; 65 def)
% Number of atoms : 17697 (2874 equ; 0 cnn)
% Maximal formula atoms : 58 ( 5 avg)
% Number of connectives : 58311 (4246 ~;2080 |;6442 &;40524 @)
% ( 226 <=>;4793 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 345 ( 342 usr; 96 con; 0-9 aty)
% Number of variables : 7289 ( 29 ^;6847 !; 348 ?;7289 :)
% ( 0 !>; 0 ?*; 0 @-; 65 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_decl,type,
v10_lattices: $i > $o ).
thf(v17_lattices_decl,type,
v17_lattices: $i > $o ).
thf(l3_lattices_decl,type,
l3_lattices: $i > $o ).
thf(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $i ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(u2_lattices_decl,type,
u2_lattices: $i > $i ).
thf(u1_lattices_decl,type,
u1_lattices: $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k7_lattices_decl,type,
k7_lattices: $i > $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(m1_nat_lat_decl,type,
m1_nat_lat: $i > $i > $i > $i > $o ).
thf(m2_subset_1_decl,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(k1_realset1_decl,type,
k1_realset1: $i > $i > $i ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g1_lattices_decl,type,
g1_lattices: $i > $i > $i ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(k3_relat_1_decl,type,
k3_relat_1: $i > $i ).
thf(l2_lattices_decl,type,
l2_lattices: $i > $o ).
thf(v2_lattices_decl,type,
v2_lattices: $i > $o ).
thf(g2_lattices_decl,type,
g2_lattices: $i > $i > $i ).
thf(l1_lattices_decl,type,
l1_lattices: $i > $o ).
thf(v1_lattices_decl,type,
v1_lattices: $i > $o ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(k5_numbers_decl,type,
k5_numbers: $i ).
thf(k1_numbers_decl,type,
k1_numbers: $i ).
thf(a_2_3_domain_1_decl,type,
a_2_3_domain_1: $i > $i > $i ).
thf(k2_binop_1_decl,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(r1_binop_1_decl,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_binop_1_decl,type,
k1_binop_1: $i > $i > $i > $i ).
thf(r6_binop_1_decl,type,
r6_binop_1: $i > $i > $i > $o ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(l2_struct_0_decl,type,
l2_struct_0: $i > $o ).
thf(v2_struct_0_decl,type,
v2_struct_0: $i > $o ).
thf(r4_binop_1_decl,type,
r4_binop_1: $i > $i > $i > $o ).
thf(r5_binop_1_decl,type,
r5_binop_1: $i > $i > $i > $o ).
thf(v7_lattices_decl,type,
v7_lattices: $i > $o ).
thf(v3_lattices_decl,type,
v3_lattices: $i > $o ).
thf(k7_domain_1_decl,type,
k7_domain_1: $i > $i > $i > $i ).
thf(v3_binop_1_decl,type,
v3_binop_1: $i > $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k5_finsub_1_decl,type,
k5_finsub_1: $i > $i ).
thf(v4_lattices_decl,type,
v4_lattices: $i > $o ).
thf(k3_binop_1_decl,type,
k3_binop_1: $i > $i > $i ).
thf(r2_binop_1_decl,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k2_subset_1_decl,type,
k2_subset_1: $i > $i ).
thf(a_2_2_domain_1_decl,type,
a_2_2_domain_1: $i > $i > $i ).
thf(r3_binop_1_decl,type,
r3_binop_1: $i > $i > $i > $o ).
thf(a_2_0_domain_1_decl,type,
a_2_0_domain_1: $i > $i > $i ).
thf(r8_relat_2_decl,type,
r8_relat_2: $i > $i > $o ).
thf(k1_subset_1_decl,type,
k1_subset_1: $i > $i ).
thf(k7_nat_lat_decl,type,
k7_nat_lat: $i ).
thf(k10_nat_lat_decl,type,
k10_nat_lat: $i ).
thf(k6_nat_1_decl,type,
k6_nat_1: $i > $i > $i ).
thf(k4_subset_1_decl,type,
k4_subset_1: $i > $i > $i > $i ).
thf(r3_relat_2_decl,type,
r3_relat_2: $i > $i > $o ).
thf(k2_nat_lat_decl,type,
k2_nat_lat: $i ).
thf(k1_nat_lat_decl,type,
k1_nat_lat: $i ).
thf(k3_nat_lat_decl,type,
k3_nat_lat: $i > $i ).
thf(k5_nat_1_decl,type,
k5_nat_1: $i > $i > $i ).
thf(r7_binop_1_decl,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k11_nat_lat_decl,type,
k11_nat_lat: $i ).
thf(v5_lattices_decl,type,
v5_lattices: $i > $o ).
thf(a_3_3_domain_1_decl,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(r1_relat_2_decl,type,
r1_relat_2: $i > $i > $o ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(v6_lattices_decl,type,
v6_lattices: $i > $o ).
thf(a_1_0_domain_1_decl,type,
a_1_0_domain_1: $i > $i ).
thf(m3_realset1_decl,type,
m3_realset1: $i > $i > $i > $o ).
thf(k7_funct_2_decl,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(k1_lattice2_decl,type,
k1_lattice2: $i > $i ).
thf(v8_lattices_decl,type,
v8_lattices: $i > $o ).
thf(v9_lattices_decl,type,
v9_lattices: $i > $o ).
thf(m1_filter_0_decl,type,
m1_filter_0: $i > $i > $o ).
thf(k5_filter_0_decl,type,
k5_filter_0: $i > $i > $i > $i ).
thf(v3_filter_0_decl,type,
v3_filter_0: $i > $o ).
thf(v11_lattices_decl,type,
v11_lattices: $i > $o ).
thf(v12_lattices_decl,type,
v12_lattices: $i > $o ).
thf(k2_lattices_decl,type,
k2_lattices: $i > $i > $i > $i ).
thf(k6_nat_lat_decl,type,
k6_nat_lat: $i ).
thf(k1_lattices_decl,type,
k1_lattices: $i > $i > $i > $i ).
thf(k12_nat_lat_decl,type,
k12_nat_lat: $i > $i ).
thf(k4_lattices_decl,type,
k4_lattices: $i > $i > $i > $i ).
thf(v14_lattices_decl,type,
v14_lattices: $i > $o ).
thf(v13_lattices_decl,type,
v13_lattices: $i > $o ).
thf(m1_filter_2_decl,type,
m1_filter_2: $i > $i > $o ).
thf(k4_filter_2_decl,type,
k4_filter_2: $i > $i > $i > $i ).
thf(v15_lattices_decl,type,
v15_lattices: $i > $o ).
thf(g2_struct_0_decl,type,
g2_struct_0: $i > $i > $i ).
thf(k2_lattice2_decl,type,
k2_lattice2: $i > $i > $i > $i > $i ).
thf(k8_funcop_1_decl,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(k6_lattices_decl,type,
k6_lattices: $i > $i ).
thf(m2_lattice4_decl,type,
m2_lattice4: $i > $i > $o ).
thf(k5_lattices_decl,type,
k5_lattices: $i > $i ).
thf(a_2_1_lattice4_decl,type,
a_2_1_lattice4: $i > $i > $i ).
thf(k3_lattice4_decl,type,
k3_lattice4: $i > $i > $i ).
thf(a_2_1_domain_1_decl,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k1_domain_1_decl,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(v6_group_1_decl,type,
v6_group_1: $i > $o ).
thf(k3_lattice2_decl,type,
k3_lattice2: $i > $i > $i > $i > $i ).
thf(k12_filter_2_decl,type,
k12_filter_2: $i > $i > $i ).
thf(k8_filter_2_decl,type,
k8_filter_2: $i > $i > $i ).
thf(r3_lattices_decl,type,
r3_lattices: $i > $i > $i > $o ).
thf(k10_filter_2_decl,type,
k10_filter_2: $i > $i > $i ).
thf(k3_filter_0_decl,type,
k3_filter_0: $i > $i > $i ).
thf(k4_filter_0_decl,type,
k4_filter_0: $i > $i > $i > $i ).
thf(m2_filter_2_decl,type,
m2_filter_2: $i > $i > $o ).
thf(k13_filter_2_decl,type,
k13_filter_2: $i > $i > $i ).
thf(k4_nat_lat_decl,type,
k4_nat_lat: $i ).
thf(p1_s2_domain_1_decl,type,
p1_s2_domain_1: $i > $i > $o ).
thf(k1_lattice4_decl,type,
k1_lattice4: $i > $i > $i ).
thf(a_0_0_domain_1_decl,type,
a_0_0_domain_1: $i ).
thf(f1_s7_domain_1_decl,type,
f1_s7_domain_1: $i ).
thf(v1_filter_0_decl,type,
v1_filter_0: $i > $i > $o ).
thf(k8_setwiseo_decl,type,
k8_setwiseo: $i > $i > $i > $i > $i ).
thf(k8_filter_0_decl,type,
k8_filter_0: $i > $i > $i ).
thf(k5_setwiseo_decl,type,
k5_setwiseo: $i > $i > $i > $i ).
thf(k2_setwiseo_decl,type,
k2_setwiseo: $i > $i > $i ).
thf(k3_lattices_decl,type,
k3_lattices: $i > $i > $i > $i ).
thf(k7_filter_2_decl,type,
k7_filter_2: $i > $i > $i ).
thf(k10_filter_0_decl,type,
k10_filter_0: $i > $i > $i ).
thf(k9_filter_0_decl,type,
k9_filter_0: $i > $i > $i > $i ).
thf(k4_lattice4_decl,type,
k4_lattice4: $i > $i > $i ).
thf(k5_lattice4_decl,type,
k5_lattice4: $i > $i ).
thf(k2_lattice4_decl,type,
k2_lattice4: $i > $i > $i ).
thf(r1_filter_2_decl,type,
r1_filter_2: $i > $i > $i > $o ).
thf(k14_filter_2_decl,type,
k14_filter_2: $i > $i > $i ).
thf(u2_struct_0_decl,type,
u2_struct_0: $i > $i ).
thf(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m1_lattice4_decl,type,
m1_lattice4: $i > $i > $i > $o ).
thf(v1_lattice2_decl,type,
v1_lattice2: $i > $o ).
thf(v2_lattice4_decl,type,
v2_lattice4: $i > $i > $i > $o ).
thf(r3_lattice4_decl,type,
r3_lattice4: $i > $i > $i > $o ).
thf(k11_filter_0_decl,type,
k11_filter_0: $i > $i > $i ).
thf(k13_nat_lat_decl,type,
k13_nat_lat: $i ).
thf(a_3_2_domain_1_decl,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(v16_lattices_decl,type,
v16_lattices: $i > $o ).
thf(v1_lattice4_decl,type,
v1_lattice4: $i > $i > $i > $o ).
thf(r1_lattices_decl,type,
r1_lattices: $i > $i > $i > $o ).
thf(m2_nat_lat_decl,type,
m2_nat_lat: $i > $i > $o ).
thf(r2_lattices_decl,type,
r2_lattices: $i > $i > $i > $o ).
thf(m1_struct_0_decl,type,
m1_struct_0: $i > $i > $i > $o ).
thf(k7_setwiseo_decl,type,
k7_setwiseo: $i > $i > $i > $i > $i > $i ).
thf(k24_filter_2_decl,type,
k24_filter_2: $i > $i > $i ).
thf(k12_domain_1_decl,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_1_2_domain_1_decl,type,
a_1_2_domain_1: $i > $i ).
thf(k6_filter_0_decl,type,
k6_filter_0: $i > $i > $i > $i ).
thf(a_3_6_domain_1_decl,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(f1_s4_funct_2_decl,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_decl,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_decl,type,
f3_s4_funct_2: $i > $i ).
thf(k1_finsub_1_decl,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(k2_filter_0_decl,type,
k2_filter_0: $i > $i > $i ).
thf(v3_lattice4_decl,type,
v3_lattice4: $i > $i > $i > $o ).
thf(r1_lattice4_decl,type,
r1_lattice4: $i > $i > $i > $o ).
thf(a_3_5_domain_1_decl,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(k1_filter_0_decl,type,
k1_filter_0: $i > $i ).
thf(a_3_4_domain_1_decl,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(k9_domain_1_decl,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(f1_s14_funct_2_decl,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_decl,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_decl,type,
p1_s14_funct_2: $i > $i > $o ).
thf(f1_s12_funct_2_decl,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_decl,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_decl,type,
f2_s12_funct_2: $i ).
thf(f1_s13_funct_2_decl,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_decl,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_decl,type,
f2_s13_funct_2: $i ).
thf(a_3_1_domain_1_decl,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(r1_lattice2_decl,type,
r1_lattice2: $i > $i > $i > $o ).
thf(k11_domain_1_decl,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k13_domain_1_decl,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k8_domain_1_decl,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(r1_nat_1_decl,type,
r1_nat_1: $i > $i > $o ).
thf(f1_s3_funct_2_decl,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_decl,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_decl,type,
p1_s3_funct_2: $i > $i > $o ).
thf(a_3_7_domain_1_decl,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(a_4_1_domain_1_decl,type,
a_4_1_domain_1: $i > $i > $i > $i > $i ).
thf(k22_filter_2_decl,type,
k22_filter_2: $i > $i > $i > $i ).
thf(r1_filter_0_decl,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(k19_filter_2_decl,type,
k19_filter_2: $i > $i > $i ).
thf(k21_filter_2_decl,type,
k21_filter_2: $i > $i > $i > $i ).
thf(k20_filter_2_decl,type,
k20_filter_2: $i > $i > $i > $i ).
thf(r2_lattice4_decl,type,
r2_lattice4: $i > $i > $i > $o ).
thf(k7_filter_0_decl,type,
k7_filter_0: $i > $i > $i > $i ).
thf(a_2_0_filter_0_decl,type,
a_2_0_filter_0: $i > $i > $i ).
thf(r4_lattice4_decl,type,
r4_lattice4: $i > $i > $i > $o ).
thf(v1_setwiseo_decl,type,
v1_setwiseo: $i > $i > $o ).
thf(a_3_0_filter_0_decl,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(a_3_1_filter_0_decl,type,
a_3_1_filter_0: $i > $i > $i > $i ).
thf(k2_struct_0_decl,type,
k2_struct_0: $i > $i > $i > $i ).
thf(v2_filter_0_decl,type,
v2_filter_0: $i > $i > $o ).
thf(k2_filter_2_decl,type,
k2_filter_2: $i > $i > $i ).
thf(m3_lattice4_decl,type,
m3_lattice4: $i > $i > $o ).
thf(a_0_2_domain_1_decl,type,
a_0_2_domain_1: $i ).
thf(f3_s9_domain_1_decl,type,
f3_s9_domain_1: $i ).
thf(p1_s7_domain_1_decl,type,
p1_s7_domain_1: $i > $o ).
thf(k3_filter_2_decl,type,
k3_filter_2: $i > $i > $i ).
thf(r1_filter_1_decl,type,
r1_filter_1: $i > $i > $o ).
thf(k16_filter_2_decl,type,
k16_filter_2: $i > $i > $i ).
thf(f3_s11_funct_2_decl,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_decl,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_decl,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_decl,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_decl,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_decl,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_decl,type,
f7_s11_funct_2: $i > $i ).
thf(k9_filter_2_decl,type,
k9_filter_2: $i > $i > $i ).
thf(k1_struct_0_decl,type,
k1_struct_0: $i > $i > $i ).
thf(a_2_0_lattice4_decl,type,
a_2_0_lattice4: $i > $i > $i ).
thf(k15_filter_2_decl,type,
k15_filter_2: $i > $i > $i ).
thf(k8_subset_1_decl,type,
k8_subset_1: $i > $i ).
thf(a_0_1_domain_1_decl,type,
a_0_1_domain_1: $i ).
thf(f2_s8_domain_1_decl,type,
f2_s8_domain_1: $i ).
thf(k1_setwiseo_decl,type,
k1_setwiseo: $i > $i ).
thf(k18_filter_2_decl,type,
k18_filter_2: $i > $i > $i ).
thf(k11_filter_2_decl,type,
k11_filter_2: $i > $i > $i ).
thf(k7_grcat_1_decl,type,
k7_grcat_1: $i > $i ).
thf(f1_s8_domain_1_decl,type,
f1_s8_domain_1: $i ).
thf(f3_s8_domain_1_decl,type,
f3_s8_domain_1: $i > $i ).
thf(p1_s8_domain_1_decl,type,
p1_s8_domain_1: $i > $o ).
thf(k1_filter_2_decl,type,
k1_filter_2: $i > $i ).
thf(f1_s9_domain_1_decl,type,
f1_s9_domain_1: $i ).
thf(f2_s9_domain_1_decl,type,
f2_s9_domain_1: $i ).
thf(f4_s9_domain_1_decl,type,
f4_s9_domain_1: $i > $i > $i ).
thf(p1_s9_domain_1_decl,type,
p1_s9_domain_1: $i > $i > $o ).
thf(f1_s4_subset_1_decl,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_decl,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_decl,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_decl,type,
f3_s4_subset_1: $i ).
thf(k5_filter_2_decl,type,
k5_filter_2: $i > $i > $i ).
thf(k23_filter_2_decl,type,
k23_filter_2: $i > $i > $i ).
thf(k7_funcop_1_decl,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k12_filter_0_decl,type,
k12_filter_0: $i > $i > $i ).
thf(k6_filter_2_decl,type,
k6_filter_2: $i > $i > $i ).
thf(k5_nat_lat_decl,type,
k5_nat_lat: $i ).
thf(k17_filter_2_decl,type,
k17_filter_2: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $o ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk21_decl,type,
sk21: $i > $i > $i ).
thf(sk56_decl,type,
sk56: $i ).
thf(sk58_decl,type,
sk58: $i ).
thf(sk71_decl,type,
sk71: $i > $i ).
thf(sk72_decl,type,
sk72: $i > $i > $i ).
thf(sk85_decl,type,
sk85: $i ).
thf(sk101_decl,type,
sk101: $i > $i > $i ).
thf(sk102_decl,type,
sk102: $i > $i > $i ).
thf(sk126_decl,type,
sk126: $i ).
thf(sk141_decl,type,
sk141: $i ).
thf(sk142_decl,type,
sk142: $i ).
thf(sk143_decl,type,
sk143: $i ).
thf(sk148_decl,type,
sk148: $i ).
thf(sk188_decl,type,
sk188: $i > $i ).
thf(sk205_decl,type,
sk205: $i ).
thf(sk217_decl,type,
sk217: $i ).
thf(sk219_decl,type,
sk219: $i ).
thf(sk253_decl,type,
sk253: $i > $i ).
thf(sk256_decl,type,
sk256: $i ).
thf(sk267_decl,type,
sk267: $i ).
thf(sk272_decl,type,
sk272: $i ).
thf(sk281_decl,type,
sk281: $i ).
thf(sk285_decl,type,
sk285: $i ).
thf(sk297_decl,type,
sk297: $i ).
thf(sk298_decl,type,
sk298: $i ).
thf(sk300_decl,type,
sk300: $i ).
thf(sk301_decl,type,
sk301: $i ).
thf(sk302_decl,type,
sk302: $i ).
thf(sk303_decl,type,
sk303: $i ).
thf(sk317_decl,type,
sk317: $i ).
thf(sk318_decl,type,
sk318: $i ).
thf(sk319_decl,type,
sk319: $i ).
thf(sk323_decl,type,
sk323: $o ).
thf(sk324_decl,type,
sk324: $i ).
thf(sk325_decl,type,
sk325: $i ).
thf(sk329_decl,type,
sk329: $o ).
thf(sk330_decl,type,
sk330: $i ).
thf(sk331_decl,type,
sk331: $i ).
thf(sk333_decl,type,
sk333: $i ).
thf(sk336_decl,type,
sk336: $i ).
thf(sk337_decl,type,
sk337: $o ).
thf(sk338_decl,type,
sk338: $i ).
thf(sk339_decl,type,
sk339: $i ).
thf(sk341_decl,type,
sk341: $i > $i ).
thf(sk349_decl,type,
sk349: $i ).
thf(sk350_decl,type,
sk350: $i ).
thf(sk353_decl,type,
sk353: $i ).
thf(sk359_decl,type,
sk359: $i > $i > $i ).
thf(sk360_decl,type,
sk360: $i > $i > $i ).
thf(sk364_decl,type,
sk364: $o ).
thf(sk365_decl,type,
sk365: $i ).
thf(sk366_decl,type,
sk366: $i ).
thf(sk378_decl,type,
sk378: $i > $i ).
thf(sk391_decl,type,
sk391: $i ).
thf(sk411_decl,type,
sk411: $i ).
thf(sk433_decl,type,
sk433: $o ).
thf(sk434_decl,type,
sk434: $i ).
thf(sk435_decl,type,
sk435: $i ).
thf(sk446_decl,type,
sk446: $i ).
thf(sk459_decl,type,
sk459: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k7_lattices ) )
= ( D @ ( B @ k7_lattices ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( sk1 @ u1_lattices @ ( sk1 @ u2_lattices @ ( sk1 @ u1_struct_0 @ g3_lattices ) ) )
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [B: $i] :
( ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B = C )
=> ( ( B @ ( sk1 @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( sk2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A = B )
=> ( ( A @ ( sk1 @ k7_lattices ) )
= ( B @ ( sk2 @ k7_lattices ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( sk2 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( sk3 = A )
=> ( ( sk3 @ ( sk1 @ k7_lattices ) )
= ( A @ ( sk2 @ k7_lattices ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i,D: $i,E: $i] :
@+[F: $i] :
~ ( ( E @ ( F @ m1_subset_1 ) )
=> ~ ( ( A
= ( F @ ( B @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ( ( A @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( ( D @ ( A @ k1_funct_1 ) )
= C )
=> ( ( C @ ( B @ k1_funct_1 ) )
= D ) )
& ( ( ( C @ ( B @ k1_funct_1 ) )
= D )
=> ( ( D @ ( A @ k1_funct_1 ) )
= C ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( B @ ( A @ sk8 ) @ r2_hidden ) ) )
=> ( ( ( ( C @ ( A @ k1_funct_1 ) )
= ( B @ ( A @ sk8 ) ) )
=> ( ( B @ ( A @ sk8 ) @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( ( B @ ( A @ sk8 ) @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( B @ ( A @ sk8 ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A
= ( C @ k1_relat_1 ) ) ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( @+[A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk58_def,definition,
( sk58
= ( @+[A: $i] :
( ( A @ v1_lattices )
& ( A @ l1_lattices ) ) ) ) ).
thf(sk71_def,definition,
( sk71
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ~ ? [C: $i] :
( ~ ? [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk72_def,definition,
( sk72
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( B @ sk71 @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk85_def,definition,
( sk85
= ( @+[A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk101_def,definition,
( sk101
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).
thf(sk102_def,definition,
( sk102
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).
thf(sk126_def,definition,
( sk126
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk141_def,definition,
( sk141
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk142_def,definition,
( sk142
= ( @+[A: $i] :
( ( A @ v2_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_lattices ) ) ) ) ).
thf(sk143_def,definition,
( sk143
= ( @+[A: $i] :
( ( A @ v1_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_lattices ) ) ) ) ).
thf(sk148_def,definition,
( sk148
= ( @+[A: $i] :
( ( A @ v2_lattices )
& ( A @ l2_lattices ) ) ) ) ).
thf(sk188_def,definition,
( sk188
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk205_def,definition,
( sk205
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk217_def,definition,
( sk217
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk219_def,definition,
( sk219
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk253_def,definition,
( sk253
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk256_def,definition,
( sk256
= ( @+[A: $i] :
( ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk267_def,definition,
( sk267
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk272_def,definition,
( sk272
= ( @+[A: $i] :
( ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk281_def,definition,
( sk281
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk285_def,definition,
( sk285
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk297_def,definition,
( sk297
= ( @+[A: $i] :
( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk298_def,definition,
( sk298
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk300_def,definition,
( sk300
= ( @+[A: $i] :
( ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v2_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_lattices ) ) ) ) ).
thf(sk301_def,definition,
( sk301
= ( @+[A: $i] :
( ( A @ v17_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk302_def,definition,
( sk302
= ( @+[A: $i] :
( ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk303_def,definition,
( sk303
= ( @+[A: $i] :
( ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk317_def,definition,
( sk317
= ( @+[A: $i] :
( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk318_def,definition,
( sk318
= ( @+[A: $i] :
( ( A @ v1_lattice2 )
& ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk319_def,definition,
( sk319
= ( @+[A: $i] :
( ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v1_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_lattices ) ) ) ) ).
thf(sk324_def,definition,
( sk324
= ( @+[A: $i] :
~ ( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) ) ) ) ).
thf(sk325_def,definition,
( sk325
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk330_def,definition,
( sk330
= ( @+[A: $i] :
~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).
thf(sk331_def,definition,
( sk331
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk333_def,definition,
( sk333
= ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).
thf(sk336_def,definition,
( sk336
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk338_def,definition,
( sk338
= ( @+[A: $i] :
~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).
thf(sk339_def,definition,
( sk339
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk341_def,definition,
( sk341
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk349_def,definition,
( sk349
= ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).
thf(sk350_def,definition,
( sk350
= ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).
thf(sk353_def,definition,
( sk353
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk359_def,definition,
( sk359
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
=> ( C = B ) ) ) ) ).
thf(sk360_def,definition,
( sk360
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk365_def,definition,
( sk365
= ( @+[A: $i] :
~ ( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) ) ) ) ).
thf(sk366_def,definition,
( sk366
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk378_def,definition,
( sk378
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk391_def,definition,
( sk391
= ( @+[A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ) ) ).
thf(sk411_def,definition,
( sk411
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk434_def,definition,
( sk434
= ( @+[A: $i] :
~ ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f2_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) ) ) ) ).
thf(sk435_def,definition,
( sk435
= ( @+[A: $i] :
~ ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f3_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) ) ) ) ).
thf(sk446_def,definition,
( sk446
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk459_def,definition,
( sk459
= ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).
thf(105,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(1633,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(581,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
<=> ( A @ k1_lattice2 @ v14_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).
thf(4262,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k1_lattice2 @ v14_lattices )
=> ( A @ v13_lattices ) )
& ( ( A @ v13_lattices )
=> ( A @ k1_lattice2 @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_tarski ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(3399,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( C
= ( B @ ( A @ k2_tarski ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(459,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k10_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_filter_2) ).
thf(3666,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k10_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(314,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(2876,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(421,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ( A @ v6_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattice2) ).
thf(3477,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ( A @ v6_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(668,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ( A @ v6_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattice2) ).
thf(4852,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ( A @ v6_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(2499,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(17,axiom,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(1079,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1080,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1079]) ).
thf(1081,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[1080]) ).
thf(1083,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1081]) ).
thf(949,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v17_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_filter_0) ).
thf(6121,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v17_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_2 ) @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_2) ).
thf(5999,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_2 ) @ m1_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(512,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(3927,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(932,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice4) ).
thf(6042,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(341,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(3009,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(3010,plain,
( ( sk205 @ v1_funct_1 )
& ( sk205 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3009]) ).
thf(3012,plain,
sk205 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3010]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_partfun1) ).
thf(1044,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ( A = k1_xboole_0 )
| ( B != k1_xboole_0 )
| ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1044]) ).
thf(1046,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 )
| ( A = k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1045]) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ~ ( k1_xboole_0 @ ( A @ ( B @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( B @ v1_funct_1 )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[1046]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k7_lattices ) )
= ( D @ ( B @ k7_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_filter_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k7_lattices ) )
= ( D @ ( B @ k7_lattices ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1002,plain,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k7_lattices ) )
= ( D @ ( B @ k7_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1003,plain,
( ( ( sk3 @ ( sk1 @ k7_lattices ) )
!= ( sk4 @ ( sk2 @ k7_lattices ) ) )
& ( sk3 = sk4 )
& ( sk2 @ u1_struct_0 @ ( sk4 @ m1_subset_1 ) )
& ( sk1 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ) )
& ( ( sk1 @ u1_lattices @ ( sk1 @ u2_lattices @ ( sk1 @ u1_struct_0 @ g3_lattices ) ) )
= ( sk2 @ u1_lattices @ ( sk2 @ u2_lattices @ ( sk2 @ u1_struct_0 @ g3_lattices ) ) ) )
& ( sk2 @ l3_lattices )
& ( sk2 @ v17_lattices )
& ( sk2 @ v10_lattices )
& ~ ( sk2 @ v3_struct_0 )
& ( sk1 @ l3_lattices )
& ( sk1 @ v17_lattices )
& ( sk1 @ v10_lattices )
& ~ ( sk1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1002]) ).
thf(1008,plain,
sk1 @ v10_lattices,
inference(cnfConj,[status(thm)],[1003]) ).
thf(7002,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( A @ ( B @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1047,1008]) ).
thf(7003,plain,
! [A: $i] :
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[7002:[bind(A,$thf( sk1 ))]]) ).
thf(7087,plain,
! [A: $i] :
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[7003]) ).
thf(8885,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3012,7087]) ).
thf(8886,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8885]) ).
thf(8887,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8886:[bind(A,$thf( sk205 ))]]) ).
thf(929,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v2_filter_0 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_0) ).
thf(6014,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) )
=> ( A @ ( B @ v2_filter_0 ) ) )
& ( ( A @ ( B @ v2_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(141,axiom,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(1864,plain,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1865,plain,
( ( sk56 @ v1_xboole_0 )
& ( sk56 @ v2_funct_1 )
& ( sk56 @ v1_funct_1 )
& ( sk56 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1864]) ).
thf(1869,plain,
sk56 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[1865]) ).
thf(362,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(3127,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(3128,plain,
( ( sk219 @ v1_relat_1 )
& ~ ( sk219 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3127]) ).
thf(3129,plain,
~ ( sk219 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3128]) ).
thf(6371,plain,
( ( ( sk219 @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,3129]) ).
thf(6372,plain,
( ( sk219 @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6371]) ).
thf(6374,plain,
sk219 != sk56,
inference(simp,[status(thm)],[6372]) ).
thf(881,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( A @ v11_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattice4) ).
thf(5810,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v11_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( A @ v11_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k16_filter_2 ) )
= ( B @ ( A @ k8_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k16_filter_2) ).
thf(5437,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k16_filter_2 ) )
= ( B @ ( A @ k8_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(806,axiom,
( ( k6_nat_lat @ l3_lattices )
& ( k6_nat_lat @ v13_lattices )
& ( k6_nat_lat @ v10_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_nat_lat) ).
thf(5504,plain,
( ( k6_nat_lat @ l3_lattices )
& ( k6_nat_lat @ v13_lattices )
& ( k6_nat_lat @ v10_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(5505,plain,
( ( k6_nat_lat @ l3_lattices )
& ( k6_nat_lat @ v13_lattices )
& ( k6_nat_lat @ v10_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[5504]) ).
thf(5509,plain,
k6_nat_lat @ l3_lattices,
inference(cnfConj,[status(thm)],[5505]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(1028,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ sk5 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ sk5 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( C @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ sk5 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( B @ ( A @ ( C @ sk5 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
| ( ( C @ k1_relat_1 )
!= A )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( B @ ( A @ ( C @ sk5 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk6 ) ) @ r2_hidden ) )
| ( ( C @ k1_relat_1 )
!= A )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1028]) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk5 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
| ( ( C @ k1_relat_1 )
!= A )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1029]) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk5 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ( ( C @ k1_relat_1 )
!= A ) ),
inference(lifteq,[status(thm)],[1031]) ).
thf(1036,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_relat_1 @ ( B @ sk5 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ ( A @ ( B @ sk6 ) ) @ ( B @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1035]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(2822,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) )
=> ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(2094,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(773,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
<=> ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_lattices) ).
thf(5365,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) )
=> ( A @ v17_lattices ) )
& ( ( A @ v17_lattices )
=> ( ( A @ v11_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(503,axiom,
( ( k13_nat_lat @ v10_lattices )
& ( k13_nat_lat @ v9_lattices )
& ( k13_nat_lat @ v8_lattices )
& ( k13_nat_lat @ v7_lattices )
& ( k13_nat_lat @ v6_lattices )
& ( k13_nat_lat @ v5_lattices )
& ( k13_nat_lat @ v4_lattices )
& ( k13_nat_lat @ v3_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_nat_lat) ).
thf(3876,plain,
( ( k13_nat_lat @ v10_lattices )
& ( k13_nat_lat @ v9_lattices )
& ( k13_nat_lat @ v8_lattices )
& ( k13_nat_lat @ v7_lattices )
& ( k13_nat_lat @ v6_lattices )
& ( k13_nat_lat @ v5_lattices )
& ( k13_nat_lat @ v4_lattices )
& ( k13_nat_lat @ v3_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(3877,plain,
( ( k13_nat_lat @ v10_lattices )
& ( k13_nat_lat @ v9_lattices )
& ( k13_nat_lat @ v8_lattices )
& ( k13_nat_lat @ v7_lattices )
& ( k13_nat_lat @ v6_lattices )
& ( k13_nat_lat @ v5_lattices )
& ( k13_nat_lat @ v4_lattices )
& ( k13_nat_lat @ v3_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[3876]) ).
thf(3883,plain,
k13_nat_lat @ v7_lattices,
inference(cnfConj,[status(thm)],[3877]) ).
thf(720,axiom,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( A @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( A @ ( A @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( B @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_nat_lat) ).
thf(5116,plain,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( A @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( A @ ( A @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( B @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(715,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice2) ).
thf(5088,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(588,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(4293,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(4294,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4293]) ).
thf(4295,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[4294]) ).
thf(10164,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,4295]) ).
thf(10165,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10164]) ).
thf(10166,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk56 ),
inference(simp,[status(thm)],[10165]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(1166,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_realset1 ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ m2_realset1 ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
& ( ( C @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_realset1 ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[1166]) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_realset1 ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1167]) ).
thf(627,axiom,
? [A: $i] :
( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_lattices) ).
thf(4565,plain,
? [A: $i] :
( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(4566,plain,
( ( sk317 @ v16_lattices )
& ( sk317 @ v15_lattices )
& ( sk317 @ v14_lattices )
& ( sk317 @ v13_lattices )
& ( sk317 @ v10_lattices )
& ( sk317 @ v9_lattices )
& ( sk317 @ v8_lattices )
& ( sk317 @ v7_lattices )
& ( sk317 @ v6_lattices )
& ( sk317 @ v5_lattices )
& ( sk317 @ v4_lattices )
& ( sk317 @ v3_lattices )
& ~ ( sk317 @ v3_struct_0 )
& ( sk317 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4565]) ).
thf(4571,plain,
sk317 @ v7_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(525,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4004,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(4005,plain,
sk281 @ v1_xboole_0,
inference(cnf,[status(esa)],[4004]) ).
thf(892,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattices) ).
thf(5857,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(2942,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(2943,plain,
( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(miniscope,[status(thm)],[2942]) ).
thf(2944,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[2943]) ).
thf(2945,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2944]) ).
thf(1016,plain,
sk1 @ l3_lattices,
inference(cnfConj,[status(thm)],[1003]) ).
thf(6725,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( A @ ( B @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1047,1016]) ).
thf(6726,plain,
! [A: $i] :
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6725:[bind(A,$thf( sk1 ))]]) ).
thf(7066,plain,
! [A: $i] :
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[6726]) ).
thf(8023,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2945,7066]) ).
thf(8024,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8023]) ).
thf(8025,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8024:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(197,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(2144,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(2145,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(cnf,[status(esa)],[2144]) ).
thf(23594,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8025,2145]) ).
thf(23595,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23594]) ).
thf(829,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice2) ).
thf(5593,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(2031,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_funct_2) ).
thf(3798,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(1102,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
inference(cnf,[status(esa)],[1102]) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[1103]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( A
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_domain_1) ).
thf(2280,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( A
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(4904,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(793,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k9_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_filter_2) ).
thf(5454,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k9_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(360,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(3115,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(3116,plain,
( ( sk217 @ v1_funct_1 )
& ( sk217 @ v1_xboole_0 )
& ( sk217 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3115]) ).
thf(3118,plain,
sk217 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[3116]) ).
thf(698,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(4999,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(5000,plain,
~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4999]) ).
thf(5001,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5000]) ).
thf(9156,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,5001]) ).
thf(9157,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9156]) ).
thf(9163,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk217 ),
inference(simp,[status(thm)],[9157]) ).
thf(594,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( C @ ( E @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( B @ ( D @ ( A @ k2_filter_0 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice4) ).
thf(4311,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ~ ( ( C @ ( E @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( B @ ( D @ ( A @ k2_filter_0 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(489,axiom,
? [A: $i] :
( ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice2) ).
thf(3811,plain,
? [A: $i] :
( ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(3812,plain,
( ( sk272 @ v1_lattice2 )
& ( sk272 @ v10_lattices )
& ( sk272 @ v9_lattices )
& ( sk272 @ v8_lattices )
& ( sk272 @ v7_lattices )
& ( sk272 @ v6_lattices )
& ( sk272 @ v5_lattices )
& ( sk272 @ v4_lattices )
& ~ ( sk272 @ v3_struct_0 )
& ( sk272 @ l3_lattices ) ),
inference(cnf,[status(esa)],[3811]) ).
thf(3813,plain,
sk272 @ l3_lattices,
inference(cnfConj,[status(thm)],[3812]) ).
thf(976,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattices) ).
thf(6219,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(746,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_filter_0 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_filter_0) ).
thf(5242,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_filter_0 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(3912,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(740,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v5_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattice2) ).
thf(5224,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v5_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(613,axiom,
( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ v1_funct_2 ) ) )
& ( k2_nat_lat @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_nat_lat) ).
thf(4467,plain,
( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ v1_funct_2 ) ) )
& ( k2_nat_lat @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(4468,plain,
( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ v1_funct_2 ) ) )
& ( k2_nat_lat @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[4467]) ).
thf(4469,plain,
k2_nat_lat @ v1_funct_1,
inference(cnfConj,[status(thm)],[4468]) ).
thf(8926,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4469,7087]) ).
thf(8927,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8926]) ).
thf(8928,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8927:[bind(A,$thf( k2_nat_lat ))]]) ).
thf(628,axiom,
? [A: $i] :
( ( A @ v1_lattice2 )
& ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice2) ).
thf(4581,plain,
? [A: $i] :
( ( A @ v1_lattice2 )
& ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(4582,plain,
( ( sk318 @ v1_lattice2 )
& ( sk318 @ v3_filter_0 )
& ( sk318 @ v13_lattices )
& ( sk318 @ v10_lattices )
& ( sk318 @ v9_lattices )
& ( sk318 @ v8_lattices )
& ( sk318 @ v7_lattices )
& ( sk318 @ v6_lattices )
& ( sk318 @ v5_lattices )
& ( sk318 @ v4_lattices )
& ( sk318 @ v3_lattices )
& ~ ( sk318 @ v3_struct_0 )
& ( sk318 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4581]) ).
thf(4592,plain,
sk318 @ v7_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(1039,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) )
| ~ ( A @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1039]) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1040]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1171,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1171]) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1172]) ).
thf(138,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(1855,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(535,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattice4) ).
thf(4043,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice2) ).
thf(3534,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) ) )
& ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(521,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( E @ ( D @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice2) ).
thf(3990,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( E @ ( D @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(934,axiom,
( ( ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s4_subset_1 ) ) )
& ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s4_subset_1 ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_subset_1) ).
thf(6047,plain,
( ( ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f3_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) )
& ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f2_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(6048,plain,
( ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk435 @ r2_hidden ) )
| ~ ( sk435 @ p1_s4_subset_1 )
| sk433 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk435 @ p1_s4_subset_1 )
| ~ ( sk435 @ p1_s4_subset_1 )
| sk433 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk435 @ r2_hidden ) )
| ( f3_s4_subset_1 @ ( sk435 @ r2_hidden ) )
| sk433 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk435 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk435 @ r2_hidden ) )
| sk433 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk435 @ m1_subset_1 ) )
| sk433 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk433
| ~ ( f2_s4_subset_1 @ ( sk434 @ r2_hidden ) )
| ~ ( sk434 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk433
| ( sk434 @ p1_s4_subset_1 )
| ~ ( sk434 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk433
| ~ ( f2_s4_subset_1 @ ( sk434 @ r2_hidden ) )
| ( f2_s4_subset_1 @ ( sk434 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk433
| ( sk434 @ p1_s4_subset_1 )
| ( f2_s4_subset_1 @ ( sk434 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk433
| ( f1_s4_subset_1 @ ( sk434 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[6047]) ).
thf(6056,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk435 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk435 @ r2_hidden ) )
| sk433 ),
inference(cnfConj,[status(thm)],[6048]) ).
thf(6063,plain,
( ( sk435 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk435 @ r2_hidden ) )
| sk433
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[6056]) ).
thf(648,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(4714,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(534,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(4037,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_tarski ) ) )
& ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).
thf(1155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( C @ k2_funct_1 @ v1_funct_1 )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1155]) ).
thf(1158,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1156]) ).
thf(255,axiom,
? [A: $i] :
( ( A @ v1_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_lattices) ).
thf(2512,plain,
? [A: $i] :
( ( A @ v1_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(601,axiom,
? [A: $i] :
( ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_lattices) ).
thf(4362,plain,
? [A: $i] :
( ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(4363,plain,
( ( sk302 @ v15_lattices )
& ( sk302 @ v14_lattices )
& ( sk302 @ v13_lattices )
& ( sk302 @ v10_lattices )
& ( sk302 @ v9_lattices )
& ( sk302 @ v8_lattices )
& ( sk302 @ v7_lattices )
& ( sk302 @ v6_lattices )
& ( sk302 @ v5_lattices )
& ( sk302 @ v4_lattices )
& ( sk302 @ v3_lattices )
& ~ ( sk302 @ v3_struct_0 )
& ( sk302 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4362]) ).
thf(4376,plain,
~ ( sk302 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4363]) ).
thf(353,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_domain_1) ).
thf(3072,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(1005,plain,
sk2 @ l3_lattices,
inference(cnfConj,[status(thm)],[1003]) ).
thf(585,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_funct_2) ).
thf(4276,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(4277,plain,
! [A: $i] :
( ( ( ( A @ ( sk298 @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s4_funct_2 ) )
| ~ ( f1_s4_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ v1_funct_2 ) ) )
& ( sk298 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[4276]) ).
thf(4280,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[4277]) ).
thf(1015,plain,
~ ( sk2 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[1003]) ).
thf(6936,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( A @ ( B @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1047,1015]) ).
thf(6937,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6936:[bind(A,$thf( sk2 ))]]) ).
thf(7043,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[6937]) ).
thf(8719,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4469,7043]) ).
thf(8720,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8719]) ).
thf(8721,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8720:[bind(A,$thf( k2_nat_lat ))]]) ).
thf(11019,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8721]) ).
thf(11020,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11019]) ).
thf(11043,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != k2_nat_lat )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11020]) ).
thf(4278,plain,
sk298 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4277]) ).
thf(7463,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4278,7043]) ).
thf(7464,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7463]) ).
thf(7465,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7464:[bind(A,$thf( sk298 ))]]) ).
thf(23693,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7465]) ).
thf(23694,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23693]) ).
thf(23791,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( sk298 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23694]) ).
thf(23846,plain,
( ( sk298 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23791]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(1068,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(320,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(2906,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(2907,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2906]) ).
thf(2908,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2907]) ).
thf(888,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
<=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_0) ).
thf(5842,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r3_lattices ) ) )
=> ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(6747,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( A @ ( B @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1047,1005]) ).
thf(6748,plain,
! [A: $i] :
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6747:[bind(A,$thf( sk2 ))]]) ).
thf(7088,plain,
! [A: $i] :
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[6748]) ).
thf(9839,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4278,7088]) ).
thf(9840,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9839]) ).
thf(9841,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9840:[bind(A,$thf( sk298 ))]]) ).
thf(10992,plain,
( ( ( k1_xboole_0 @ ( sk2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9841]) ).
thf(10993,plain,
( ( ( k1_xboole_0 @ ( sk2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10992]) ).
thf(11059,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk298 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10993]) ).
thf(11090,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[11059]) ).
thf(10910,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,1105]) ).
thf(10911,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[10910]) ).
thf(10912,plain,
f2_s4_funct_2 @ ( sk298 @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[10911:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk298 ))]]) ).
thf(603,axiom,
? [A: $i] :
( ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_filter_0) ).
thf(4381,plain,
? [A: $i] :
( ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(4382,plain,
( ( sk303 @ v3_filter_0 )
& ( sk303 @ v10_lattices )
& ( sk303 @ v9_lattices )
& ( sk303 @ v8_lattices )
& ( sk303 @ v7_lattices )
& ( sk303 @ v6_lattices )
& ( sk303 @ v5_lattices )
& ( sk303 @ v4_lattices )
& ( sk303 @ v3_lattices )
& ~ ( sk303 @ v3_struct_0 )
& ( sk303 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4381]) ).
thf(4391,plain,
sk303 @ v6_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(475,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(3740,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(3741,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[3740]) ).
thf(3742,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[3741]) ).
thf(9043,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,3742]) ).
thf(9044,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9043]) ).
thf(9045,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk56 ),
inference(simp,[status(thm)],[9044]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(1401,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(331,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(2953,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1867,plain,
sk56 @ v1_funct_1,
inference(cnfConj,[status(thm)],[1865]) ).
thf(7994,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1867,7066]) ).
thf(7995,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7994]) ).
thf(7996,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7995:[bind(A,$thf( sk56 ))]]) ).
thf(23738,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7996]) ).
thf(23739,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23738]) ).
thf(23772,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk56 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23739]) ).
thf(23825,plain,
( ( sk56 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23772]) ).
thf(418,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ( A @ v6_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattice2) ).
thf(3460,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ( A @ v6_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(1422,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).
thf(2947,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(1569,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(1939,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(482,axiom,
( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ v1_funct_2 ) ) )
& ( k10_nat_lat @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_nat_lat) ).
thf(3777,plain,
( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ v1_funct_2 ) ) )
& ( k10_nat_lat @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(3778,plain,
( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ v1_funct_2 ) ) )
& ( k10_nat_lat @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[3777]) ).
thf(3779,plain,
k10_nat_lat @ v1_funct_1,
inference(cnfConj,[status(thm)],[3778]) ).
thf(7220,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3779,7043]) ).
thf(7221,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7220]) ).
thf(7222,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7221:[bind(A,$thf( k10_nat_lat ))]]) ).
thf(23667,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7222]) ).
thf(23668,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23667]) ).
thf(23759,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( k10_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23668]) ).
thf(23810,plain,
( ( k10_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23759]) ).
thf(728,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D
= ( B @ ( C @ k1_realset1 ) ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
=> ( B @ ( D @ v2_binop_1 ) ) )
& ( ( A @ ( C @ v3_binop_1 ) )
=> ( B @ ( D @ v3_binop_1 ) ) )
& ( ( A @ ( C @ v1_binop_1 ) )
=> ( B @ ( D @ v1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_2) ).
thf(5173,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D
= ( B @ ( C @ k1_realset1 ) ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
=> ( B @ ( D @ v2_binop_1 ) ) )
& ( ( A @ ( C @ v3_binop_1 ) )
=> ( B @ ( D @ v3_binop_1 ) ) )
& ( ( A @ ( C @ v1_binop_1 ) )
=> ( B @ ( D @ v1_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1011,plain,
sk2 @ u1_struct_0 @ ( sk4 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[1003]) ).
thf(1006,plain,
sk3 = sk4,
inference(cnfConj,[status(thm)],[1003]) ).
thf(1017,plain,
sk4 = sk3,
inference(lifteq,[status(thm)],[1006]) ).
thf(6338,plain,
sk2 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ),
inference(rewrite,[status(thm)],[1011,1017]) ).
thf(647,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(4711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(631,axiom,
? [A: $i] :
( ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v1_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_lattices) ).
thf(4600,plain,
? [A: $i] :
( ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v1_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(4601,plain,
( ( sk319 @ v7_lattices )
& ( sk319 @ v6_lattices )
& ( sk319 @ v1_lattices )
& ~ ( sk319 @ v3_struct_0 )
& ( sk319 @ l1_lattices ) ),
inference(cnf,[status(esa)],[4600]) ).
thf(4603,plain,
sk319 @ v6_lattices,
inference(cnfConj,[status(thm)],[4601]) ).
thf(306,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(2831,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(2832,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[2831]) ).
thf(2833,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk188 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2832]) ).
thf(2834,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2833]) ).
thf(2836,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2834]) ).
thf(2837,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[2836]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
<=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
thf(1133,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( ( D @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= D ) )
& ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk9 ) ) )
| ( ( A @ ( B @ sk9 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk8 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk9 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk8 ) ) )
| ( ( A @ ( B @ sk9 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk8 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk9 ) ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk9 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk9 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk8 ) ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk9 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( B @ k1_relat_1 @ ( A @ ( B @ sk9 ) @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( B
= ( A @ k2_funct_1 ) )
| ( A @ k1_relat_1 @ ( A @ ( B @ sk8 ) @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1133]) ).
thf(1136,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( A @ k1_relat_1 @ ( A @ ( B @ sk8 ) @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1134]) ).
thf(1142,plain,
! [B: $i,A: $i] :
( ( A @ k1_relat_1 @ ( A @ ( B @ sk8 ) @ r2_hidden ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1136]) ).
thf(7223,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2945,7043]) ).
thf(7224,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7223]) ).
thf(7225,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7224:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(23600,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7225,2145]) ).
thf(23601,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23600]) ).
thf(750,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_setwiseo ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_lattice2) ).
thf(5265,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_setwiseo ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(779,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k5_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice4) ).
thf(5383,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) )
=> ( B
= ( A @ k5_lattice4 ) ) )
& ( ( B
= ( A @ k5_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k7_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(137,axiom,
k1_numbers @ ( k5_numbers @ r1_tarski ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_numbers) ).
thf(1854,plain,
k1_numbers @ ( k5_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(1065,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1066,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(miniscope,[status(thm)],[1065]) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[1066]) ).
thf(10448,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1854,1067]) ).
thf(10449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_numbers @ ( k5_numbers @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[10448]) ).
thf(10450,plain,
! [A: $i] : ( k1_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[10449:[bind(A,$thf( k5_numbers )),bind(B,$thf( k1_numbers ))]]) ).
thf(10463,plain,
! [A: $i] : ( k1_numbers @ ( A @ ( k5_numbers @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[10450]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).
thf(1305,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(504,axiom,
( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ v1_funct_2 ) ) )
& ( k11_nat_lat @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_nat_lat) ).
thf(3887,plain,
( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ v1_funct_2 ) ) )
& ( k11_nat_lat @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(3888,plain,
( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ v1_funct_2 ) ) )
& ( k11_nat_lat @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[3887]) ).
thf(3889,plain,
k11_nat_lat @ v1_funct_1,
inference(cnfConj,[status(thm)],[3888]) ).
thf(9816,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3889,7088]) ).
thf(9817,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9816]) ).
thf(9818,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9817:[bind(A,$thf( k11_nat_lat ))]]) ).
thf(361,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_binop_1) ).
thf(3120,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r2_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(828,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_0) ).
thf(5589,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(765,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattices) ).
thf(5316,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(3781,plain,
k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[3778]) ).
thf(937,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r3_relat_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_filter_0) ).
thf(6078,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r3_relat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(538,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
= B ) ) )
=> ( ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) )
= B )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_lattice2) ).
thf(4058,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
= B ) ) )
=> ( ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) )
= B )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(608,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
= B ) ) )
=> ( ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) )
= B )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice2) ).
thf(4435,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
= B ) ) )
=> ( ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) )
= B )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(2146,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k9_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_2) ).
thf(3848,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(91,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k2_funct_1 ) )
<=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(1497,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B
= ( A @ k2_funct_1 ) ) )
& ( ( B
= ( A @ k2_funct_1 ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(16,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(1077,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1078,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[1077]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(1788,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(985,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k16_filter_2 ) @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_filter_2) ).
thf(6278,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k16_filter_2 ) @ m1_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( A @ k4_lattice4 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(5814,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( B @ ( A @ k4_lattice4 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(486,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(3794,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).
thf(1608,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(4575,plain,
~ ( sk317 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4566]) ).
thf(902,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ k1_lattice2 )
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_filter_2) ).
thf(5906,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ k1_lattice2 )
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(982,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_nat_lat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_nat_lat) ).
thf(6246,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_nat_lat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(3367,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(453,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ? [F: $i] :
( ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( F @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_lattice2) ).
thf(3648,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ? [F: $i] :
( ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( F @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(4097,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(4011,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(583,axiom,
( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ v1_funct_2 ) ) )
& ( k1_nat_lat @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_nat_lat) ).
thf(4268,plain,
( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ v1_funct_2 ) ) )
& ( k1_nat_lat @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(4269,plain,
( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ v1_funct_2 ) ) )
& ( k1_nat_lat @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[4268]) ).
thf(4272,plain,
k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[4269]) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[1103]) ).
thf(13169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4272,1104]) ).
thf(13170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[13169]) ).
thf(13171,plain,
k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[13170:[bind(A,$thf( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) )),bind(B,$thf( k5_numbers )),bind(C,$thf( k1_nat_lat ))]]) ).
thf(17964,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13171,1067]) ).
thf(17965,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17964]) ).
thf(17966,plain,
! [A: $i] : ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ ( k1_nat_lat @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17965:[bind(A,$thf( k1_nat_lat @ k1_relat_1 )),bind(B,$thf( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) )),bind(C,$thf( C ))]]) ).
thf(17988,plain,
! [A: $i] : ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ ( k1_nat_lat @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17966]) ).
thf(673,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(4883,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(4884,plain,
sk350 @ l2_lattices,
inference(cnf,[status(esa)],[4883]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k4_filter_2 ) ) @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_2) ).
thf(3365,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k4_filter_2 ) ) @ m1_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(3044,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(5288,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(11015,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7996]) ).
thf(11016,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11015]) ).
thf(11058,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk56 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[11016]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(2184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(4638,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(319,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(2898,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(2899,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[2898]) ).
thf(2900,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_xboole_0 )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[2899]) ).
thf(2902,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2900]) ).
thf(2904,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2902]) ).
thf(2905,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[2904]) ).
thf(40,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(1184,plain,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1185,plain,
! [A: $i] :
( ( ~ ( A @ k1_tarski @ ( sk11 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk11 @ ( A @ m1_subset_1 ) ) )
& ~ ( sk11 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1184]) ).
thf(1186,plain,
~ ( sk11 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1185]) ).
thf(6412,plain,
( ( ( sk11 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,1186]) ).
thf(6413,plain,
( ( sk11 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6412]) ).
thf(6416,plain,
sk11 != k1_xboole_0,
inference(simp,[status(thm)],[6413]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(1872,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(1233,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(4279,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[4277]) ).
thf(849,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m3_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattice4) ).
thf(5674,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m3_lattice4 ) ) )
& ( ( A @ ( B @ m3_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(3253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(980,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_filter_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_2) ).
thf(6241,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_filter_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(1761,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k4_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(727,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).
thf(5161,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_2) ).
thf(1640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(4270,plain,
k1_nat_lat @ v1_funct_1,
inference(cnfConj,[status(thm)],[4269]) ).
thf(9801,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4270,7088]) ).
thf(9802,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9801]) ).
thf(9803,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9802:[bind(A,$thf( k1_nat_lat ))]]) ).
thf(23691,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,9803]) ).
thf(23692,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23691]) ).
thf(23769,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( k1_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23692]) ).
thf(23821,plain,
( ( k1_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23769]) ).
thf(10160,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,4295]) ).
thf(10161,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10160]) ).
thf(10170,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk217 ),
inference(simp,[status(thm)],[10161]) ).
thf(873,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_filter_0 ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(5782,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_filter_0 ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1001,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k17_filter_2 @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_filter_2) ).
thf(6336,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k17_filter_2 @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(856,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
<=> ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattices) ).
thf(5708,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) )
& ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
=> ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(10913,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8887]) ).
thf(10914,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10913]) ).
thf(11055,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk205 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[10914]) ).
thf(506,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r2_hidden ) ) ) )
& ( B
!= ( A @ k5_lattices ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_0) ).
thf(3895,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r2_hidden ) ) ) )
& ( B
!= ( A @ k5_lattices ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ m2_lattice4 ) )
& ~ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k22_filter_2) ).
thf(5192,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ m2_lattice4 ) )
& ~ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(655,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice4) ).
thf(4762,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(1458,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(406,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).
thf(3370,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(599,axiom,
? [A: $i] :
( ( A @ v17_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_lattices) ).
thf(4341,plain,
? [A: $i] :
( ( A @ v17_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(4342,plain,
( ( sk301 @ v17_lattices )
& ( sk301 @ v16_lattices )
& ( sk301 @ v15_lattices )
& ( sk301 @ v14_lattices )
& ( sk301 @ v13_lattices )
& ( sk301 @ v11_lattices )
& ( sk301 @ v10_lattices )
& ( sk301 @ v9_lattices )
& ( sk301 @ v8_lattices )
& ( sk301 @ v7_lattices )
& ( sk301 @ v6_lattices )
& ( sk301 @ v5_lattices )
& ( sk301 @ v4_lattices )
& ( sk301 @ v3_lattices )
& ~ ( sk301 @ v3_struct_0 )
& ( sk301 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4341]) ).
thf(4343,plain,
sk301 @ v15_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(760,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_0) ).
thf(5301,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(185,axiom,
? [A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_struct_0) ).
thf(2080,plain,
? [A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(2081,plain,
( ( sk85 @ v2_struct_0 )
& ( sk85 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[2080]) ).
thf(2082,plain,
sk85 @ l2_struct_0,
inference(cnfConj,[status(thm)],[2081]) ).
thf(3119,plain,
sk217 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3116]) ).
thf(8909,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3119,7087]) ).
thf(8910,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8909]) ).
thf(8911,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8910:[bind(A,$thf( sk217 ))]]) ).
thf(952,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k4_lattices ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattices) ).
thf(6138,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_lattices @ ( A @ k4_lattices ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(536,axiom,
( k13_nat_lat
= ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_nat_lat) ).
thf(4046,plain,
( k13_nat_lat
= ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(4047,plain,
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) )
= k13_nat_lat ),
inference(lifteq,[status(thm)],[4046]) ).
thf(978,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_2 )
= ( A @ k1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).
thf(6236,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_2 )
= ( A @ k1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(661,axiom,
( ( k6_nat_lat @ v10_lattices )
& ( k6_nat_lat @ v9_lattices )
& ( k6_nat_lat @ v8_lattices )
& ( k6_nat_lat @ v7_lattices )
& ( k6_nat_lat @ v6_lattices )
& ( k6_nat_lat @ v5_lattices )
& ( k6_nat_lat @ v4_lattices )
& ( k6_nat_lat @ v3_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_nat_lat) ).
thf(4792,plain,
( ( k6_nat_lat @ v10_lattices )
& ( k6_nat_lat @ v9_lattices )
& ( k6_nat_lat @ v8_lattices )
& ( k6_nat_lat @ v7_lattices )
& ( k6_nat_lat @ v6_lattices )
& ( k6_nat_lat @ v5_lattices )
& ( k6_nat_lat @ v4_lattices )
& ( k6_nat_lat @ v3_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(1835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(181,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(2046,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(335,axiom,
! [A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k11_nat_lat )
<=> ! [B: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( B @ m1_nat_lat ) ) ) )
=> ! [C: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( C @ m1_nat_lat ) ) ) )
=> ( ( C @ ( B @ ( A @ ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k5_nat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_nat_lat) ).
thf(2972,plain,
! [A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( B @ m1_nat_lat ) ) ) )
=> ! [C: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( C @ m1_nat_lat ) ) ) )
=> ( ( C @ ( B @ ( A @ ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k5_nat_1 ) ) ) ) )
=> ( A = k11_nat_lat ) )
& ( ( A = k11_nat_lat )
=> ! [B: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( B @ m1_nat_lat ) ) ) )
=> ! [C: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( C @ m1_nat_lat ) ) ) )
=> ( ( C @ ( B @ ( A @ ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k5_nat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(450,axiom,
? [A: $i] :
( ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_lattices) ).
thf(3631,plain,
? [A: $i] :
( ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(3632,plain,
( ( sk256 @ v10_lattices )
& ( sk256 @ v9_lattices )
& ( sk256 @ v8_lattices )
& ( sk256 @ v7_lattices )
& ( sk256 @ v6_lattices )
& ( sk256 @ v5_lattices )
& ( sk256 @ v4_lattices )
& ( sk256 @ v3_lattices )
& ~ ( sk256 @ v3_struct_0 )
& ( sk256 @ l3_lattices ) ),
inference(cnf,[status(esa)],[3631]) ).
thf(3634,plain,
sk256 @ v3_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(1243,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(802,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v16_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r2_lattices ) ) )
& ( D = F )
& ( C = E ) )
=> ( F @ ( E @ ( B @ r2_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_2) ).
thf(5486,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v16_lattices )
& ( B @ v15_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r2_lattices ) ) )
& ( D = F )
& ( C = E ) )
=> ( F @ ( E @ ( B @ r2_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(4371,plain,
sk302 @ v9_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(582,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(4266,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(633,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v5_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattices) ).
thf(4618,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) )
=> ( A @ v5_lattices ) )
& ( ( A @ v5_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(927,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_0) ).
thf(6009,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
= ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(908,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(5921,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(158,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(1935,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(662,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_filter_0) ).
thf(4803,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m1_filter_0 ) ) )
& ( ( A @ ( B @ m1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) ) ) )
& ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(109,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(1650,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(7324,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4270,7043]) ).
thf(7325,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7324]) ).
thf(7326,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7325:[bind(A,$thf( k1_nat_lat ))]]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ~ ( ! [E: $i,F: $i] :
~ ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( C
= ( F @ ( E @ k4_tarski ) ) ) )
& ( D @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relset_1) ).
thf(1921,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ~ ( ! [E: $i,F: $i] :
~ ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( C
= ( F @ ( E @ k4_tarski ) ) ) )
& ( D @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(709,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v11_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_0) ).
thf(5056,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v11_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(556,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D != k1_xboole_0 )
=> ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( E @ ( B @ ( A @ u2_lattices @ ( C @ ( A @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice2) ).
thf(4137,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D != k1_xboole_0 )
=> ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( E @ ( B @ ( A @ u2_lattices @ ( C @ ( A @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(116,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(1724,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(2173,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(632,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_lattices) ).
thf(4607,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1789,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1788]) ).
thf(1790,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1789]) ).
thf(1174,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1173]) ).
thf(1175,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk10 ) )
= A ),
inference(cnf,[status(esa)],[1174]) ).
thf(26414,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk10 ) )
= A ),
inference(lifteq,[status(thm)],[1175]) ).
thf(26433,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk10 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1790,26414]) ).
thf(26434,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk10 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[26433:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(2513,plain,
( ( sk143 @ v1_lattices )
& ~ ( sk143 @ v3_struct_0 )
& ( sk143 @ l1_lattices ) ),
inference(cnf,[status(esa)],[2512]) ).
thf(2516,plain,
sk143 @ v1_lattices,
inference(cnfConj,[status(thm)],[2513]) ).
thf(654,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice4) ).
thf(4760,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(695,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_lattice2) ).
thf(4963,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice2) ).
thf(2819,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(3880,plain,
k13_nat_lat @ v8_lattices,
inference(cnfConj,[status(thm)],[3877]) ).
thf(3878,plain,
k13_nat_lat @ v3_lattices,
inference(cnfConj,[status(thm)],[3877]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(2136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(865,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( D @ ( E @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattice2) ).
thf(5750,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( D @ ( E @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(1228,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(104,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(1623,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ v1_lattices )
=> ( A
= ( A @ u1_lattices @ ( A @ u1_struct_0 @ g1_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_lattices) ).
thf(1482,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ v1_lattices )
=> ( A
= ( A @ u1_lattices @ ( A @ u1_struct_0 @ g1_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(139,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1857,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1858,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[1857]) ).
thf(247,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(2485,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(2486,plain,
( ( sk141 @ v1_relat_1 )
& ( sk141 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2485]) ).
thf(2487,plain,
sk141 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[2486]) ).
thf(9039,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,3742]) ).
thf(9040,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9039]) ).
thf(9046,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk141 ),
inference(simp,[status(thm)],[9040]) ).
thf(10500,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk141 ) ),
inference(paramod_ordered,[status(thm)],[1858,9046]) ).
thf(10501,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk141 ),
inference(pattern_uni,[status(thm)],[10500:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(7991,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3012,7066]) ).
thf(7992,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7991]) ).
thf(7993,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7992:[bind(A,$thf( sk205 ))]]) ).
thf(580,axiom,
? [A: $i] :
( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_lattices) ).
thf(4246,plain,
? [A: $i] :
( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(4247,plain,
( ( sk297 @ v14_lattices )
& ( sk297 @ v13_lattices )
& ( sk297 @ v12_lattices )
& ( sk297 @ v11_lattices )
& ( sk297 @ v10_lattices )
& ( sk297 @ v9_lattices )
& ( sk297 @ v8_lattices )
& ( sk297 @ v7_lattices )
& ( sk297 @ v6_lattices )
& ( sk297 @ v5_lattices )
& ( sk297 @ v4_lattices )
& ( sk297 @ v3_lattices )
& ~ ( sk297 @ v3_struct_0 )
& ( sk297 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4246]) ).
thf(4249,plain,
sk297 @ v9_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(879,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( B
= ( A @ k6_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattice2) ).
thf(5797,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( B
= ( A @ k6_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(771,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_lattice2) ).
thf(5342,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) )
=> ( ( A @ l3_lattices )
& ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l3_lattices )
& ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(1887,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(4386,plain,
sk303 @ v10_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(2957,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(6702,plain,
( ( ( sk281 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,1186]) ).
thf(6703,plain,
( ( sk281 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6702]) ).
thf(6707,plain,
sk281 != sk11,
inference(simp,[status(thm)],[6703]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(3221,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_lattices ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattices) ).
thf(4563,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_lattices ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(931,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v9_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattices) ).
thf(6034,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
=> ( A @ v9_lattices ) )
& ( ( A @ v9_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(4070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(3046,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(216,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(2269,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(686,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(4927,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(4928,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4927]) ).
thf(4929,plain,
~ ( sk353 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[4928]) ).
thf(6717,plain,
( ( ( sk353 @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,4929]) ).
thf(6718,plain,
( ( sk353 @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6717]) ).
thf(6723,plain,
sk353 != sk56,
inference(simp,[status(thm)],[6718]) ).
thf(3821,plain,
sk272 @ v1_lattice2,
inference(cnfConj,[status(thm)],[3812]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_nat_lat) ).
thf(1907,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_realset1) ).
thf(2274,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(3820,plain,
sk272 @ v10_lattices,
inference(cnfConj,[status(thm)],[3812]) ).
thf(3891,plain,
k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[3888]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_binop_1) ).
thf(2654,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r2_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_partfun1) ).
thf(3248,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(1055,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(918,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k7_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_0) ).
thf(5953,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k7_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(4348,plain,
sk301 @ v6_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(10929,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7993]) ).
thf(10930,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10929]) ).
thf(11068,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk205 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10930]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ~ ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(2698,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ~ ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ~ ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
<=> ( B
= ( A @ k1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(3131,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) )
& ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B
= ( A @ k1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(693,axiom,
! [A: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( A @ k12_nat_lat @ m1_nat_lat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_nat_lat) ).
thf(4956,plain,
! [A: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( A @ k12_nat_lat @ m1_nat_lat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( C @ ( E @ r2_hidden ) )
<=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(4224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ~ ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ~ ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(437,axiom,
( k6_nat_lat
= ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_nat_lat) ).
thf(3573,plain,
( k6_nat_lat
= ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(3574,plain,
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) )
= k6_nat_lat ),
inference(lifteq,[status(thm)],[3573]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(4654,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v9_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v8_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v7_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v6_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v5_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v4_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v3_lattices )
& ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_filter_0) ).
thf(3617,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v9_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v8_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v7_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v6_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v5_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v4_lattices )
& ( B @ ( A @ k8_filter_0 ) @ v3_lattices )
& ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(1330,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(597,axiom,
? [A: $i] :
( ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v2_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_lattices) ).
thf(4330,plain,
? [A: $i] :
( ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v2_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(4331,plain,
( ( sk300 @ v5_lattices )
& ( sk300 @ v4_lattices )
& ( sk300 @ v2_lattices )
& ~ ( sk300 @ v3_struct_0 )
& ( sk300 @ l2_lattices ) ),
inference(cnf,[status(esa)],[4330]) ).
thf(4334,plain,
sk300 @ v5_lattices,
inference(cnfConj,[status(thm)],[4331]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_2) ).
thf(1323,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(3612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ g1_lattices ) @ l1_lattices )
& ( B @ ( A @ g1_lattices ) @ v1_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_lattices) ).
thf(3148,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ g1_lattices ) @ l1_lattices )
& ( B @ ( A @ g1_lattices ) @ v1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1010,plain,
~ ( sk1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[1003]) ).
thf(7004,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( A @ ( B @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1047,1010]) ).
thf(7005,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[7004:[bind(A,$thf( sk1 ))]]) ).
thf(7089,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[7005]) ).
thf(10679,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4270,7089]) ).
thf(10680,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10679]) ).
thf(10681,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10680:[bind(A,$thf( k1_nat_lat ))]]) ).
thf(11165,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,10681]) ).
thf(11166,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11165]) ).
thf(11178,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != k1_nat_lat )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11166]) ).
thf(441,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(3592,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(3593,plain,
! [A: $i] :
( ( A @ sk253 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk253 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[3592]) ).
thf(3595,plain,
! [A: $i] : ( A @ sk253 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3593]) ).
thf(12057,plain,
! [A: $i] :
( ( ( A @ sk253 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3595,1186]) ).
thf(12058,plain,
! [A: $i] :
( ( A @ sk253 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12057]) ).
thf(12065,plain,
! [A: $i] :
( ( A @ sk253 )
!= sk11 ),
inference(simp,[status(thm)],[12058]) ).
thf(994,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattice2) ).
thf(6315,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(4349,plain,
sk301 @ v4_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(389,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_0) ).
thf(3280,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(726,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(5159,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(5160,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(cnf,[status(esa)],[5159]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(1577,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(495,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_domain_1) ).
thf(3845,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(267,axiom,
? [A: $i] :
( ( A @ v2_lattices )
& ( A @ l2_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattices) ).
thf(2562,plain,
? [A: $i] :
( ( A @ v2_lattices )
& ( A @ l2_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(840,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattices) ).
thf(5640,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(2488,plain,
sk141 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2486]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(1832,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(1191,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(999,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(6332,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(7192,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3012,7043]) ).
thf(7193,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7192]) ).
thf(7194,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7193:[bind(A,$thf( sk205 ))]]) ).
thf(10942,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7194]) ).
thf(10943,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10942]) ).
thf(11051,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk205 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10943]) ).
thf(855,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ m2_nat_lat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_nat_lat) ).
thf(5706,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ m2_nat_lat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(4568,plain,
sk317 @ v15_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(7997,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4270,7066]) ).
thf(7998,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7997]) ).
thf(7999,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7998:[bind(A,$thf( k1_nat_lat ))]]) ).
thf(23649,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7999]) ).
thf(23650,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23649]) ).
thf(23765,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( k1_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23650]) ).
thf(23817,plain,
( ( k1_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23765]) ).
thf(8020,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3779,7066]) ).
thf(8021,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8020]) ).
thf(8022,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8021:[bind(A,$thf( k10_nat_lat ))]]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_2) ).
thf(2466,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(717,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k14_filter_2 ) @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_filter_2) ).
thf(5108,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k14_filter_2 ) @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_2) ).
thf(4766,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(84,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(1462,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(1059,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_funct_2) ).
thf(1128,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( ( C @ k1_relat_1 )
= A )
| ~ ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1128]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ k1_relat_1 )
= A )
| ~ ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1129]) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ( ( C @ k1_relat_1 )
= A ) ),
inference(lifteq,[status(thm)],[1130]) ).
thf(972,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_filter_0) ).
thf(6208,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(2745,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(467,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( ( A @ v2_struct_0 )
=> ( A
= ( A @ u2_struct_0 @ ( A @ u1_struct_0 @ g2_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v2_struct_0) ).
thf(3713,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( ( A @ v2_struct_0 )
=> ( A
= ( A @ u2_struct_0 @ ( A @ u1_struct_0 @ g2_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(796,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_filter_2) ).
thf(5461,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(579,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_lattices @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_filter_0) ).
thf(4243,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k6_lattices @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(8015,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3119,7066]) ).
thf(8016,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8015]) ).
thf(8017,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8016:[bind(A,$thf( sk217 ))]]) ).
thf(10975,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8017]) ).
thf(10976,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10975]) ).
thf(11040,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk217 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10976]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(2691,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(3638,plain,
sk256 @ v8_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_lattices ) )
= ( D @ ( C @ g1_lattices ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_lattices) ).
thf(1147,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_lattices ) )
= ( D @ ( C @ g1_lattices ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4358,plain,
sk301 @ v16_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(1479,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(355,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
<=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(3084,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ v1_relat_1 ) )
& ( ( A @ v1_relat_1 )
=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(4383,plain,
sk303 @ l3_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(69,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
<=> ( C = k1_xboole_0 ) ) )
& ( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
<=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(1362,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( ( C = k1_xboole_0 )
=> ( C
= ( B @ ( A @ k1_funct_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
=> ( C = k1_xboole_0 ) ) ) )
& ( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C
= ( B @ ( A @ k1_funct_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(3557,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(642,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
<=> ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice4) ).
thf(4669,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) )
=> ( B @ ( A @ ( C @ v2_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ k2_relat_1 )
= ( B @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ g2_struct_0 ) @ l2_struct_0 )
& ( B @ ( A @ g2_struct_0 ) @ v2_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g2_struct_0) ).
thf(3374,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ g2_struct_0 ) @ l2_struct_0 )
& ( B @ ( A @ g2_struct_0 ) @ v2_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(9798,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1867,7088]) ).
thf(9799,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9798]) ).
thf(9800,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9799:[bind(A,$thf( sk56 ))]]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(4788,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(4353,plain,
sk301 @ v5_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(11441,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk298 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10912,1067]) ).
thf(11442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk298 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11441]) ).
thf(11443,plain,
! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk298 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[11442:[bind(A,$thf( sk298 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(11463,plain,
! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk298 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[11443]) ).
thf(566,axiom,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( C @ ( B @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_nat_lat) ).
thf(4179,plain,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( C @ ( B @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(992,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_lattice4 ) )
= ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice4) ).
thf(6310,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_lattice4 ) )
= ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(232,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(2371,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(2372,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(cnf,[status(esa)],[2371]) ).
thf(2373,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(lifteq,[status(thm)],[2372]) ).
thf(511,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v11_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( B @ ( G @ r2_hidden ) )
=> ( ( G @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) ) ) ) )
=> ( ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) )
= ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_lattice2) ).
thf(3919,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v11_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( B @ ( G @ r2_hidden ) )
=> ( ( G @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) ) ) ) )
=> ( ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) )
= ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1013,plain,
sk1 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[1003]) ).
thf(6362,plain,
( ( ( sk141 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,1186]) ).
thf(6363,plain,
( ( sk141 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6362]) ).
thf(6365,plain,
sk141 != sk11,
inference(simp,[status(thm)],[6363]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_realset1) ).
thf(1115,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(4675,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(3312,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(456,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(3657,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(4368,plain,
sk302 @ v10_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(2520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(285,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(2730,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(4390,plain,
sk303 @ v9_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(4471,plain,
k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[4468]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m2_lattice4 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_1_lattice4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( B @ k4_lattice4 ) @ ( D @ r1_tarski ) )
& ( A
= ( D @ ( B @ k2_lattice4 ) ) )
& ( B @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).
thf(4771,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m2_lattice4 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( B @ k4_lattice4 ) @ ( D @ r1_tarski ) )
& ( A
= ( D @ ( B @ k2_lattice4 ) ) )
& ( B @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_lattice4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_lattice4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( B @ k4_lattice4 ) @ ( D @ r1_tarski ) )
& ( A
= ( D @ ( B @ k2_lattice4 ) ) )
& ( B @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_lattice2) ).
thf(3231,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(4302,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(2388,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) )
=> ( B @ k1_tarski @ ( A @ r1_tarski ) ) )
& ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(501,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(3866,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
=> ( B @ ( A @ ( D @ m2_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_nat_lat) ).
thf(1100,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
=> ( B @ ( A @ ( D @ m2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10944,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,1104]) ).
thf(10945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[10944]) ).
thf(10946,plain,
f1_s4_funct_2 @ ( sk298 @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[10945:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk298 ))]]) ).
thf(11474,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk298 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10946,1067]) ).
thf(11475,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk298 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11474]) ).
thf(11476,plain,
! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk298 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[11475:[bind(A,$thf( sk298 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(11495,plain,
! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk298 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[11476]) ).
thf(4253,plain,
sk297 @ v12_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(527,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_0 ) @ v3_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_filter_0) ).
thf(4008,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k8_filter_0 ) @ v3_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(387,axiom,
! [A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k1_nat_lat )
<=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k6_nat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_nat_lat) ).
thf(3258,plain,
! [A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k6_nat_1 ) ) ) ) )
=> ( A = k1_nat_lat ) )
& ( ( A = k1_nat_lat )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k6_nat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(201,axiom,
~ ( k1_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_numbers) ).
thf(2182,plain,
~ ( k1_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(2183,plain,
~ ( k1_numbers @ v1_xboole_0 ),
inference(polarity_switch,[status(thm)],[2182]) ).
thf(6360,plain,
( ( ( sk141 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,2183]) ).
thf(6361,plain,
( ( sk141 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6360]) ).
thf(6364,plain,
sk141 != k1_numbers,
inference(simp,[status(thm)],[6361]) ).
thf(9037,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,3742]) ).
thf(9038,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9037]) ).
thf(9049,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[9038]) ).
thf(10496,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1858,9049]) ).
thf(10497,plain,
( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[10496:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(2270,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[2269]) ).
thf(2271,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[2270]) ).
thf(10021,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,2271]) ).
thf(10022,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10021]) ).
thf(10025,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk217 ),
inference(simp,[status(thm)],[10022]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(3788,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(4595,plain,
sk318 @ l3_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(877,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_lattice4 ) )
= ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattice4) ).
thf(5792,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_lattice4 ) )
= ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(875,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k11_filter_2 ) @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_filter_2) ).
thf(5787,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k11_filter_2 ) @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(845,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_nat_lat ) )
=> ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_nat_lat) ).
thf(5663,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_nat_lat ) )
=> ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(4258,plain,
sk297 @ v11_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(524,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D != k1_xboole_0 )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( E @ ( B @ ( A @ u1_lattices @ ( C @ ( A @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_lattice2) ).
thf(4001,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D != k1_xboole_0 )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( E @ ( B @ ( A @ u1_lattices @ ( C @ ( A @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(964,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) )
= ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_0) ).
thf(6176,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) )
= ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(2925,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(4793,plain,
( ( k6_nat_lat @ v10_lattices )
& ( k6_nat_lat @ v9_lattices )
& ( k6_nat_lat @ v8_lattices )
& ( k6_nat_lat @ v7_lattices )
& ( k6_nat_lat @ v6_lattices )
& ( k6_nat_lat @ v5_lattices )
& ( k6_nat_lat @ v4_lattices )
& ( k6_nat_lat @ v3_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[4792]) ).
thf(4798,plain,
k6_nat_lat @ v6_lattices,
inference(cnfConj,[status(thm)],[4793]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(1182,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1183,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ ( C @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1182]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(1489,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A ) )
& ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r3_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(4205,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( B @ ( A @ r3_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( B @ ( A @ k3_binop_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(2324,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( B @ ( A @ k3_binop_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(231,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(2366,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(2367,plain,
( ( sk126 @ v2_funct_1 )
& ( sk126 @ v1_funct_1 )
& ( sk126 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2366]) ).
thf(2368,plain,
sk126 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2367]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(1042,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1042]) ).
thf(6667,plain,
! [B: $i,A: $i] :
( ( ( sk126 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2368,1043]) ).
thf(6668,plain,
! [B: $i,A: $i] :
( ( ( sk126 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[6667]) ).
thf(6669,plain,
! [A: $i] : ( sk126 @ k1_relat_1 @ ( sk126 @ k9_relat_1 ) @ ( A @ ( sk126 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6668:[bind(A,$thf( A )),bind(B,$thf( sk126 ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(1112,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1113,plain,
! [A: $i] :
( ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1112]) ).
thf(1114,plain,
! [A: $i] :
( ~ ( A @ v1_relat_1 )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1113]) ).
thf(10794,plain,
! [A: $i] :
( ( ( sk126 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ~ $true
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(paramod_ordered,[status(thm)],[2368,1114]) ).
thf(10795,plain,
! [A: $i] :
( ( ( sk126 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[10794]) ).
thf(10796,plain,
( ( sk126 @ k1_relat_1 @ ( sk126 @ k9_relat_1 ) )
= ( sk126 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[10795:[bind(A,$thf( sk126 ))]]) ).
thf(26571,plain,
! [A: $i] : ( sk126 @ k2_relat_1 @ ( A @ ( sk126 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6669,10796]) ).
thf(4583,plain,
sk318 @ v5_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(10673,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3012,7089]) ).
thf(10674,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10673]) ).
thf(10675,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10674:[bind(A,$thf( sk205 ))]]) ).
thf(10988,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,10675]) ).
thf(10989,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10988]) ).
thf(11064,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk205 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10989]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(3199,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(898,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k3_lattices ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattices) ).
thf(5888,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k3_lattices ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(4443,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(12055,plain,
! [A: $i] :
( ( ( A @ sk253 @ v1_xboole_0 )
!= ( sk219 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3595,3129]) ).
thf(12056,plain,
! [A: $i] :
( ( A @ sk253 @ v1_xboole_0 )
!= ( sk219 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12055]) ).
thf(12069,plain,
! [A: $i] :
( ( A @ sk253 )
!= sk219 ),
inference(simp,[status(thm)],[12056]) ).
thf(4578,plain,
sk317 @ v4_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_binop_1) ).
thf(3075,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(5027,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(411,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_0) ).
thf(3393,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(2369,plain,
sk126 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2367]) ).
thf(9830,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2369,7088]) ).
thf(9831,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9830]) ).
thf(9832,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9831:[bind(A,$thf( sk126 ))]]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ g2_lattices ) @ v2_lattices )
& ~ ( B @ ( A @ g2_lattices ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattices) ).
thf(2782,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ g2_lattices ) @ v2_lattices )
& ~ ( B @ ( A @ g2_lattices ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(1109,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r3_binop_1 ) ) )
<=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_binop_1) ).
thf(2893,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
=> ( C @ ( B @ ( A @ r3_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_binop_1 ) ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k14_filter_2 ) )
= ( B @ ( A @ k8_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).
thf(3702,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k14_filter_2 ) )
= ( B @ ( A @ k8_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(966,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(6185,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(6186,plain,
( ( sk446 @ v3_lattices )
& ~ ( sk446 @ v3_struct_0 )
& ( sk446 @ l3_lattices ) ),
inference(cnf,[status(esa)],[6185]) ).
thf(6189,plain,
sk446 @ v3_lattices,
inference(cnfConj,[status(thm)],[6186]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(2880,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(666,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(4846,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(4847,plain,
sk349 @ l2_struct_0,
inference(cnf,[status(esa)],[4846]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).
thf(3438,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(6187,plain,
sk446 @ l3_lattices,
inference(cnfConj,[status(thm)],[6186]) ).
thf(905,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( B @ ( C @ ( A @ k2_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(5914,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( B @ ( C @ ( A @ k2_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(704,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v11_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ k4_lattices ) ) )
= ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_lattice2) ).
thf(5032,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v11_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ k4_lattices ) ) )
= ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(725,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(5156,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B = D )
| ( ( B @ ( A @ g1_lattices ) )
!= ( D @ ( C @ g1_lattices ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( A = C )
| ( ( B @ ( A @ g1_lattices ) )
!= ( D @ ( C @ g1_lattices ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1147]) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ g1_lattices ) )
!= ( D @ ( C @ g1_lattices ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1148]) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( A = C )
| ( ( B @ ( A @ g1_lattices ) )
!= ( D @ ( C @ g1_lattices ) ) ) ),
inference(lifteq,[status(thm)],[1149]) ).
thf(10784,plain,
! [A: $i] :
( ( ( sk141 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ~ $true
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(paramod_ordered,[status(thm)],[2488,1114]) ).
thf(10785,plain,
! [A: $i] :
( ( ( sk141 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[10784]) ).
thf(10786,plain,
( ( sk141 @ k1_relat_1 @ ( sk141 @ k9_relat_1 ) )
= ( sk141 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[10785:[bind(A,$thf( sk141 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( E
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
=> ( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relat_1) ).
thf(1020,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( E
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
=> ( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(402,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
<=> ( A @ k1_lattice2 @ v13_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_lattice2) ).
thf(3357,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k1_lattice2 @ v13_lattices )
=> ( A @ v14_lattices ) )
& ( ( A @ v14_lattices )
=> ( A @ k1_lattice2 @ v13_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(436,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_2 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_2) ).
thf(3569,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_2 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_partfun1) ).
thf(2540,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(670,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
& ( B
= ( A @ k1_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_0) ).
thf(4871,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
& ( B
= ( A @ k1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(551,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k6_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_0) ).
thf(4115,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k6_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(23637,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7194]) ).
thf(23638,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23637]) ).
thf(23785,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( sk205 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23638]) ).
thf(23839,plain,
( ( sk205 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23785]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m2_filter_2 ) )
& ( A @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k21_filter_2 ) ) @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k21_filter_2) ).
thf(5457,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m2_filter_2 ) )
& ( A @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k21_filter_2 ) ) @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(2777,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(368,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 )
& ( A @ u1_lattices @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice2) ).
thf(3152,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 )
& ( A @ u1_lattices @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(1048,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1049,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ? [E: $i] :
( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[1048]) ).
thf(1050,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E
= ( A @ ( B @ ( C @ ( D @ ( E @ sk7 ) ) ) ) @ ( D @ k1_funct_1 ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
| ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 ) )
& ( ( C @ ( A @ ( B @ ( C @ ( D @ ( E @ sk7 ) ) ) ) @ r2_hidden ) )
| ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
| ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 ) )
& ( ( A @ ( A @ ( B @ ( C @ ( D @ ( E @ sk7 ) ) ) ) @ m1_subset_1 ) )
| ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
| ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1049]) ).
thf(1051,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ ( E @ sk7 ) ) ) ) @ m1_subset_1 ) )
| ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
| ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1050]) ).
thf(971,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(6204,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(9819,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3119,7088]) ).
thf(9820,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9819]) ).
thf(9821,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9820:[bind(A,$thf( sk217 ))]]) ).
thf(10982,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9821]) ).
thf(10983,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10982]) ).
thf(11036,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk217 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10983]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_binop_1) ).
thf(2964,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) )
=> ( A @ ( B @ v1_binop_1 ) ) )
& ( ( A @ ( B @ v1_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k8_filter_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_2) ).
thf(5379,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k8_filter_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(944,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(6110,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(146,axiom,
? [A: $i] :
( ( A @ v1_lattices )
& ( A @ l1_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattices) ).
thf(1883,plain,
? [A: $i] :
( ( A @ v1_lattices )
& ( A @ l1_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1884,plain,
( ( sk58 @ v1_lattices )
& ( sk58 @ l1_lattices ) ),
inference(cnf,[status(esa)],[1883]) ).
thf(1886,plain,
sk58 @ v1_lattices,
inference(cnfConj,[status(thm)],[1884]) ).
thf(998,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
<=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice4) ).
thf(6327,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) )
=> ( B @ ( A @ ( C @ v3_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
& ( B @ ( A @ ( C @ v1_lattice4 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_binop_1) ).
thf(2718,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r5_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k11_filter_2 ) )
= ( B @ ( A @ k8_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_filter_2) ).
thf(6210,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k11_filter_2 ) )
= ( B @ ( A @ k8_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(10017,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,2271]) ).
thf(10018,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10017]) ).
thf(10029,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10018]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(1843,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(910,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_filter_0) ).
thf(5929,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(649,axiom,
( ! [A: $i] :
( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s13_funct_2) ).
thf(4718,plain,
( ! [A: $i] :
( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1169,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ m2_realset1 ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1167]) ).
thf(3130,plain,
sk219 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3128]) ).
thf(10797,plain,
! [A: $i] :
( ( ( sk219 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ~ $true
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(paramod_ordered,[status(thm)],[3130,1114]) ).
thf(10798,plain,
! [A: $i] :
( ( ( sk219 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[10797]) ).
thf(10799,plain,
( ( sk219 @ k1_relat_1 @ ( sk219 @ k9_relat_1 ) )
= ( sk219 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[10798:[bind(A,$thf( sk219 ))]]) ).
thf(641,axiom,
( ! [A: $i] :
( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s12_funct_2) ).
thf(4660,plain,
( ! [A: $i] :
( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(2437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(1928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( ( A @ v2_lattices )
=> ( A
= ( A @ u2_lattices @ ( A @ u1_struct_0 @ g2_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v2_lattices) ).
thf(1377,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( ( A @ v2_lattices )
=> ( A
= ( A @ u2_lattices @ ( A @ u1_struct_0 @ g2_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(792,axiom,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s11_funct_2) ).
thf(5440,plain,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(5441,plain,
! [A: $i] :
( ( ( ( A @ ( sk391 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f7_s11_funct_2 ) )
| ( A = f4_s11_funct_2 )
| ( A = f3_s11_funct_2 )
| ~ ( f1_s11_funct_2 @ ( A @ m1_subset_1 ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( ( f4_s11_funct_2 @ ( sk391 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( ( f3_s11_funct_2 @ ( sk391 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( sk391 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ) ),
inference(cnf,[status(esa)],[5440]) ).
thf(5444,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5441]) ).
thf(5448,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ m2_relset_1 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5444]) ).
thf(322,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(2912,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(2913,plain,
~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[2912]) ).
thf(2914,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[2913]) ).
thf(10132,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,2914]) ).
thf(10133,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10132]) ).
thf(10145,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk281 ),
inference(simp,[status(thm)],[10133]) ).
thf(841,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattice2) ).
thf(5643,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(2190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(871,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_0) ).
thf(5772,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(2523,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(546,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(4087,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(1009,plain,
( ( sk3 @ ( sk1 @ k7_lattices ) )
!= ( sk4 @ ( sk2 @ k7_lattices ) ) ),
inference(cnfConj,[status(thm)],[1003]) ).
thf(1019,plain,
( ( sk4 @ ( sk2 @ k7_lattices ) )
!= ( sk3 @ ( sk1 @ k7_lattices ) ) ),
inference(lifteq,[status(thm)],[1009]) ).
thf(6345,plain,
( ( sk3 @ ( sk2 @ k7_lattices ) )
!= ( sk3 @ ( sk1 @ k7_lattices ) ) ),
inference(rewrite,[status(thm)],[1019,1017]) ).
thf(6346,plain,
( ( sk3 != sk3 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[6345]) ).
thf(6347,plain,
sk2 != sk1,
inference(simp,[status(thm)],[6346]) ).
thf(4364,plain,
sk302 @ v8_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(1116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( B @ k1_realset1 ) @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1115]) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1116]) ).
thf(10701,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3119,7089]) ).
thf(10702,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10701]) ).
thf(10703,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10702:[bind(A,$thf( sk217 ))]]) ).
thf(23685,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,10703]) ).
thf(23686,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23685]) ).
thf(23763,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk217 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23686]) ).
thf(23814,plain,
( ( sk217 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23763]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(1394,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(747,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(5246,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(889,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_lattice2) ).
thf(5846,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(685,axiom,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( A @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_nat_lat) ).
thf(4924,plain,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( A @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(403,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_binop_1) ).
thf(3361,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(173,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2005,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(2006,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ~ ? [C: $i] :
( ~ ? [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[2005]) ).
thf(2007,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk71 @ ( F @ r2_hidden ) )
| ( A @ sk71 @ ( F @ r2_tarski ) )
| ~ ( A @ sk71 @ ( F @ r1_tarski ) ) )
& ( ( A @ ( D @ sk72 ) @ ( E @ r2_hidden ) )
| ~ ( D @ ( E @ r1_tarski ) )
| ~ ( A @ sk71 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk71 @ ( A @ ( D @ sk72 ) @ r2_hidden ) )
| ~ ( A @ sk71 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk71 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk71 @ ( B @ r2_hidden ) ) )
& ( A @ sk71 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[2006]) ).
thf(2008,plain,
! [A: $i] : ( A @ sk71 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2007]) ).
thf(23533,plain,
! [B: $i,A: $i] :
( ( ( A @ sk71 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2008,2837]) ).
thf(23534,plain,
! [B: $i,A: $i] :
( ( A @ sk71 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[23533]) ).
thf(23561,plain,
! [B: $i,A: $i] :
( ( ( A @ sk71 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[23534]) ).
thf(23570,plain,
! [A: $i] :
( ( A @ sk71 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[23561]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(2242,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(220,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(2286,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(10718,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4469,7089]) ).
thf(10719,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10718]) ).
thf(10720,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10719:[bind(A,$thf( k2_nat_lat ))]]) ).
thf(23680,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,10720]) ).
thf(23681,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23680]) ).
thf(23776,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23681]) ).
thf(23829,plain,
( ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23776]) ).
thf(6661,plain,
! [B: $i,A: $i] :
( ( ( sk141 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2488,1043]) ).
thf(6662,plain,
! [B: $i,A: $i] :
( ( ( sk141 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[6661]) ).
thf(6663,plain,
! [A: $i] : ( sk141 @ k1_relat_1 @ ( sk141 @ k9_relat_1 ) @ ( A @ ( sk141 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6662:[bind(A,$thf( A )),bind(B,$thf( sk141 ))]]) ).
thf(25144,plain,
! [A: $i] : ( sk141 @ k2_relat_1 @ ( A @ ( sk141 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6663,10786]) ).
thf(189,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v7_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 )
& ( A @ u1_lattices @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_lattice2) ).
thf(2103,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v7_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
& ( A @ u1_lattices @ v1_funct_1 )
& ( A @ u1_lattices @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_funct_2) ).
thf(1405,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_realset1) ).
thf(3226,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m3_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(638,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
thf(4643,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(1600,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ~ ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(723,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattices) ).
thf(5137,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
=> ( A @ v14_lattices ) )
& ( ( A @ v14_lattices )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(677,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r1_lattices ) ) )
& ( C @ ( B @ ( A @ r1_lattices ) ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
thf(4892,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r1_lattices ) ) )
& ( C @ ( B @ ( A @ r1_lattices ) ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(507,axiom,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( A @ k3_nat_lat )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_nat_lat) ).
thf(3906,plain,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( A @ k3_nat_lat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(4588,plain,
sk318 @ v13_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(6470,plain,
( ( ( sk217 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,2183]) ).
thf(6471,plain,
( ( sk217 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6470]) ).
thf(6474,plain,
sk217 != k1_numbers,
inference(simp,[status(thm)],[6471]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(3378,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( ( A @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(23618,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7326]) ).
thf(23619,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23618]) ).
thf(23790,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( k1_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23619]) ).
thf(23845,plain,
( ( k1_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23790]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( B @ ( A @ k2_tarski ) )
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(3503,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( B @ ( A @ k2_tarski ) )
= ( C @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(625,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( C
= ( B @ ( A @ k8_filter_0 ) ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( B @ g3_lattices ) ) ) )
& ( E
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_filter_0) ).
thf(4531,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( B @ g3_lattices ) ) ) )
& ( E
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C
= ( B @ ( A @ k8_filter_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k8_filter_0 ) ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( B @ g3_lattices ) ) ) )
& ( E
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(9795,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3012,7088]) ).
thf(9796,plain,
! [A: $i] :
( ( ( sk205 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9795]) ).
thf(9797,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9796:[bind(A,$thf( sk205 ))]]) ).
thf(2047,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[2046]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(2641,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(9033,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,3742]) ).
thf(9034,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9033]) ).
thf(9048,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk281 ),
inference(simp,[status(thm)],[9034]) ).
thf(415,axiom,
! [A: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ k2_lattices ) ) )
= ( B @ k12_nat_lat @ ( A @ k12_nat_lat @ k6_nat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_nat_lat) ).
thf(3435,plain,
! [A: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ k2_lattices ) ) )
= ( B @ k12_nat_lat @ ( A @ k12_nat_lat @ k6_nat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(7195,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1867,7043]) ).
thf(7196,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7195]) ).
thf(7197,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7196:[bind(A,$thf( sk56 ))]]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_partfun1) ).
thf(2922,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(3011,plain,
sk205 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3010]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(1206,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(4604,plain,
sk319 @ v1_lattices,
inference(cnfConj,[status(thm)],[4601]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v3_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_binop_1) ).
thf(2204,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) )
=> ( A @ ( B @ v3_binop_1 ) ) )
& ( ( A @ ( B @ v3_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(392,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v7_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lattices) ).
thf(3303,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) )
=> ( A @ v7_lattices ) )
& ( ( A @ v7_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k4_lattice4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(5530,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k4_lattice4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(4589,plain,
sk318 @ v9_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(635,axiom,
( ! [A: $i] :
( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s14_funct_2) ).
thf(4629,plain,
( ! [A: $i] :
( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(2574,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(675,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k2_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice4) ).
thf(4888,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k2_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(785,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice2) ).
thf(5411,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(4480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(1199,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3635,plain,
sk256 @ v6_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(230,axiom,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(2364,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(1153,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(851,axiom,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1) ).
thf(5697,plain,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(818,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_lattice4 ) @ ( A @ k7_lattices ) )
= ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice4) ).
thf(5545,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_lattice4 ) @ ( A @ k7_lattices ) )
= ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(9152,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,5001]) ).
thf(9153,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9152]) ).
thf(9164,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[9153]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(4076,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(4370,plain,
sk302 @ v5_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_2) ).
thf(1311,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(894,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_0) ).
thf(5862,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
<=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(2232,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) )
=> ( B @ v2_funct_1 ) )
& ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(4576,plain,
sk317 @ v14_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(3047,plain,
( ! [A: $i,B: $i] :
( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[3046]) ).
thf(3048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( D != k1_xboole_0 ) )
& ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( C != k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3047]) ).
thf(3050,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3048]) ).
thf(3053,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3050]) ).
thf(3054,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3053]) ).
thf(816,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_filter_0) ).
thf(5540,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ u1_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(2083,plain,
sk85 @ v2_struct_0,
inference(cnfConj,[status(thm)],[2081]) ).
thf(19,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(1094,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1095,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[1094]) ).
thf(1096,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[1095]) ).
thf(26427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( A @ ( C @ sk10 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1096,26414]) ).
thf(26428,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk10 ) )
= A ),
inference(pattern_uni,[status(thm)],[26427:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_lattice2) ).
thf(2496,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1868,plain,
sk56 @ v2_funct_1,
inference(cnfConj,[status(thm)],[1865]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(2000,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(1730,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(1057,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(1163,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_binop_1) ).
thf(2409,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(6339,plain,
( ( ( sk56 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,2183]) ).
thf(6340,plain,
( ( sk56 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6339]) ).
thf(6343,plain,
sk56 != k1_numbers,
inference(simp,[status(thm)],[6340]) ).
thf(835,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).
thf(5611,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(3827,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(67,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(1333,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1334,plain,
~ ? [A: $i,B: $i] :
( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[1333]) ).
thf(1335,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk21 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) )
& ( ( B
= ( A @ ( B @ sk21 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( B @ sk21 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( B @ sk21 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( A @ ( B @ sk21 ) @ k2_relat_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) )
& ( ( B
= ( A @ ( B @ sk21 ) @ k1_relat_1 ) )
| ( A = k1_xboole_0 ) )
& ( ( A @ ( B @ sk21 ) @ v1_funct_1 )
| ( A = k1_xboole_0 ) )
& ( ( A @ ( B @ sk21 ) @ v1_relat_1 )
| ( A = k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1334]) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ sk21 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1335]) ).
thf(1354,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk21 ) @ k1_relat_1 )
= B )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1341]) ).
thf(1355,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk21 ) @ k1_relat_1 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1354]) ).
thf(4375,plain,
sk302 @ v7_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k1_funct_2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_2) ).
thf(1666,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) )
=> ( C
= ( B @ ( A @ k1_funct_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_2 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(3884,plain,
k13_nat_lat @ v9_lattices,
inference(cnfConj,[status(thm)],[3877]) ).
thf(610,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_lattice2) ).
thf(4449,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(58,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(1274,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(736,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ m2_nat_lat ) )
<=> ( ( ( B @ u1_lattices )
= ( B @ u1_struct_0 @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ u2_lattices )
= ( B @ u1_struct_0 @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_nat_lat) ).
thf(5206,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( ( ( B @ u1_lattices )
= ( B @ u1_struct_0 @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ u2_lattices )
= ( B @ u1_struct_0 @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) )
=> ( A @ ( B @ m2_nat_lat ) ) )
& ( ( A @ ( B @ m2_nat_lat ) )
=> ( ( ( B @ u1_lattices )
= ( B @ u1_struct_0 @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ u2_lattices )
= ( B @ u1_struct_0 @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(10706,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3779,7089]) ).
thf(10707,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10706]) ).
thf(10708,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10707:[bind(A,$thf( k10_nat_lat ))]]) ).
thf(23678,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,10708]) ).
thf(23679,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23678]) ).
thf(23775,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( k10_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23679]) ).
thf(23828,plain,
( ( k10_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23775]) ).
thf(707,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_0) ).
thf(5049,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(3735,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
| ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_funct_2) ).
thf(2733,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
| ( C = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(847,axiom,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(5670,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( D @ k1_funct_1 ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice2) ).
thf(2805,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( D @ k1_funct_1 ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(3867,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(cnf,[status(esa)],[3866]) ).
thf(699,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v6_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_lattice2 )
& ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattice2) ).
thf(5002,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v6_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_lattice2 )
& ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_funct_2) ).
thf(1123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6664,plain,
! [B: $i,A: $i] :
( ( ( sk205 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3011,1043]) ).
thf(6665,plain,
! [B: $i,A: $i] :
( ( ( sk205 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[6664]) ).
thf(6666,plain,
! [A: $i] : ( sk205 @ k1_relat_1 @ ( sk205 @ k9_relat_1 ) @ ( A @ ( sk205 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6665:[bind(A,$thf( A )),bind(B,$thf( sk205 ))]]) ).
thf(10791,plain,
! [A: $i] :
( ( ( sk205 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ~ $true
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(paramod_ordered,[status(thm)],[3011,1114]) ).
thf(10792,plain,
! [A: $i] :
( ( ( sk205 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[10791]) ).
thf(10793,plain,
( ( sk205 @ k1_relat_1 @ ( sk205 @ k9_relat_1 ) )
= ( sk205 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[10792:[bind(A,$thf( sk205 ))]]) ).
thf(25594,plain,
! [A: $i] : ( sk205 @ k2_relat_1 @ ( A @ ( sk205 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6666,10793]) ).
thf(697,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice4) ).
thf(4989,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) )
=> ( B @ ( A @ ( C @ m1_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(706,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_lattice2) ).
thf(5044,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_partfun1) ).
thf(1751,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(4252,plain,
sk297 @ v13_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(919,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattices) ).
thf(5956,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(4344,plain,
sk301 @ v8_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(4521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(3239,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(866,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 @ ( A @ k8_filter_0 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_0) ).
thf(5754,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 @ ( A @ k8_filter_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(587,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(4284,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(943,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattices) ).
thf(6107,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(3816,plain,
sk272 @ v5_lattices,
inference(cnfConj,[status(thm)],[3812]) ).
thf(103,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(1619,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(900,axiom,
! [A: $i] :
( ( a_0_2_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).
thf(5893,plain,
! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_2_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_2_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(3814,plain,
sk272 @ v4_lattices,
inference(cnfConj,[status(thm)],[3812]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k7_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(5396,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k7_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(3471,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(4585,plain,
sk318 @ v4_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(2563,plain,
( ( sk148 @ v2_lattices )
& ( sk148 @ l2_lattices ) ),
inference(cnf,[status(esa)],[2562]) ).
thf(2565,plain,
sk148 @ v2_lattices,
inference(cnfConj,[status(thm)],[2563]) ).
thf(4385,plain,
sk303 @ v8_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(6704,plain,
( ( ( sk281 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,2183]) ).
thf(6705,plain,
( ( sk281 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6704]) ).
thf(6708,plain,
sk281 != k1_numbers,
inference(simp,[status(thm)],[6705]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(5534,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(954,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_lattice4 ) )
= ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_lattice4) ).
thf(6143,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_lattice4 ) )
= ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(2179,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(2211,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(1106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ sk5 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1029]) ).
thf(913,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ! [B: $i] :
( ( B @ l3_lattices )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ( ( A @ k1_lattice2 )
= ( B @ k1_lattice2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_filter_2) ).
thf(5937,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ! [B: $i] :
( ( B @ l3_lattices )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ( ( A @ k1_lattice2 )
= ( B @ k1_lattice2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(388,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v10_lattices )
& ( A @ k1_lattice2 @ v9_lattices )
& ( A @ k1_lattice2 @ v8_lattices )
& ( A @ k1_lattice2 @ v7_lattices )
& ( A @ k1_lattice2 @ v6_lattices )
& ( A @ k1_lattice2 @ v5_lattices )
& ( A @ k1_lattice2 @ v4_lattices )
& ( A @ k1_lattice2 @ v3_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
thf(3269,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v10_lattices )
& ( A @ k1_lattice2 @ v9_lattices )
& ( A @ k1_lattice2 @ v8_lattices )
& ( A @ k1_lattice2 @ v7_lattices )
& ( A @ k1_lattice2 @ v6_lattices )
& ( A @ k1_lattice2 @ v5_lattices )
& ( A @ k1_lattice2 @ v4_lattices )
& ( A @ k1_lattice2 @ v3_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(922,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v12_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v16_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_filter_0) ).
thf(5983,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v12_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v16_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices )
& ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
& ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k6_domain_1 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(4140,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k6_domain_1 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(798,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v8_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).
thf(5465,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) )
= C ) ) )
=> ( A @ v8_lattices ) )
& ( ( A @ v8_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(959,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k15_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
thf(6163,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k15_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_funct_2) ).
thf(4155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(394,axiom,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( B @ ( A @ ( C @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( A @ ( B @ ( C @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( B @ ( C @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( C @ ( A @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_nat_lat) ).
thf(3314,plain,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( B @ ( A @ ( C @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( A @ ( B @ ( C @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( B @ ( C @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( C @ ( A @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ ( B @ ( A @ k10_filter_2 ) @ m2_lattice4 ) )
& ~ ( B @ ( A @ k10_filter_2 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_2) ).
thf(3499,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ ( B @ ( A @ k10_filter_2 ) @ m2_lattice4 ) )
& ~ ( B @ ( A @ k10_filter_2 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(352,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v5_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 )
& ( A @ u2_lattices @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattice2) ).
thf(3065,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v5_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 )
& ( A @ u2_lattices @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1866,plain,
sk56 @ v1_relat_1,
inference(cnfConj,[status(thm)],[1865]) ).
thf(6678,plain,
! [B: $i,A: $i] :
( ( ( sk56 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1866,1043]) ).
thf(6679,plain,
! [B: $i,A: $i] :
( ( ( sk56 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[6678]) ).
thf(6680,plain,
! [A: $i] : ( sk56 @ k1_relat_1 @ ( sk56 @ k9_relat_1 ) @ ( A @ ( sk56 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6679:[bind(A,$thf( A )),bind(B,$thf( sk56 ))]]) ).
thf(10811,plain,
! [A: $i] :
( ( ( sk56 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ~ $true
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1866,1114]) ).
thf(10812,plain,
! [A: $i] :
( ( ( sk56 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[10811]) ).
thf(10813,plain,
( ( sk56 @ k1_relat_1 @ ( sk56 @ k9_relat_1 ) )
= ( sk56 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[10812:[bind(A,$thf( sk56 ))]]) ).
thf(27188,plain,
! [A: $i] : ( sk56 @ k2_relat_1 @ ( A @ ( sk56 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6680,10813]) ).
thf(401,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_binop_1) ).
thf(3349,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(34,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(1159,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(652,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k5_lattices ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).
thf(4746,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
=> ( B
= ( A @ k5_lattices ) ) )
& ( ( B
= ( A @ k5_lattices ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_lattices ) )
= ( D @ ( C @ g2_lattices ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_lattices) ).
thf(1656,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_lattices ) )
= ( D @ ( C @ g2_lattices ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(12847,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3891,1104]) ).
thf(12848,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[12847]) ).
thf(12849,plain,
k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[12848:[bind(A,$thf( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) )),bind(B,$thf( k7_nat_lat )),bind(C,$thf( k11_nat_lat ))]]) ).
thf(6049,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk435 @ m1_subset_1 ) )
| sk433 ),
inference(cnfConj,[status(thm)],[6048]) ).
thf(6060,plain,
( ( f1_s4_subset_1 @ ( sk435 @ m1_subset_1 ) )
| sk433
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[6049]) ).
thf(1021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
| ( E
!= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
| ~ ( E @ v1_relat_1 ) )
& ( ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) )
| ( E
!= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
| ~ ( E @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1020]) ).
thf(1023,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
| ( E
!= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
| ~ ( E @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1021]) ).
thf(1026,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ v1_relat_1 )
| ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
| ( E
!= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
inference(lifteq,[status(thm)],[1023]) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 )
| ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) ) ),
inference(simp,[status(thm)],[1026]) ).
thf(651,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(4737,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(4738,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[4737]) ).
thf(4739,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk341 @ ( E @ r2_hidden ) )
| ( A @ sk341 @ ( E @ r2_tarski ) )
| ~ ( A @ sk341 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk341 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk341 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk341 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk341 @ ( B @ r2_hidden ) ) )
& ( A @ sk341 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[4738]) ).
thf(4740,plain,
! [A: $i] : ( A @ sk341 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[4739]) ).
thf(961,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k23_filter_2 ) @ m2_nat_lat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k23_filter_2) ).
thf(6168,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k23_filter_2 ) @ m2_nat_lat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(8026,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2369,7066]) ).
thf(8027,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8026]) ).
thf(8028,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8027:[bind(A,$thf( sk126 ))]]) ).
thf(11013,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8028]) ).
thf(11014,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11013]) ).
thf(11042,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk126 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[11014]) ).
thf(249,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_binop_1) ).
thf(2492,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(472,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice2) ).
thf(3727,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(861,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(5726,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(5727,plain,
( ~ ( sk411 @ v3_struct_0 )
& ( sk411 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[5726]) ).
thf(5729,plain,
~ ( sk411 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5727]) ).
thf(8029,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4278,7066]) ).
thf(8030,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8029]) ).
thf(8031,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8030:[bind(A,$thf( sk298 ))]]) ).
thf(1012,plain,
sk2 @ v10_lattices,
inference(cnfConj,[status(thm)],[1003]) ).
thf(595,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice2) ).
thf(4316,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(755,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_0) ).
thf(5285,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(307,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_subset_1 ) ) )
=> ( ( ( F = E )
& ( D
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( ( ( C @ ( E @ ( A @ r3_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r3_binop_1 ) ) ) )
& ( ( C @ ( E @ ( A @ r2_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r2_binop_1 ) ) ) )
& ( ( C @ ( E @ ( A @ r1_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r1_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_2) ).
thf(2840,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_subset_1 ) ) )
=> ( ( ( F = E )
& ( D
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( ( ( C @ ( E @ ( A @ r3_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r3_binop_1 ) ) ) )
& ( ( C @ ( E @ ( A @ r2_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r2_binop_1 ) ) ) )
& ( ( C @ ( E @ ( A @ r1_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r1_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(500,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v3_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
thf(3862,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v3_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(836,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k7_lattices ) ) )
<=> ( B @ ( C @ ( A @ r2_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattices) ).
thf(5615,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r2_lattices ) ) )
=> ( C
= ( B @ ( A @ k7_lattices ) ) ) )
& ( ( C
= ( B @ ( A @ k7_lattices ) ) )
=> ( B @ ( C @ ( A @ r2_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(4630,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk325 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
| ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk323 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk325 @ m2_relset_1 ) ) )
| ~ sk323 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk325 @ v1_funct_2 ) ) )
| ~ sk323 )
& ( ( sk325 @ v1_funct_1 )
| ~ sk323 )
& ( sk323
| ~ ( A @ ( sk324 @ p1_s14_funct_2 ) )
| ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk323
| ( f1_s14_funct_2 @ ( sk324 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4629]) ).
thf(4636,plain,
( sk323
| ( f1_s14_funct_2 @ ( sk324 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4630]) ).
thf(7217,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3119,7043]) ).
thf(7218,plain,
! [A: $i] :
( ( ( sk217 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7217]) ).
thf(7219,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7218:[bind(A,$thf( sk217 ))]]) ).
thf(23740,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7219]) ).
thf(23741,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23740]) ).
thf(23783,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( sk217 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23741]) ).
thf(23837,plain,
( ( sk217 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23783]) ).
thf(454,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(3650,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(956,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_0) ).
thf(6148,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(4123,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ k2_relat_1 )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_2) ).
thf(2245,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1936,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(cnf,[status(esa)],[1935]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(5189,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(5626,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(23647,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,9797]) ).
thf(23648,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23647]) ).
thf(23779,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( sk205 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23648]) ).
thf(23832,plain,
( ( sk205 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23779]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(2300,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(508,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_domain_1) ).
thf(3909,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_lattice4) ).
thf(3782,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(901,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
=> ( A @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_filter_0) ).
thf(5904,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
=> ( A @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ g1_lattices ) @ v1_lattices )
& ~ ( B @ ( A @ g1_lattices ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattices) ).
thf(1983,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ g1_lattices ) @ v1_lattices )
& ~ ( B @ ( A @ g1_lattices ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(996,axiom,
? [A: $i] : ( A @ l3_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(6324,plain,
? [A: $i] : ( A @ l3_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_struct_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(5714,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_struct_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(708,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice2) ).
thf(5053,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(2515,plain,
~ ( sk143 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2513]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(1851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(12402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3781,1104]) ).
thf(12403,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[12402]) ).
thf(12404,plain,
k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[12403:[bind(A,$thf( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) )),bind(B,$thf( k7_nat_lat )),bind(C,$thf( k10_nat_lat ))]]) ).
thf(337,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(2990,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(8920,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2369,7087]) ).
thf(8921,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8920]) ).
thf(8922,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8921:[bind(A,$thf( sk126 ))]]) ).
thf(23706,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,8922]) ).
thf(23707,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23706]) ).
thf(23770,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk126 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[23707]) ).
thf(23822,plain,
( ( sk126 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[23770]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( D @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(2801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( D @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_lattices ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(5238,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_lattices ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(10935,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9800]) ).
thf(10936,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10935]) ).
thf(11056,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk56 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10936]) ).
thf(4248,plain,
sk297 @ v7_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(951,axiom,
( ( k13_nat_lat @ l3_lattices )
& ( k13_nat_lat @ v10_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_nat_lat) ).
thf(6133,plain,
( ( k13_nat_lat @ l3_lattices )
& ( k13_nat_lat @ v10_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_2) ).
thf(1062,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1063,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A )
| ~ ( A @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1062]) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[1063]) ).
thf(1110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[1109]) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1110]) ).
thf(824,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice4) ).
thf(5577,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(12061,plain,
! [A: $i] :
( ( ( A @ sk253 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3595,2183]) ).
thf(12062,plain,
! [A: $i] :
( ( A @ sk253 @ v1_xboole_0 )
!= ( k1_numbers @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12061]) ).
thf(12063,plain,
! [A: $i] :
( ( A @ sk253 )
!= k1_numbers ),
inference(simp,[status(thm)],[12062]) ).
thf(377,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(3218,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(537,axiom,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( A @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( A @ ( A @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( B @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_nat_lat) ).
thf(4048,plain,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( A @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( A @ ( A @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) )
= A )
& ( ( B @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1856,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(cnf,[status(esa)],[1855]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( C @ k3_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relat_1) ).
thf(2694,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( C @ k3_relat_1 )
= ( B @ ( A @ k2_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(8929,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4278,7087]) ).
thf(8930,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8929]) ).
thf(8931,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8930:[bind(A,$thf( sk298 ))]]) ).
thf(79,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(1425,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(8012,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3889,7066]) ).
thf(8013,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8012]) ).
thf(8014,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8013:[bind(A,$thf( k11_nat_lat ))]]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_2 ) )
= ( B @ ( A @ k2_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
thf(5362,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k2_filter_2 ) )
= ( B @ ( A @ k2_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(826,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
<=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_0) ).
thf(5583,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(687,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice2) ).
thf(4930,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(114,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(1719,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(907,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ r1_filter_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_filter_0) ).
thf(5919,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( C @ ( D @ ( A @ r1_filter_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(920,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 )
= ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice2) ).
thf(5978,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 )
= ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_partfun1) ).
thf(2858,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ k2_tarski ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_subset_1) ).
thf(2537,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ k2_tarski ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(775,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D )
& ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_lattice2) ).
thf(5373,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D )
& ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1116]) ).
thf(8914,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3779,7087]) ).
thf(8915,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8914]) ).
thf(8916,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8915:[bind(A,$thf( k10_nat_lat ))]]) ).
thf(13728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4471,1104]) ).
thf(13729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[13728]) ).
thf(13730,plain,
k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[13729:[bind(A,$thf( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) )),bind(B,$thf( k5_numbers )),bind(C,$thf( k2_nat_lat ))]]) ).
thf(18019,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13730,1067]) ).
thf(18020,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[18019]) ).
thf(18021,plain,
! [A: $i] : ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ ( k2_nat_lat @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[18020:[bind(A,$thf( k2_nat_lat @ k1_relat_1 )),bind(B,$thf( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) )),bind(C,$thf( C ))]]) ).
thf(18039,plain,
! [A: $i] : ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ ( k2_nat_lat @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[18021]) ).
thf(10676,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1867,7089]) ).
thf(10677,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10676]) ).
thf(10678,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10677:[bind(A,$thf( sk56 ))]]) ).
thf(576,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( B @ ( C @ ( A @ k3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
thf(4219,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( B @ ( C @ ( A @ k3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(10721,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4278,7089]) ).
thf(10722,plain,
! [A: $i] :
( ( ( sk298 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10721]) ).
thf(10723,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10722:[bind(A,$thf( sk298 ))]]) ).
thf(11862,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,10723]) ).
thf(11863,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11862]) ).
thf(11873,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk298 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11863]) ).
thf(11877,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11873]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).
thf(3018,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(3594,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk253 @ m1_subset_1 ) ),
inference(cnfConj,[status(thm)],[3593]) ).
thf(25878,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( A @ sk253 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1858,3594]) ).
thf(25879,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ sk253 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[25878:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(4333,plain,
sk300 @ v2_lattices,
inference(cnfConj,[status(thm)],[4331]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(3775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(805,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r1_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice4) ).
thf(5496,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r1_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(947,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice4) ).
thf(6116,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(10698,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3889,7089]) ).
thf(10699,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10698]) ).
thf(10700,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10699:[bind(A,$thf( k11_nat_lat ))]]) ).
thf(23689,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,10700]) ).
thf(23690,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23689]) ).
thf(23795,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( k11_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23690]) ).
thf(23850,plain,
( ( k11_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23795]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ~ ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(4406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
=> ~ ( C @ ( E @ r2_hidden ) ) )
& ( ~ ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
=> ~ ( C @ ( E @ r2_hidden ) ) )
& ( ~ ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(895,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_0) ).
thf(5865,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ! [E: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( C = F )
& ( B = E ) )
=> ( ( ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(2023,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(885,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_lattices) ).
thf(5818,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) )
=> ( A @ v12_lattices ) )
& ( ( A @ v12_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_binop_1) ).
thf(1942,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(6715,plain,
( ( ( sk353 @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,4929]) ).
thf(6716,plain,
( ( sk353 @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6715]) ).
thf(6720,plain,
sk353 != sk217,
inference(simp,[status(thm)],[6716]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(3094,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(606,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).
thf(4425,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v17_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v11_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(3596,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(3117,plain,
sk217 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3116]) ).
thf(6675,plain,
! [B: $i,A: $i] :
( ( ( sk217 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3117,1043]) ).
thf(6676,plain,
! [B: $i,A: $i] :
( ( ( sk217 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[6675]) ).
thf(6677,plain,
! [A: $i] : ( sk217 @ k1_relat_1 @ ( sk217 @ k9_relat_1 ) @ ( A @ ( sk217 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6676:[bind(A,$thf( A )),bind(B,$thf( sk217 ))]]) ).
thf(10808,plain,
! [A: $i] :
( ( ( sk217 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ~ $true
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(paramod_ordered,[status(thm)],[3117,1114]) ).
thf(10809,plain,
! [A: $i] :
( ( ( sk217 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[10808]) ).
thf(10810,plain,
( ( sk217 @ k1_relat_1 @ ( sk217 @ k9_relat_1 ) )
= ( sk217 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[10809:[bind(A,$thf( sk217 ))]]) ).
thf(26954,plain,
! [A: $i] : ( sk217 @ k2_relat_1 @ ( A @ ( sk217 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6677,10810]) ).
thf(4389,plain,
sk303 @ v3_filter_0,
inference(cnfConj,[status(thm)],[4382]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).
thf(5337,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(9824,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3779,7088]) ).
thf(9825,plain,
! [A: $i] :
( ( ( k10_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9824]) ).
thf(9826,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9825:[bind(A,$thf( k10_nat_lat ))]]) ).
thf(10996,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9826]) ).
thf(10997,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10996]) ).
thf(11046,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != k10_nat_lat )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10997]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(3032,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t165_funct_2) ).
thf(1937,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(1810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(265,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).
thf(2551,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(461,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k10_filter_0 ) ) )
<=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
<=> ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) )
& ( A @ u1_struct_0 @ ( C @ k3_relat_1 @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_filter_0) ).
thf(3671,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
=> ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) )
& ( A @ u1_struct_0 @ ( C @ k3_relat_1 @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k10_filter_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_filter_0 ) ) )
=> ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
=> ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) )
& ( A @ u1_struct_0 @ ( C @ k3_relat_1 @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(3723,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(451,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_lattice4) ).
thf(3643,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(9827,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2945,7088]) ).
thf(9828,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9827]) ).
thf(9829,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9828:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(23598,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[9829,2145]) ).
thf(23599,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23598]) ).
thf(10486,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk281 ) ),
inference(paramod_ordered,[status(thm)],[1858,9048]) ).
thf(10487,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk281 ),
inference(pattern_uni,[status(thm)],[10486:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_2) ).
thf(1744,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(11237,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,10700]) ).
thf(11238,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11237]) ).
thf(11248,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != k11_nat_lat )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11238]) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_binop_1) ).
thf(3935,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(724,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
thf(5149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( B = C )
=> ( C @ ( B @ ( A @ r1_filter_2 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(10013,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,2271]) ).
thf(10014,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10013]) ).
thf(10026,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk281 ),
inference(simp,[status(thm)],[10014]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_2) ).
thf(2851,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(850,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m3_lattice4 ) )
=> ( ( C
= ( B @ ( A @ k3_lattice4 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattice4) ).
thf(5683,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m3_lattice4 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k3_lattice4 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_lattice4 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(2862,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(292,axiom,
! [A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k2_nat_lat )
<=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k5_nat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_nat_lat) ).
thf(2766,plain,
! [A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k5_nat_1 ) ) ) ) )
=> ( A = k2_nat_lat ) )
& ( ( A = k2_nat_lat )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k5_nat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( B @ ( C @ ( A @ k4_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(4953,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( B @ ( C @ ( A @ k4_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(217,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relat_1) ).
thf(2272,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
<=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(3201,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) )
=> ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k2_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( A @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(1825,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k2_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( A @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(252,axiom,
? [A: $i] :
( ( A @ v2_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_lattices) ).
thf(2502,plain,
? [A: $i] :
( ( A @ v2_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l2_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(2503,plain,
( ( sk142 @ v2_lattices )
& ~ ( sk142 @ v3_struct_0 )
& ( sk142 @ l2_lattices ) ),
inference(cnf,[status(esa)],[2502]) ).
thf(2504,plain,
sk142 @ l2_lattices,
inference(cnfConj,[status(thm)],[2503]) ).
thf(917,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) )
& ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k3_filter_0 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_0) ).
thf(5947,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) )
& ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k3_filter_0 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(455,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_lattice4 ) @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattice4) ).
thf(3654,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_lattice4 ) @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(1097,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1097]) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1098]) ).
thf(4384,plain,
sk303 @ v3_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(941,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_lattice4 ) )
= ( A @ k7_grcat_1 @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_setwiseo ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_lattice4) ).
thf(6097,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_lattice4 ) )
= ( A @ k7_grcat_1 @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_setwiseo ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(484,axiom,
k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( k4_nat_lat @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_nat_lat) ).
thf(3787,plain,
k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( k4_nat_lat @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(93,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(1530,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k9_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).
thf(1456,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_subset_1) ).
thf(3059,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(23632,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,9832]) ).
thf(23633,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23632]) ).
thf(23766,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( sk126 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23633]) ).
thf(23818,plain,
( ( sk126 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23766]) ).
thf(540,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4068,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(1231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1129]) ).
thf(476,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
thf(3743,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(2505,plain,
~ ( sk142 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2503]) ).
thf(3819,plain,
sk272 @ v9_lattices,
inference(cnfConj,[status(thm)],[3812]) ).
thf(10140,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,2914]) ).
thf(10141,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10140]) ).
thf(10148,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk217 ),
inference(simp,[status(thm)],[10141]) ).
thf(979,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k6_filter_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_2) ).
thf(6239,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k6_filter_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(2566,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k12_filter_2 ) @ m2_lattice4 ) )
& ~ ( B @ ( A @ k12_filter_2 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_filter_2) ).
thf(5058,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ ( B @ ( A @ k12_filter_2 ) @ m2_lattice4 ) )
& ~ ( B @ ( A @ k12_filter_2 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(4715,plain,
( ( sk336 @ v3_lattices )
& ( sk336 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4714]) ).
thf(4717,plain,
sk336 @ v3_lattices,
inference(cnfConj,[status(thm)],[4715]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(2813,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(4347,plain,
~ ( sk301 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4342]) ).
thf(449,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) )
= ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_lattice2) ).
thf(3628,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) )
= ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(1874,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(7226,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2369,7043]) ).
thf(7227,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7226]) ).
thf(7228,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7227:[bind(A,$thf( sk126 ))]]) ).
thf(23715,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7228]) ).
thf(23716,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23715]) ).
thf(23780,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( sk126 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23716]) ).
thf(23833,plain,
( ( sk126 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23780]) ).
thf(762,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_0) ).
thf(5305,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(11017,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7219]) ).
thf(11018,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11017]) ).
thf(11061,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk217 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11018]) ).
thf(4259,plain,
sk297 @ l3_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(3109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
<=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).
thf(1979,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(645,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(4688,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(4689,plain,
sk333 @ l1_lattices,
inference(cnf,[status(esa)],[4688]) ).
thf(4069,plain,
sk285 @ l1_struct_0,
inference(cnf,[status(esa)],[4068]) ).
thf(2370,plain,
sk126 @ v2_funct_1,
inference(cnfConj,[status(thm)],[2367]) ).
thf(800,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( E @ v1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
<=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice4) ).
thf(5479,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( B @ ( A @ ( E @ v1_lattice4 ) ) )
=> ( ( ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) )
=> ( D @ ( C @ ( A @ r3_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(488,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v2_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_binop_1) ).
thf(3802,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( A @ ( B @ v2_binop_1 ) ) )
& ( ( A @ ( B @ v2_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(4352,plain,
sk301 @ v11_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(14006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(paramod_ordered,[status(thm)],[5448,1104]) ).
thf(14007,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[14006]) ).
thf(14008,plain,
( ( f1_s11_funct_2 @ ( sk391 @ k1_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[14007:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk391 ))]]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(3856,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(94,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice2) ).
thf(1563,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_realset1 ) ) )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1167]) ).
thf(790,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ v3_lattices )
=> ( A
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(5434,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ v3_lattices )
=> ( A
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(1071,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10994,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8922]) ).
thf(10995,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10994]) ).
thf(11065,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk126 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[10995]) ).
thf(208,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(2221,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(721,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(5126,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(321,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_numbers) ).
thf(2909,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(26197,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1858,5160]) ).
thf(26198,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[26197:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(2365,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[2364]) ).
thf(26307,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ),
inference(rewrite,[status(thm)],[26198,2365]) ).
thf(8906,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3889,7087]) ).
thf(8907,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8906]) ).
thf(8908,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8907:[bind(A,$thf( k11_nat_lat ))]]) ).
thf(11023,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8908]) ).
thf(11024,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11023]) ).
thf(11031,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != k11_nat_lat )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11024]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ k2_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(3755,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ k2_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(820,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices )
= ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_lattice2) ).
thf(5557,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices )
= ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(864,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_0) ).
thf(5747,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(719,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(5112,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(289,axiom,
! [A: $i] :
( ( A @ v1_funct_1 )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(2749,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
=> ( A @ v1_funct_1 ) )
& ( ( A @ v1_funct_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(1991,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(492,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice4) ).
thf(3834,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( D
= ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_subset_1) ).
thf(2546,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(2761,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(4567,plain,
sk317 @ v5_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(545,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(4081,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(2883,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(2954,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2953]) ).
thf(2956,plain,
k1_xboole_0 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2954]) ).
thf(6681,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2956,1043]) ).
thf(6682,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[6681]) ).
thf(6683,plain,
! [A: $i] : ( k1_xboole_0 @ k1_relat_1 @ ( k1_xboole_0 @ k9_relat_1 ) @ ( A @ ( k1_xboole_0 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6682:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(27268,plain,
k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ),
inference(rewrite,[status(thm)],[6683,2908]) ).
thf(1053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
= ( A @ ( B @ ( C @ ( D @ ( E @ sk7 ) ) ) ) @ ( D @ k1_funct_1 ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
| ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1050]) ).
thf(1054,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
| ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ( ( A @ ( B @ ( C @ ( D @ ( E @ sk7 ) ) ) ) @ ( D @ k1_funct_1 ) )
= E ) ),
inference(lifteq,[status(thm)],[1053]) ).
thf(523,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(3999,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_binop_1) ).
thf(4906,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( C
= ( B @ ( A @ k3_binop_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(3639,plain,
sk256 @ l3_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(323,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_binop_1) ).
thf(2915,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(23674,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,10678]) ).
thf(23675,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23674]) ).
thf(23771,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk56 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23675]) ).
thf(23823,plain,
( ( sk56 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23771]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(3508,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(148,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ a_2_3_domain_1 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_domain_1) ).
thf(1895,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ a_2_3_domain_1 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice4) ).
thf(5513,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(2995,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(903,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u2_lattices @ v3_binop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattice2) ).
thf(5909,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u2_lattices @ v3_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(494,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(3841,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).
thf(2617,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(1732,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(4572,plain,
sk317 @ v3_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(23658,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,8031]) ).
thf(23659,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23658]) ).
thf(23762,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk298 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23659]) ).
thf(23813,plain,
( ( sk298 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23762]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( B @ ( A @ r1_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).
thf(4921,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( B @ ( A @ r1_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(930,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) )
<=> ( A @ ( B @ v1_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_0) ).
thf(6026,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ ( B @ v1_filter_0 ) )
=> ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) ) )
& ( ( ( A @ ( B @ v2_filter_0 ) )
& ( B
!= ( A @ k1_filter_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(4354,plain,
sk301 @ v17_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_funct_2) ).
thf(2033,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(3042,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(742,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v7_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattice2) ).
thf(5230,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v7_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(4256,plain,
sk297 @ v14_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(4359,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(4365,plain,
sk302 @ v4_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(412,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
=> ( ( B @ ( A @ a_2_1_lattice4 ) )
= ( B @ ( A @ k3_lattice4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice4) ).
thf(3396,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
=> ( ( B @ ( A @ a_2_1_lattice4 ) )
= ( B @ ( A @ k3_lattice4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(831,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_binop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattice2) ).
thf(5598,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(215,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_binop_1) ).
thf(2260,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r5_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(12366,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3781,1105]) ).
thf(12367,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[12366]) ).
thf(12368,plain,
k7_nat_lat @ ( k10_nat_lat @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[12367:[bind(A,$thf( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) )),bind(B,$thf( k7_nat_lat )),bind(C,$thf( k10_nat_lat ))]]) ).
thf(12608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k10_nat_lat @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12368,1067]) ).
thf(12609,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k10_nat_lat @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[12608]) ).
thf(12610,plain,
! [A: $i] : ( k7_nat_lat @ ( A @ ( k10_nat_lat @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[12609:[bind(A,$thf( k10_nat_lat @ k2_relat_1 )),bind(B,$thf( k7_nat_lat )),bind(C,$thf( C ))]]) ).
thf(12628,plain,
! [A: $i] : ( k7_nat_lat @ ( A @ ( k10_nat_lat @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[12610]) ).
thf(968,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_filter_0) ).
thf(6192,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
& ( C @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( ( C @ ( E @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( E @ ( C @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(55,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(1251,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(801,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices )
= ( A @ u2_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_lattice2) ).
thf(5483,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices )
= ( A @ u2_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(859,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice2) ).
thf(5722,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(809,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_filter_0) ).
thf(5524,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(4470,plain,
k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[4468]) ).
thf(11002,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7228]) ).
thf(11003,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11002]) ).
thf(11033,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk126 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11003]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(4685,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(4594,plain,
sk318 @ v6_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(12811,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3891,1105]) ).
thf(12812,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[12811]) ).
thf(12813,plain,
k7_nat_lat @ ( k11_nat_lat @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[12812:[bind(A,$thf( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) )),bind(B,$thf( k7_nat_lat )),bind(C,$thf( k11_nat_lat ))]]) ).
thf(5442,plain,
( ( ( f3_s11_funct_2 @ ( sk391 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5441]) ).
thf(5451,plain,
( ( ( f3_s11_funct_2 @ ( sk391 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5442]) ).
thf(3890,plain,
k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[3888]) ).
thf(5508,plain,
k6_nat_lat @ v13_lattices,
inference(cnfConj,[status(thm)],[5505]) ).
thf(423,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_lattice2) ).
thf(3491,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(13133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4272,1105]) ).
thf(13134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[13133]) ).
thf(13135,plain,
k5_numbers @ ( k1_nat_lat @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[13134:[bind(A,$thf( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) )),bind(B,$thf( k5_numbers )),bind(C,$thf( k1_nat_lat ))]]) ).
thf(981,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) )
= ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattices) ).
thf(6243,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) )
= ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(4393,plain,
sk303 @ v7_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(926,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattice2) ).
thf(6001,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( ( C = E )
& ( B = D ) )
=> ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(834,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v14_lattices )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k6_lattices )
= ( A @ k6_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_filter_0) ).
thf(5608,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v14_lattices )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k6_lattices )
= ( A @ k6_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(4797,plain,
~ ( k6_nat_lat @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4793]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(2028,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(1301,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(493,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(3839,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(429,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_binop_1) ).
thf(3523,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(619,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
= ( D @ ( C @ ( B @ u1_lattices @ ( B @ u1_struct_0 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice2) ).
thf(4503,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
= ( D @ ( C @ ( B @ u1_lattices @ ( B @ u1_struct_0 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(4577,plain,
sk317 @ l3_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(10973,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8014]) ).
thf(10974,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10973]) ).
thf(11063,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != k11_nat_lat )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10974]) ).
thf(843,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v11_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_lattice2) ).
thf(5647,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v11_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) )
=> ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v11_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(530,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
= ( D @ ( C @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice2) ).
thf(4017,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
= ( D @ ( C @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(852,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(5698,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk101 ) @ v1_funct_1 )
& ( A @ ( B @ sk101 ) @ v1_relat_1 )
& ( B @ ( A @ ( A @ ( B @ sk101 ) @ m1_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[2221]) ).
thf(2225,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk101 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2222]) ).
thf(712,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_lattices ) ) )
<=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattices) ).
thf(5065,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B )
=> ( C @ ( B @ ( A @ r1_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(2489,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(6341,plain,
( ( ( sk56 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,1186]) ).
thf(6342,plain,
( ( sk56 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6341]) ).
thf(6344,plain,
sk56 != sk11,
inference(simp,[status(thm)],[6342]) ).
thf(1154,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1153]) ).
thf(690,axiom,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ r1_lattices ) ) )
=> ( B @ k3_nat_lat @ ( A @ k3_nat_lat @ r1_nat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_nat_lat) ).
thf(4943,plain,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ r1_lattices ) ) )
=> ( B @ k3_nat_lat @ ( A @ k3_nat_lat @ r1_nat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(433,axiom,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( ( k4_nat_lat @ ( A @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ k2_lattices ) ) )
= k4_nat_lat )
& ( ( A @ ( k4_nat_lat @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ k2_lattices ) ) )
= k4_nat_lat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_nat_lat) ).
thf(3547,plain,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( ( k4_nat_lat @ ( A @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ k2_lattices ) ) )
= k4_nat_lat )
& ( ( A @ ( k4_nat_lat @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ k2_lattices ) ) )
= k4_nat_lat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(4661,plain,
! [A: $i] :
( ( ( ( A @ ( sk331 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s12_funct_2 ) )
| ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk329 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk331 @ m2_relset_1 ) ) )
| ~ sk329 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk331 @ v1_funct_2 ) ) )
| ~ sk329 )
& ( ( sk331 @ v1_funct_1 )
| ~ sk329 )
& ( sk329
| ~ ( f2_s12_funct_2 @ ( sk330 @ f3_s12_funct_2 @ r2_hidden ) ) )
& ( sk329
| ( f1_s12_funct_2 @ ( sk330 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4660]) ).
thf(4662,plain,
( sk329
| ( f1_s12_funct_2 @ ( sk330 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4661]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(2727,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(3636,plain,
sk256 @ v9_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(2048,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(586,axiom,
k5_numbers @ k1_zfmisc_1 @ ( k7_nat_lat @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_nat_lat) ).
thf(4283,plain,
k5_numbers @ k1_zfmisc_1 @ ( k7_nat_lat @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(13970,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(paramod_ordered,[status(thm)],[5448,1105]) ).
thf(13971,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[13970]) ).
thf(13972,plain,
( ( f2_s11_funct_2 @ ( sk391 @ k2_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[13971:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk391 ))]]) ).
thf(781,axiom,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s9_domain_1) ).
thf(5395,plain,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(2791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(9836,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4469,7088]) ).
thf(9837,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9836]) ).
thf(9838,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9837:[bind(A,$thf( k2_nat_lat ))]]) ).
thf(23757,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,9838]) ).
thf(23758,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23757]) ).
thf(23761,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23758]) ).
thf(23812,plain,
( ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23761]) ).
thf(593,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4309,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(479,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C
= ( B @ ( A @ k3_filter_0 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_filter_0) ).
thf(3758,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k3_filter_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_filter_0 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(914,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r1_relat_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_filter_0) ).
thf(5940,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r1_relat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(8739,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4469,7066]) ).
thf(8740,plain,
! [A: $i] :
( ( ( k2_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8739]) ).
thf(8741,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8740:[bind(A,$thf( k2_nat_lat ))]]) ).
thf(23755,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,8741]) ).
thf(23756,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23755]) ).
thf(23774,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23756]) ).
thf(23827,plain,
( ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23774]) ).
thf(174,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ m1_relset_1 ) ) )
=> ( ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( k1_xboole_0 @ ( A @ v2_binop_1 ) )
& ( k1_xboole_0 @ ( A @ v1_binop_1 ) )
& ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_xboole_0 )
& ( A @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(2016,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ m1_relset_1 ) ) )
=> ( ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( k1_xboole_0 @ ( A @ v2_binop_1 ) )
& ( k1_xboole_0 @ ( A @ v1_binop_1 ) )
& ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_xboole_0 )
& ( A @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(2514,plain,
sk143 @ l1_lattices,
inference(cnfConj,[status(thm)],[2513]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(1388,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
& ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(4801,plain,
k6_nat_lat @ v3_lattices,
inference(cnfConj,[status(thm)],[4793]) ).
thf(4605,plain,
~ ( sk319 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4601]) ).
thf(716,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_2) ).
thf(5099,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( C @ ( B @ ( A @ r1_filter_2 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(897,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_0) ).
thf(5876,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) )
& ( ( A @ ( B @ v1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(1795,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(440,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k1_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice4) ).
thf(3590,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k1_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(596,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(4328,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(445,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_0) ).
thf(3604,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ~ ( ( A @ ( C @ v1_filter_0 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(4590,plain,
sk318 @ v3_filter_0,
inference(cnfConj,[status(thm)],[4582]) ).
thf(502,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D = E )
=> ( ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
= ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k2_lattice2 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
= ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattice2) ).
thf(3868,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D = E )
=> ( ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
= ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k2_lattice2 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
= ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(2817,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(653,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(4758,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(6670,plain,
! [B: $i,A: $i] :
( ( ( sk219 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3130,1043]) ).
thf(6671,plain,
! [B: $i,A: $i] :
( ( ( sk219 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[6670]) ).
thf(6672,plain,
! [A: $i] : ( sk219 @ k1_relat_1 @ ( sk219 @ k9_relat_1 ) @ ( A @ ( sk219 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6671:[bind(A,$thf( A )),bind(B,$thf( sk219 ))]]) ).
thf(26804,plain,
! [A: $i] : ( sk219 @ k2_relat_1 @ ( A @ ( sk219 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6672,10799]) ).
thf(444,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( E @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_lattice2) ).
thf(3599,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( E @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
=> ( E @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(4251,plain,
sk297 @ v4_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(3795,plain,
( ~ ( sk267 @ v3_struct_0 )
& ( sk267 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[3794]) ).
thf(3796,plain,
sk267 @ l1_struct_0,
inference(cnfConj,[status(thm)],[3795]) ).
thf(788,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( B @ ( A @ r1_filter_1 ) )
<=> ? [C: $i] :
( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
& ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattice4) ).
thf(5427,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [C: $i] :
( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
& ( B @ ( A @ ( C @ m1_lattice4 ) ) ) )
=> ( B @ ( A @ r1_filter_1 ) ) )
& ( ( B @ ( A @ r1_filter_1 ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
& ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).
thf(2326,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(221,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 )
& ( A @ u2_lattices @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattice2) ).
thf(2293,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_partfun1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 )
& ( A @ u2_lattices @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(452,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(3646,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(754,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_0) ).
thf(5282,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(1085,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1086,plain,
! [B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
| ( ( B @ k1_relat_1 )
!= k1_xboole_0 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) )
& ( ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
| ( ( B @ k1_relat_1 )
!= k1_xboole_0 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) )
& ( ( B @ v1_funct_1 )
| ( ( B @ k1_relat_1 )
!= k1_xboole_0 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1085]) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
| ( ( B @ k1_relat_1 )
!= k1_xboole_0 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1086]) ).
thf(1092,plain,
! [B: $i,A: $i] :
( ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ( ( B @ k1_relat_1 )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1088]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).
thf(3579,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(984,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
<=> ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_0) ).
thf(6261,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
=> ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(825,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattices) ).
thf(5580,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(430,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ ( B @ ( A @ k13_filter_2 ) @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_filter_2) ).
thf(3532,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ ( B @ ( A @ k13_filter_2 ) @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(4796,plain,
k6_nat_lat @ v5_lattices,
inference(cnfConj,[status(thm)],[4793]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).
thf(1271,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(12059,plain,
! [B: $i,A: $i] :
( ( ( A @ sk253 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3595,5001]) ).
thf(12060,plain,
! [B: $i,A: $i] :
( ( A @ sk253 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12059]) ).
thf(12067,plain,
! [B: $i,A: $i] :
( ( A @ sk253 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[12060]) ).
thf(639,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattice4) ).
thf(4645,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m2_lattice4 ) ) )
& ( ( A @ ( B @ m2_lattice4 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(10947,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk56 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7197]) ).
thf(10948,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk56 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10947]) ).
thf(11060,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk56 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10948]) ).
thf(10709,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2945,7089]) ).
thf(10710,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10709]) ).
thf(10711,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10710:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(23592,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[10711,2145]) ).
thf(23593,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23592]) ).
thf(1058,plain,
! [B: $i,A: $i] :
( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1057]) ).
thf(990,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) )
=> ( ( A @ k6_lattices )
= ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice2) ).
thf(6302,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) )
=> ( ( A @ k6_lattices )
= ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(4573,plain,
sk317 @ v8_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(714,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).
thf(5086,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_binop_1) ).
thf(3340,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r2_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
=> ( B @ ( C @ ( A @ r1_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
thf(3700,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
=> ( B @ ( C @ ( A @ r1_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(854,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k1_lattice4 ) )
= ( A @ k5_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattice4) ).
thf(5703,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k1_lattice4 ) )
= ( A @ k5_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(5443,plain,
( ( ( f4_s11_funct_2 @ ( sk391 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5441]) ).
thf(5449,plain,
( ( ( f4_s11_funct_2 @ ( sk391 @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5443]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(1897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( A = C ) )
=> ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(3641,plain,
sk256 @ v10_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(584,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_lattice4 ) @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice4) ).
thf(4273,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_lattice4 ) @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) )
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(983,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v3_filter_0 )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
=> ( D @ ( E @ ( A @ r1_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_0) ).
thf(6248,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
=> ( D @ ( E @ ( A @ r1_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) )
=> ( A @ v3_filter_0 ) )
& ( ( A @ v3_filter_0 )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
=> ( D @ ( E @ ( A @ r1_lattices ) ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(1000,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(6334,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_lattices ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(5997,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_lattices ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(874,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ( ( A @ k6_lattices )
= ( B @ k6_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_filter_2) ).
thf(5784,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ( ( A @ k6_lattices )
= ( B @ k6_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(1464,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(246,axiom,
! [A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k10_nat_lat )
<=> ! [B: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( B @ m1_nat_lat ) ) ) )
=> ! [C: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( C @ m1_nat_lat ) ) ) )
=> ( ( C @ ( B @ ( A @ ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k6_nat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_nat_lat) ).
thf(2474,plain,
! [A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( B @ m1_nat_lat ) ) ) )
=> ! [C: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( C @ m1_nat_lat ) ) ) )
=> ( ( C @ ( B @ ( A @ ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k6_nat_1 ) ) ) ) )
=> ( A = k10_nat_lat ) )
& ( ( A = k10_nat_lat )
=> ! [B: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( B @ m1_nat_lat ) ) ) )
=> ! [C: $i] :
( ( k7_nat_lat @ ( k5_numbers @ ( k1_numbers @ ( C @ m1_nat_lat ) ) ) )
=> ( ( C @ ( B @ ( A @ ( k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k6_nat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(10921,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8911]) ).
thf(10922,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10921]) ).
thf(11053,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk217 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[10922]) ).
thf(789,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v3_filter_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_0) ).
thf(5432,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v3_filter_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(8888,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1867,7087]) ).
thf(8889,plain,
! [A: $i] :
( ( ( sk56 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8888]) ).
thf(8890,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8889:[bind(A,$thf( sk56 ))]]) ).
thf(11000,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8890]) ).
thf(11001,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11000]) ).
thf(11038,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk56 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11001]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(4433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(1356,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relat_1) ).
thf(2510,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_relat_1 @ ( A @ k3_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(4716,plain,
sk336 @ l3_lattices,
inference(cnfConj,[status(thm)],[4715]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_lattice2) ).
thf(2361,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(357,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r1_relat_2 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
thf(3101,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r1_relat_2 ) ) )
& ( ( B @ ( A @ r1_relat_2 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(598,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_lattice4 ) ) )
<=> ( C @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice4) ).
thf(4337,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ v1_lattice4 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_lattice4 ) ) )
=> ( C @ v2_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(890,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(5848,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(4586,plain,
sk318 @ v8_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(969,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k3_filter_0 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_0) ).
thf(6196,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k3_filter_0 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(621,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(4509,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
& ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(2119,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
& ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(5071,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(5671,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[5670]) ).
thf(23753,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,10723]) ).
thf(23754,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23753]) ).
thf(23793,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk298 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23754]) ).
thf(23848,plain,
( ( sk298 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23793]) ).
thf(617,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices )
= ( A @ k1_lattice2 @ k6_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_lattice2) ).
thf(4498,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices )
= ( A @ k1_lattice2 @ k6_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(3251,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(4369,plain,
sk302 @ v6_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(209,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(2226,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(2227,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk102 ) @ v1_funct_2 ) ) )
& ( A @ ( B @ sk102 ) @ v1_funct_1 )
& ( A @ ( B @ sk102 ) @ v1_relat_1 )
& ( B @ ( A @ ( A @ ( B @ sk102 ) @ m1_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[2226]) ).
thf(2229,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk102 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2227]) ).
thf(3815,plain,
~ ( sk272 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3812]) ).
thf(186,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( ( ( D @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( F @ ( E @ ( B @ r5_binop_1 ) ) ) )
& ( ( D @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( F @ ( E @ ( B @ r4_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_2) ).
thf(2084,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( ( ( D @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( F @ ( E @ ( B @ r5_binop_1 ) ) ) )
& ( ( D @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( F @ ( E @ ( B @ r4_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(9154,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,5001]) ).
thf(9155,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9154]) ).
thf(9161,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk141 ),
inference(simp,[status(thm)],[9155]) ).
thf(965,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r2_lattice4 ) ) )
<=> ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lattice4) ).
thf(6179,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) )
=> ( C @ ( B @ ( A @ r2_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_lattice4 ) ) )
=> ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k6_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(4305,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k1_realset1 ) @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ m1_realset1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1116]) ).
thf(23607,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,8928]) ).
thf(23608,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23607]) ).
thf(23764,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[23608]) ).
thf(23816,plain,
( ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[23764]) ).
thf(945,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(6112,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(1343,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk21 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1335]) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk21 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1343]) ).
thf(1349,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk21 ) @ v1_funct_1 ),
inference(simp,[status(thm)],[1348]) ).
thf(761,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattices) ).
thf(5303,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(9041,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,3742]) ).
thf(9042,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9041]) ).
thf(9047,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk217 ),
inference(simp,[status(thm)],[9042]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(23623,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,8911]) ).
thf(23624,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23623]) ).
thf(23778,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk217 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[23624]) ).
thf(23831,plain,
( ( sk217 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk217 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[23778]) ).
thf(995,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
thf(6321,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(739,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5222,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( B @ k1_relat_1 @ ( A @ ( B @ sk9 ) @ r2_hidden ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1134]) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( B @ k1_relat_1 @ ( A @ ( B @ sk9 ) @ r2_hidden ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1135]) ).
thf(694,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).
thf(4958,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v15_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(784,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(5407,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(542,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) )
= ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice4) ).
thf(4073,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) )
= ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_filter_0 ) )
& ( B @ ( C @ m1_filter_0 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(6289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_filter_0 ) )
& ( B @ ( C @ m1_filter_0 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(3138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(565,axiom,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(4176,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(957,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) )
= ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ( A @ v11_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattices) ).
thf(6154,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) )
= ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
=> ( A @ v11_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(1120,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ k2_relat_1 )
!= ( A @ k1_tarski ) )
| ( ( B @ k2_relat_1 )
!= ( A @ k1_tarski ) )
| ( ( B @ k1_relat_1 )
!= ( C @ k1_relat_1 ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1120]) ).
thf(1122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ( B = C )
| ( ( C @ k2_relat_1 )
!= ( A @ k1_tarski ) )
| ( ( B @ k2_relat_1 )
!= ( A @ k1_tarski ) )
| ( ( B @ k1_relat_1 )
!= ( C @ k1_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1121]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(4300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(778,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice4) ).
thf(5381,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(2378,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(878,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k6_lattices @ ( B @ ( A @ r3_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattices) ).
thf(5795,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( A @ k6_lattices @ ( B @ ( A @ r3_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(4374,plain,
sk302 @ v15_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(12045,plain,
! [B: $i,A: $i] :
( ( ( A @ sk253 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3595,3742]) ).
thf(12046,plain,
! [B: $i,A: $i] :
( ( A @ sk253 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12045]) ).
thf(12064,plain,
! [B: $i,A: $i] :
( ( A @ sk253 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[12046]) ).
thf(751,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices )
= ( A @ k1_lattice2 @ u2_lattices ) )
& ( ( A @ u2_lattices )
= ( A @ k1_lattice2 @ u1_lattices ) )
& ( ( A @ u1_struct_0 )
= ( A @ k1_lattice2 @ u1_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattice2) ).
thf(5267,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices )
= ( A @ k1_lattice2 @ u2_lattices ) )
& ( ( A @ u2_lattices )
= ( A @ k1_lattice2 @ u1_lattices ) )
& ( ( A @ u1_struct_0 )
= ( A @ k1_lattice2 @ u1_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(1307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(2065,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k12_filter_0 ) )
= ( B @ ( A @ k10_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_filter_0) ).
thf(6216,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k12_filter_0 ) )
= ( B @ ( A @ k10_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(4388,plain,
~ ( sk303 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4382]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k1_lattice4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice4) ).
thf(5816,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k1_lattice4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(4569,plain,
sk317 @ v13_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(243,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_subset_1) ).
thf(2446,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_struct_0) ).
thf(4208,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).
thf(3006,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(589,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_binop_1) ).
thf(4296,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(822,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice4) ).
thf(5563,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( C
= ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
& ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
& ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(4203,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(705,axiom,
( ! [A: $i] :
( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_2) ).
thf(5035,plain,
( ! [A: $i] :
( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(734,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice2) ).
thf(5202,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(477,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( B @ ( C @ ( A @ k2_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattices) ).
thf(3747,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( B @ ( C @ ( A @ k2_lattices ) ) ) ) ) )
=> ( A @ v6_lattices ) )
& ( ( A @ v6_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( B @ ( C @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(862,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) )
=> ( A @ v11_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice2) ).
thf(5730,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) )
=> ( A @ v11_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(663,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(4833,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(2780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(7214,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3889,7043]) ).
thf(7215,plain,
! [A: $i] :
( ( ( k11_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7214]) ).
thf(7216,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7215:[bind(A,$thf( k11_nat_lat ))]]) ).
thf(11021,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7216]) ).
thf(11022,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11021]) ).
thf(11073,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != k11_nat_lat )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11022]) ).
thf(768,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(5335,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(1909,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(679,axiom,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ k2_lattices ) ) )
= ( B @ k3_nat_lat @ ( A @ k3_nat_lat @ k6_nat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_nat_lat) ).
thf(4897,plain,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ k2_lattices ) ) )
= ( B @ k3_nat_lat @ ( A @ k3_nat_lat @ k6_nat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1160,plain,
~ ? [A: $i,B: $i] :
( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(miniscope,[status(thm)],[1159]) ).
thf(1161,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1160]) ).
thf(1162,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1161]) ).
thf(6408,plain,
( ( ( k1_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,2183]) ).
thf(6409,plain,
( ( k1_numbers @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6408]) ).
thf(6414,plain,
k1_numbers != k1_xboole_0,
inference(simp,[status(thm)],[6409]) ).
thf(4332,plain,
sk300 @ v4_lattices,
inference(cnfConj,[status(thm)],[4331]) ).
thf(372,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(3192,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(780,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattices) ).
thf(5392,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_lattices @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(447,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( D @ ( C @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattice4) ).
thf(3614,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( D @ ( C @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(2874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(766,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( ( F @ ( E @ ( B @ r1_lattices ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ r1_lattices ) ) )
=> ( F @ ( E @ ( B @ r1_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ k2_lattices ) ) )
= ( F @ ( E @ ( B @ k2_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ k1_lattices ) ) )
= ( F @ ( E @ ( B @ k1_lattices ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_filter_2) ).
thf(5318,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( ( F @ ( E @ ( B @ r1_lattices ) ) )
=> ( D @ ( C @ ( A @ r1_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ r1_lattices ) ) )
=> ( F @ ( E @ ( B @ r1_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ k2_lattices ) ) )
= ( F @ ( E @ ( B @ k2_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ k1_lattices ) ) )
= ( F @ ( E @ ( B @ k1_lattices ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(6080,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(1460,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(933,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_lattice4 ) @ ( A @ k7_lattices ) )
= ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice4) ).
thf(6044,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_lattice4 ) @ ( A @ k7_lattices ) )
= ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(10963,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8031]) ).
thf(10964,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10963]) ).
thf(11074,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk298 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10964]) ).
thf(11095,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[11074]) ).
thf(795,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( D @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_0) ).
thf(5459,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( D @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(887,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_filter_0) ).
thf(5838,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1060,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k9_relat_1 ) )
!= k1_xboole_0 )
| ~ ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
| ( A = k1_xboole_0 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1059]) ).
thf(1061,plain,
! [B: $i,A: $i] :
( ~ ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( ( A @ ( B @ k9_relat_1 ) )
!= k1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1060]) ).
thf(872,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k18_filter_2 ) @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k18_filter_2) ).
thf(5780,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k18_filter_2 ) @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_2) ).
thf(2710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(2910,plain,
k5_numbers != k1_numbers,
inference(polarity_switch,[status(thm)],[2909]) ).
thf(2911,plain,
k1_numbers != k5_numbers,
inference(lifteq,[status(thm)],[2910]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_tarski ) )
<=> ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( D = F )
<=> ( E = G ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tarski) ).
thf(2578,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( E = G )
=> ( D = F ) )
& ( ( D = F )
=> ( E = G ) ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) )
=> ( B @ ( A @ r2_tarski ) ) )
& ( ( B @ ( A @ r2_tarski ) )
=> ? [C: $i] :
( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( E = G )
=> ( D = F ) )
& ( ( D = F )
=> ( E = G ) ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(911,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattice4) ).
thf(5931,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(23630,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,9800]) ).
thf(23631,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk56 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23630]) ).
thf(23781,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( sk56 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23631]) ).
thf(23834,plain,
( ( sk56 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk56 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23781]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(5377,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(4373,plain,
sk302 @ l3_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_partfun1) ).
thf(1176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_binop_1) ).
thf(2931,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r7_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B
= ( A @ k1_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(1435,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k1_relat_1 ) ) )
& ( ( B
= ( A @ k1_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice2) ).
thf(4890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(2506,plain,
sk142 @ v2_lattices,
inference(cnfConj,[status(thm)],[2503]) ).
thf(10136,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,2914]) ).
thf(10137,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10136]) ).
thf(10147,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10137]) ).
thf(240,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( A @ a_2_0_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_domain_1) ).
thf(2418,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( A @ a_2_0_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(770,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_lattice4) ).
thf(5340,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(10986,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9803]) ).
thf(10987,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10986]) ).
thf(11041,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != k1_nat_lat )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10987]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(1245,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(738,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r2_lattice4 ) ) )
& ( A @ v14_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattice4) ).
thf(5218,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v14_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r2_lattice4 ) ) )
& ( A @ v14_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(510,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ ( B @ ( C @ v1_lattice4 ) ) ) )
=> ( F @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice4) ).
thf(3917,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( A @ ( B @ ( C @ v1_lattice4 ) ) ) )
=> ( F @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(369,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_binop_1) ).
thf(3159,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(517,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v10_lattices )
& ( B @ v9_lattices )
& ( B @ v8_lattices )
& ( B @ v7_lattices )
& ( B @ v6_lattices )
& ( B @ v5_lattices )
& ( B @ v4_lattices )
& ( B @ v3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m2_nat_lat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_nat_lat) ).
thf(3953,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v10_lattices )
& ( B @ v9_lattices )
& ( B @ v8_lattices )
& ( B @ v7_lattices )
& ( B @ v6_lattices )
& ( B @ v5_lattices )
& ( B @ v4_lattices )
& ( B @ v3_lattices )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ m2_nat_lat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(3241,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_partfun1) ).
thf(1477,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(942,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v16_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r2_lattices ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_lattices) ).
thf(6100,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r2_lattices ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) )
=> ( A @ v16_lattices ) )
& ( ( A @ v16_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r2_lattices ) ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(3142,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(759,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_2) ).
thf(5299,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(6325,plain,
sk459 @ l3_lattices,
inference(cnf,[status(esa)],[6324]) ).
thf(10498,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk217 ) ),
inference(paramod_ordered,[status(thm)],[1858,9047]) ).
thf(10499,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk217 ),
inference(pattern_uni,[status(thm)],[10498:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) )
= ( D @ ( C @ k4_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(4158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) )
= ( D @ ( C @ k4_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(819,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v11_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( B @ ( A @ k2_lattices ) ) @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_lattices) ).
thf(5548,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( B @ ( A @ k2_lattices ) ) @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) )
=> ( A @ v11_lattices ) )
& ( ( A @ v11_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
= ( D @ ( B @ ( A @ k2_lattices ) ) @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(787,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_filter_2 ) )
= ( B @ ( A @ k3_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
thf(5424,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k3_filter_2 ) )
= ( B @ ( A @ k3_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(3193,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(1208,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(10937,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9832]) ).
thf(10938,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk126 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10937]) ).
thf(11062,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk126 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk126 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10938]) ).
thf(630,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ? [F: $i] :
( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( D @ ( F @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice2) ).
thf(4598,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ? [F: $i] :
( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( D @ ( F @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(4879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(244,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(2449,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(274,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r3_relat_2 ) )
<=> ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_2) ).
thf(2629,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r3_relat_2 ) ) )
& ( ( B @ ( A @ r3_relat_2 ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(962,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( B @ ( C @ ( A @ k7_grcat_1 @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funcop_1 ) ) ) ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattice4) ).
thf(6170,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k3_lattices ) ) )
= ( B @ ( C @ ( A @ k7_grcat_1 @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funcop_1 ) ) ) ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
!= ( C @ k1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) )
| ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1176]) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
!= ( C @ k1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1177]) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 )
| ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
!= ( C @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[1179]) ).
thf(563,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_struct_0 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_struct_0) ).
thf(4168,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m1_struct_0 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_struct_0 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(786,axiom,
! [A: $i] :
( ( a_0_0_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).
thf(5414,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_0_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_0_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(1413,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(882,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice4) ).
thf(5812,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) )
| ( ( D @ k1_relat_1 )
!= ( A @ k1_tarski ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) )
& ( ( D @ v1_funct_1 )
| ~ ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) )
| ( ( D @ k1_relat_1 )
!= ( A @ k1_tarski ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1071]) ).
thf(1074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) )
| ( ( D @ k1_relat_1 )
!= ( A @ k1_tarski ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1072]) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 )
| ( ( D @ k1_relat_1 )
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[1074]) ).
thf(3881,plain,
~ ( k13_nat_lat @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3877]) ).
thf(844,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_lattices @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_lattice2) ).
thf(5661,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_lattices @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(797,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v11_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_0) ).
thf(5463,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v11_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(1583,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) )
=> ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(4690,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) )
=> ( B
= ( A @ k1_zfmisc_1 ) ) )
& ( ( B
= ( A @ k1_zfmisc_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(815,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) )
& ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_binop_1 ) ) )
=> ( A @ v10_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattice2) ).
thf(5538,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) )
& ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
& ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_binop_1 ) ) )
=> ( A @ v10_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(827,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_0) ).
thf(5587,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(1662,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(604,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k6_lattices ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattices) ).
thf(4394,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) )
=> ( B
= ( A @ k6_lattices ) ) )
& ( ( B
= ( A @ k6_lattices ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(4260,plain,
sk297 @ v3_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(4580,plain,
sk317 @ v9_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(867,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
thf(5757,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i] :
~ ( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(2037,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i] :
~ ( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk9 ) ) )
| ( ( A @ ( B @ sk9 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk8 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1134]) ).
thf(1145,plain,
! [B: $i,A: $i] :
( ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk9 ) )
!= ( A @ ( B @ sk8 ) @ ( A @ k1_funct_1 ) ) )
| ( ( A @ ( B @ sk9 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk8 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1139]) ).
thf(1007,plain,
( ( sk1 @ u1_lattices @ ( sk1 @ u2_lattices @ ( sk1 @ u1_struct_0 @ g3_lattices ) ) )
= ( sk2 @ u1_lattices @ ( sk2 @ u2_lattices @ ( sk2 @ u1_struct_0 @ g3_lattices ) ) ) ),
inference(cnfConj,[status(thm)],[1003]) ).
thf(1018,plain,
( ( sk2 @ u1_lattices @ ( sk2 @ u2_lattices @ ( sk2 @ u1_struct_0 @ g3_lattices ) ) )
= ( sk1 @ u1_lattices @ ( sk1 @ u2_lattices @ ( sk1 @ u1_struct_0 @ g3_lattices ) ) ) ),
inference(lifteq,[status(thm)],[1007]) ).
thf(23742,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,8721]) ).
thf(23743,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23742]) ).
thf(23767,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23743]) ).
thf(23819,plain,
( ( k2_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23767]) ).
thf(550,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_domain_1) ).
thf(4113,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(2564,plain,
sk148 @ l2_lattices,
inference(cnfConj,[status(thm)],[2563]) ).
thf(4355,plain,
sk301 @ v14_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(869,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_0) ).
thf(5763,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(6711,plain,
( ( ( sk353 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,4929]) ).
thf(6712,plain,
( ( sk353 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6711]) ).
thf(6719,plain,
sk353 != k1_xboole_0,
inference(simp,[status(thm)],[6712]) ).
thf(4336,plain,
~ ( sk300 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4331]) ).
thf(4255,plain,
~ ( sk297 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4247]) ).
thf(5446,plain,
( ( sk391 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5441]) ).
thf(5452,plain,
( ( sk391 @ v1_funct_1 )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5446]) ).
thf(3640,plain,
sk256 @ v5_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(1647,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(457,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices )
= ( A @ k1_lattice2 @ k5_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_lattice2) ).
thf(3659,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices )
= ( A @ k1_lattice2 @ k5_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(571,axiom,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( C @ ( B @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_nat_lat) ).
thf(4200,plain,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( C @ ( B @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) @ ( k2_nat_lat @ k1_binop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(602,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v3_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
& ( A @ v3_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice4) ).
thf(4377,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v3_filter_0 )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v3_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
& ( A @ v3_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(4593,plain,
~ ( sk318 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4582]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k6_filter_0 ) ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(6012,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k6_filter_0 ) ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(935,axiom,
! [A: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( A @ k12_nat_lat )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_nat_lat) ).
thf(6069,plain,
! [A: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( A @ k12_nat_lat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(410,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(3391,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_struct_0 ) )
= ( D @ ( C @ g2_struct_0 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(5716,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_struct_0 ) )
= ( D @ ( C @ g2_struct_0 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_subset_1) ).
thf(3737,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_binop_1) ).
thf(1961,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r6_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(4035,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(6466,plain,
( ( ( sk219 @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,3129]) ).
thf(6467,plain,
( ( sk219 @ v1_xboole_0 )
!= ( sk217 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6466]) ).
thf(6472,plain,
sk219 != sk217,
inference(simp,[status(thm)],[6467]) ).
thf(1022,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) )
| ( E
!= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
| ~ ( E @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1021]) ).
thf(1024,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ v1_relat_1 )
| ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) )
| ( E
!= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
inference(lifteq,[status(thm)],[1022]) ).
thf(1025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 )
| ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) ) ),
inference(simp,[status(thm)],[1024]) ).
thf(833,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r3_lattice4 ) ) )
<=> ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice4) ).
thf(5602,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) )
=> ( C @ ( B @ ( A @ r3_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattice4 ) ) )
=> ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( B @ k5_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1069,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] : ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(miniscope,[status(thm)],[1068]) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[1069]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(3112,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(1225,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(783,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k8_filter_0 ) @ u1_lattices )
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k8_filter_0 ) @ u2_lattices )
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k8_filter_0 ) @ u1_struct_0 )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_filter_0) ).
thf(5399,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( B @ ( A @ k8_filter_0 ) @ u1_lattices )
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k8_filter_0 ) @ u2_lattices )
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k8_filter_0 ) @ u1_struct_0 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(4366,plain,
sk302 @ v14_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(1566,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(1753,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relat_1) ).
thf(1267,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(2881,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2880]) ).
thf(2882,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2881]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(5018,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(10023,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,2271]) ).
thf(10024,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10023]) ).
thf(10027,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk56 ),
inference(simp,[status(thm)],[10024]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k20_filter_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k20_filter_2) ).
thf(6146,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k20_filter_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(1711,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(417,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).
thf(3448,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
=> ( A @ v13_lattices ) )
& ( ( A @ v13_lattices )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= B )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= B ) ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(8917,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2945,7087]) ).
thf(8918,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8917]) ).
thf(8919,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8918:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(23596,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8919,2145]) ).
thf(23597,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23596]) ).
thf(1034,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk5 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk6 ) ) @ r2_hidden ) )
| ( ( C @ k1_relat_1 )
!= A )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1029]) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk5 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk6 ) ) @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ( ( C @ k1_relat_1 )
!= A ) ),
inference(lifteq,[status(thm)],[1034]) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_relat_1 @ ( B @ sk5 ) ) )
| ( B @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ ( B @ sk6 ) ) @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1037]) ).
thf(399,axiom,
! [A: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ k1_lattices ) ) )
= ( B @ k12_nat_lat @ ( A @ k12_nat_lat @ k5_nat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_nat_lat) ).
thf(3344,plain,
! [A: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k10_nat_lat @ ( k11_nat_lat @ ( k7_nat_lat @ g3_lattices ) ) @ k1_lattices ) ) )
= ( B @ k12_nat_lat @ ( A @ k12_nat_lat @ k5_nat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(10138,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,2914]) ).
thf(10139,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10138]) ).
thf(10144,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk141 ),
inference(simp,[status(thm)],[10139]) ).
thf(13615,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k1_nat_lat @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13135,1067]) ).
thf(13616,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k1_nat_lat @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[13615]) ).
thf(13617,plain,
! [A: $i] : ( k5_numbers @ ( A @ ( k1_nat_lat @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[13616:[bind(A,$thf( k1_nat_lat @ k2_relat_1 )),bind(B,$thf( k5_numbers )),bind(C,$thf( C ))]]) ).
thf(13634,plain,
! [A: $i] : ( k5_numbers @ ( A @ ( k1_nat_lat @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[13617]) ).
thf(870,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ v1_funct_2 ) ) )
& ( A @ k5_lattice4 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice4) ).
thf(5767,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ v1_funct_2 ) ) )
& ( A @ k5_lattice4 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(986,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
<=> ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_0) ).
thf(6280,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
=> ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
=> ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(24704,plain,
! [B: $i,A: $i] :
( ( ( A @ sk341 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4740,2837]) ).
thf(24705,plain,
! [B: $i,A: $i] :
( ( A @ sk341 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[24704]) ).
thf(24735,plain,
! [B: $i,A: $i] :
( ( ( A @ sk341 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[24705]) ).
thf(24749,plain,
! [A: $i] :
( ( A @ sk341 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[24735]) ).
thf(3642,plain,
~ ( sk256 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3632]) ).
thf(4346,plain,
sk301 @ v7_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relat_1) ).
thf(2092,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(12049,plain,
! [A: $i] :
( ( ( A @ sk253 @ v1_xboole_0 )
!= ( sk353 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3595,4929]) ).
thf(12050,plain,
! [A: $i] :
( ( A @ sk253 @ v1_xboole_0 )
!= ( sk353 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[12049]) ).
thf(12071,plain,
! [A: $i] :
( ( A @ sk253 )
!= sk353 ),
inference(simp,[status(thm)],[12050]) ).
thf(547,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(4092,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
( ( E @ ( D @ k4_tarski ) )
!= A )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(1987,plain,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
( ( E @ ( D @ k4_tarski ) )
!= A )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(2224,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk101 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2222]) ).
thf(3818,plain,
sk272 @ v6_lattices,
inference(cnfConj,[status(thm)],[3812]) ).
thf(3885,plain,
k13_nat_lat @ v10_lattices,
inference(cnfConj,[status(thm)],[3877]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(1637,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(3334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice2) ).
thf(1188,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(700,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k4_lattices ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattices) ).
thf(5015,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k4_lattices ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_nat_lat ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ ( B @ ( A @ k24_filter_2 ) @ m2_nat_lat ) )
& ( B @ ( A @ k24_filter_2 ) @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k24_filter_2) ).
thf(4020,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_nat_lat ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ ( B @ ( A @ k24_filter_2 ) @ m2_nat_lat ) )
& ( B @ ( A @ k24_filter_2 ) @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(13692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4471,1105]) ).
thf(13693,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k2_nat_lat @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[13692]) ).
thf(13694,plain,
k5_numbers @ ( k2_nat_lat @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[13693:[bind(A,$thf( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) )),bind(B,$thf( k5_numbers )),bind(C,$thf( k2_nat_lat ))]]) ).
thf(577,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).
thf(4222,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(490,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r3_lattice4 ) ) )
& ( A @ v13_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice4) ).
thf(3823,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r3_lattice4 ) ) )
& ( A @ v13_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(821,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( B @ ( A @ k3_filter_0 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_0) ).
thf(5560,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( B @ ( A @ k3_filter_0 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(923,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_filter_0) ).
thf(5995,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(4351,plain,
sk301 @ v3_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(3544,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(2322,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k2_lattice4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice4) ).
thf(6313,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k2_lattice4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ ( B @ ( A @ k9_filter_2 ) @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_2) ).
thf(5543,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ ( B @ ( A @ k9_filter_2 ) @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(4800,plain,
k6_nat_lat @ v8_lattices,
inference(cnfConj,[status(thm)],[4793]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(4968,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ( ( B
= ( A @ k1_tarski ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(4969,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[4968]) ).
thf(4970,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk360 ) @ r2_hidden ) )
| ( ( E @ ( F @ sk359 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk360 ) )
= E )
| ( ( E @ ( F @ sk359 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk360 ) @ r2_hidden ) )
| ( F @ ( E @ ( F @ sk359 ) @ r2_hidden ) ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk360 ) )
= E )
| ( F @ ( E @ ( F @ sk359 ) @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
| ( D != A )
| ( B
!= ( A @ k1_tarski ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ r2_hidden ) )
| ( B
!= ( A @ k1_tarski ) ) ) ),
inference(cnf,[status(esa)],[4969]) ).
thf(4975,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[4970]) ).
thf(4981,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[4975]) ).
thf(4982,plain,
! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[4981]) ).
thf(3558,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(miniscope,[status(thm)],[3557]) ).
thf(3559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C = D )
| ~ ( C @ ( D @ r1_tarski ) )
| ~ ( D @ ( C @ r1_tarski ) ) )
& ( ( A @ ( B @ r1_tarski ) )
| ( A != B ) )
& ( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[3558]) ).
thf(3560,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[3559]) ).
thf(3563,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[3560]) ).
thf(3564,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[3563]) ).
thf(10917,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9818]) ).
thf(10918,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10917]) ).
thf(11049,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != k11_nat_lat )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10918]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).
thf(2044,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(839,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v12_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v12_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_filter_0) ).
thf(5638,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v12_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v12_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(1579,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(1218,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(5447,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5441]) ).
thf(5450,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk391 @ v1_funct_2 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5447]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k11_filter_0 ) )
= ( B @ ( A @ k10_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).
thf(3853,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k11_filter_0 ) )
= ( B @ ( A @ k10_filter_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(753,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_0) ).
thf(5277,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(711,axiom,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( A @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_nat_lat) ).
thf(5062,plain,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k2_nat_lat @ k1_binop_1 ) ) )
= ( A @ ( B @ ( k2_nat_lat @ k1_binop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(4164,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
<=> ( B
= ( A @ k2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_subset_1) ).
thf(2354,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k2_subset_1 ) )
=> ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) )
& ( ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B
= ( A @ k2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(4802,plain,
k6_nat_lat @ v4_lattices,
inference(cnfConj,[status(thm)],[4793]) ).
thf(519,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_lattice2) ).
thf(3970,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relat_1) ).
thf(1802,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(409,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v11_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ u1_lattices @ ( C @ u1_struct_0 @ ( C @ u1_struct_0 @ ( C @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_lattice2) ).
thf(3388,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v11_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ u1_lattices @ ( C @ u1_struct_0 @ ( C @ u1_struct_0 @ ( C @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(3024,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(2939,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(13056,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k11_nat_lat @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12813,1067]) ).
thf(13057,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k11_nat_lat @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[13056]) ).
thf(13058,plain,
! [A: $i] : ( k7_nat_lat @ ( A @ ( k11_nat_lat @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[13057:[bind(A,$thf( k11_nat_lat @ k2_relat_1 )),bind(B,$thf( k7_nat_lat )),bind(C,$thf( C ))]]) ).
thf(13076,plain,
! [A: $i] : ( k7_nat_lat @ ( A @ ( k11_nat_lat @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[13058]) ).
thf(4257,plain,
sk297 @ v5_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(4111,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(4392,plain,
sk303 @ v5_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(10712,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2369,7089]) ).
thf(10713,plain,
! [A: $i] :
( ( ( sk126 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10712]) ).
thf(10714,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk126 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10713:[bind(A,$thf( sk126 ))]]) ).
thf(8891,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4270,7087]) ).
thf(8892,plain,
! [A: $i] :
( ( ( k1_nat_lat @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8891]) ).
thf(8893,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8892:[bind(A,$thf( k1_nat_lat ))]]) ).
thf(23748,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,7216]) ).
thf(23749,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23748]) ).
thf(23773,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( k11_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23749]) ).
thf(23826,plain,
( ( k11_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k11_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23773]) ).
thf(6188,plain,
~ ( sk446 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[6186]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k12_filter_2 ) )
= ( B @ ( A @ k8_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_filter_2) ).
thf(3488,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k12_filter_2 ) )
= ( B @ ( A @ k8_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(6410,plain,
( ( ( sk219 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,3129]) ).
thf(6411,plain,
( ( sk219 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6410]) ).
thf(6415,plain,
sk219 != k1_xboole_0,
inference(simp,[status(thm)],[6411]) ).
thf(5223,plain,
! [A: $i] : ( A @ ( A @ sk378 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[5222]) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk9 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk8 ) ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk9 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) )
| ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1134]) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk9 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk8 ) ) )
| ( ( A @ ( B @ sk9 ) )
= ( A @ ( B @ sk8 ) @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1137]) ).
thf(555,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_0) ).
thf(4133,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( ( E @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(2543,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(5240,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(89,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(1485,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).
thf(1972,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r1_realset1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1052,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( C @ ( D @ ( E @ sk7 ) ) ) ) @ r2_hidden ) )
| ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
| ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1050]) ).
thf(974,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices @ ( A @ k7_lattices ) )
= ( A @ k5_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice4) ).
thf(6213,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k6_lattices @ ( A @ k7_lattices ) )
= ( A @ k5_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(10019,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,2271]) ).
thf(10020,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10019]) ).
thf(10028,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk141 ),
inference(simp,[status(thm)],[10020]) ).
thf(558,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m1_filter_0 ) )
<=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
<=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_0) ).
thf(4143,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m1_filter_0 ) ) )
& ( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(3224,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(688,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r1_lattice2 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice2) ).
thf(4932,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) )
=> ( C @ ( B @ ( A @ r1_lattice2 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_lattice2 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(741,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_0) ).
thf(5226,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(958,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(6161,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(4795,plain,
k6_nat_lat @ v7_lattices,
inference(cnfConj,[status(thm)],[4793]) ).
thf(428,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(3520,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(830,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) )
=> ( A @ v11_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice2) ).
thf(5596,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) )
=> ( A @ v11_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1082,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[1080]) ).
thf(1084,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1082]) ).
thf(25044,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( B @ k1_zfmisc_1 ) )
| ( ( A @ sk253 )
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1858,12064]) ).
thf(25045,plain,
! [A: $i] :
( ( A @ sk253 )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[25044:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(2885,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(1949,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ~ ( B @ ( D @ r2_hidden ) ) )
& ( ~ ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ k2_funct_1 @ v1_funct_1 )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1156]) ).
thf(6134,plain,
( ( k13_nat_lat @ l3_lattices )
& ( k13_nat_lat @ v10_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[6133]) ).
thf(6137,plain,
k13_nat_lat @ l3_lattices,
inference(cnfConj,[status(thm)],[6134]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_binop_1) ).
thf(2347,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r2_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( C @ ( B @ ( A @ r1_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(4185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( C @ ( B @ ( A @ r1_lattices ) ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ r1_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(987,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
= ( A @ k6_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice4) ).
thf(6284,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
= ( A @ k6_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(3168,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(390,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_filter_0) ).
thf(3284,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(6700,plain,
( ( ( sk281 @ v1_xboole_0 )
!= ( sk219 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,3129]) ).
thf(6701,plain,
( ( sk281 @ v1_xboole_0 )
!= ( sk219 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6700]) ).
thf(6706,plain,
sk281 != sk219,
inference(simp,[status(thm)],[6701]) ).
thf(896,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k13_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k13_filter_2) ).
thf(5873,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k13_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(803,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_0) ).
thf(5490,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(921,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lattice4) ).
thf(5981,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m3_lattice4 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(16249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12404,1067]) ).
thf(16250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[16249]) ).
thf(16251,plain,
! [A: $i] : ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ ( k10_nat_lat @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[16250:[bind(A,$thf( k10_nat_lat @ k1_relat_1 )),bind(B,$thf( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) )),bind(C,$thf( C ))]]) ).
thf(16277,plain,
! [A: $i] : ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ ( k10_nat_lat @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[16251]) ).
thf(4606,plain,
sk319 @ v7_lattices,
inference(cnfConj,[status(thm)],[4601]) ).
thf(650,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(4727,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(906,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_lattices @ v3_binop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice2) ).
thf(5917,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_lattices @ v3_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(4587,plain,
sk318 @ v10_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(691,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ~ ( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( B
= ( F @ ( E @ ( A @ k4_lattices ) ) ) ) ) ) )
& ( D @ ( C @ ( A @ k5_filter_0 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_0) ).
thf(4945,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ~ ( ! [E: $i] :
( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ~ ( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( B
= ( F @ ( E @ ( A @ k4_lattices ) ) ) ) ) ) )
& ( D @ ( C @ ( A @ k5_filter_0 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) )
| ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1177]) ).
thf(1180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 )
| ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[1178]) ).
thf(814,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ k5_lattices @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_lattice2) ).
thf(5536,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ k5_lattices @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice2) ).
thf(1817,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(6709,plain,
( ( ( sk353 @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,4929]) ).
thf(6710,plain,
( ( sk353 @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6709]) ).
thf(6721,plain,
sk353 != sk281,
inference(simp,[status(thm)],[6710]) ).
thf(371,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(3171,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(333,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(2960,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(807,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_struct_0 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(5510,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k1_struct_0 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(912,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_nat_lat ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k24_filter_2 ) )
= ( B @ k1_lattice2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k24_filter_2) ).
thf(5934,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_nat_lat ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k24_filter_2 ) )
= ( B @ k1_lattice2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(658,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(4780,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1124,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( C @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ) ),
inference(cnf,[status(esa)],[1123]) ).
thf(1126,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1124]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(4078,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(471,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v14_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_0) ).
thf(3725,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ v14_lattices )
=> ( B @ ( A @ k8_filter_0 ) @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(763,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_filter_0 ) )
=> ! [H: $i] :
( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
=> ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
=> ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
& ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
=> ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_filter_0) ).
thf(5308,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v3_filter_0 )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_filter_0 ) )
=> ! [H: $i] :
( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
=> ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
& ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
=> ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
& ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
=> ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v2_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_binop_1) ).
thf(2997,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) )
=> ( A @ ( B @ v2_binop_1 ) ) )
& ( ( A @ ( B @ v2_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_struct_0 ) ) )
=> ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_struct_0) ).
thf(4006,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_struct_0 ) ) )
=> ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(190,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
~ ( ( B
= ( D @ ( C @ k4_tarski ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(2110,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
~ ( ( B
= ( D @ ( C @ k4_tarski ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(1575,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(3051,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3048]) ).
thf(3055,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3051]) ).
thf(3056,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3055]) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_filter_2 ) @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_2) ).
thf(5860,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_filter_2 ) @ m1_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(767,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ( ( A @ k5_lattices )
= ( B @ k5_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_filter_2) ).
thf(5332,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v13_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
=> ( ( A @ k5_lattices )
= ( B @ k5_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(2658,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(513,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
thf(3929,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
<=> ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(1734,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(729,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(5184,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
& ( A @ u2_lattices @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(1107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 )
| ~ ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1106]) ).
thf(1108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1107]) ).
thf(23627,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,8022]) ).
thf(23628,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23627]) ).
thf(23760,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( k10_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23628]) ).
thf(23811,plain,
( ( k10_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23760]) ).
thf(20125,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1858,2047]) ).
thf(20126,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[20125:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(4574,plain,
sk317 @ v16_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(3797,plain,
~ ( sk267 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3795]) ).
thf(10923,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7326]) ).
thf(10924,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10923]) ).
thf(11076,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != k1_nat_lat )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10924]) ).
thf(683,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_binop_1) ).
thf(4913,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r7_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(1721,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(2273,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(cnf,[status(esa)],[2272]) ).
thf(860,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_0) ).
thf(5724,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
<=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_binop_1) ).
thf(2853,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
=> ( C @ ( B @ ( A @ r6_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(237,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ a_2_2_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_domain_1) ).
thf(2406,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ a_2_2_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(2554,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(291,axiom,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k3_nat_lat @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_nat_lat) ).
thf(2764,plain,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k3_nat_lat @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(4881,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(10984,plain,
( ( ( k1_xboole_0 @ ( sk2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7465]) ).
thf(10985,plain,
( ( ( k1_xboole_0 @ ( sk2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10984]) ).
thf(11066,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk298 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10985]) ).
thf(11091,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11066]) ).
thf(680,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_2) ).
thf(4900,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(349,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(3057,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(3058,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[3057]) ).
thf(25823,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
inference(rewrite,[status(thm)],[3058,2373]) ).
thf(13937,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k2_nat_lat @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13694,1067]) ).
thf(13938,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k5_numbers @ ( k2_nat_lat @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[13937]) ).
thf(13939,plain,
! [A: $i] : ( k5_numbers @ ( A @ ( k2_nat_lat @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[13938:[bind(A,$thf( k2_nat_lat @ k2_relat_1 )),bind(B,$thf( k5_numbers )),bind(C,$thf( C ))]]) ).
thf(13959,plain,
! [A: $i] : ( k5_numbers @ ( A @ ( k2_nat_lat @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[13939]) ).
thf(10158,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,4295]) ).
thf(10159,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10158]) ).
thf(10169,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk141 ),
inference(simp,[status(thm)],[10159]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(3709,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(4250,plain,
sk297 @ v10_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(1101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ m2_subset_1 ) ) )
| ~ ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
| ~ ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ( C @ v1_xboole_0 )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1100]) ).
thf(616,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ k1_lattice2 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice2) ).
thf(4495,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ k1_lattice2 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(2130,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(458,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(3662,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(624,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(4527,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(239,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(2416,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(3780,plain,
k7_nat_lat @ ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k10_nat_lat @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[3778]) ).
thf(4261,plain,
sk297 @ v8_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(9158,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,5001]) ).
thf(9159,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9158]) ).
thf(9160,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk56 ),
inference(simp,[status(thm)],[9159]) ).
thf(611,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v4_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( B @ ( C @ ( A @ k1_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattices) ).
thf(4451,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( B @ ( C @ ( A @ k1_lattices ) ) ) ) ) )
=> ( A @ v4_lattices ) )
& ( ( A @ v4_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( B @ ( C @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(832,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_lattice4) ).
thf(5600,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(520,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r2_lattices ) ) )
<=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_lattices) ).
thf(3978,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) ) )
=> ( C @ ( B @ ( A @ r2_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r2_lattices ) ) )
=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( C @ ( B @ ( A @ k2_lattices ) ) )
= ( A @ k5_lattices ) )
& ( ( B @ ( C @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) )
& ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= ( A @ k6_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(3879,plain,
k13_nat_lat @ v5_lattices,
inference(cnfConj,[status(thm)],[3877]) ).
thf(4591,plain,
sk318 @ v3_lattices,
inference(cnfConj,[status(thm)],[4582]) ).
thf(4387,plain,
sk303 @ v4_lattices,
inference(cnfConj,[status(thm)],[4382]) ).
thf(960,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_0) ).
thf(6166,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_filter_0 ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
& ( E @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) )
=> ( E @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(11029,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9838]) ).
thf(11030,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11029]) ).
thf(11071,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != k2_nat_lat )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k2_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[11030]) ).
thf(722,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_binop_1) ).
thf(5128,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(970,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_2 ) )
<=> ( A @ ( B @ m1_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
thf(6198,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
=> ( A @ ( B @ m1_filter_2 ) ) )
& ( ( A @ ( B @ m1_filter_2 ) )
=> ( A @ ( B @ m1_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(241,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r8_relat_2 ) )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( E @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
thf(2421,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( E @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r8_relat_2 ) ) )
& ( ( B @ ( A @ r8_relat_2 ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( E @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ k1_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
thf(4182,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l2_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( C @ ( B @ ( A @ k1_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(886,axiom,
! [A: $i] :
( ( a_0_1_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).
thf(5828,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_1_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_1_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ sk5 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1029]) ).
thf(462,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( D @ ( A @ k2_lattice4 ) ) )
& ( B @ ( A @ k4_lattice4 ) @ ( D @ r1_tarski ) ) ) )
& ( B @ ( A @ k4_lattice4 ) @ ( C @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice4) ).
thf(3694,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
= ( D @ ( A @ k2_lattice4 ) ) )
& ( B @ ( A @ k4_lattice4 ) @ ( D @ r1_tarski ) ) ) )
& ( B @ ( A @ k4_lattice4 ) @ ( C @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(296,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(2786,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(4602,plain,
sk319 @ l1_lattices,
inference(cnfConj,[status(thm)],[4601]) ).
thf(570,axiom,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ k1_lattices ) ) )
= ( B @ k3_nat_lat @ ( A @ k3_nat_lat @ k5_nat_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_nat_lat) ).
thf(4197,plain,
! [A: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ k1_lattices ) ) )
= ( B @ k3_nat_lat @ ( A @ k3_nat_lat @ k5_nat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(395,axiom,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( B @ ( A @ ( C @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( A @ ( B @ ( C @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( B @ ( C @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( C @ ( A @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_nat_lat) ).
thf(3324,plain,
! [A: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k6_nat_lat @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( B @ ( A @ ( C @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( A @ ( B @ ( C @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( B @ ( C @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( A @ ( k1_nat_lat @ k1_binop_1 ) ) )
= ( C @ ( A @ ( B @ ( k1_nat_lat @ k1_binop_1 ) ) @ ( k1_nat_lat @ k1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(991,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_lattice2 )
<=> ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice2) ).
thf(6305,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) )
=> ( A @ v1_lattice2 ) )
& ( ( A @ v1_lattice2 )
=> ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(5532,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
thf(2399,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(443,axiom,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s7_domain_1) ).
thf(3598,plain,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(5036,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk366 @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) )
| ~ ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk364 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk366 @ m2_relset_1 ) ) )
| ~ sk364 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk366 @ v1_funct_2 ) ) )
| ~ sk364 )
& ( ( sk366 @ v1_funct_1 )
| ~ sk364 )
& ( sk364
| ~ ( A @ ( sk365 @ p1_s3_funct_2 ) )
| ~ ( f2_s3_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk364
| ( f1_s3_funct_2 @ ( sk365 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[5035]) ).
thf(5040,plain,
( sk364
| ( f1_s3_funct_2 @ ( sk365 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[5036]) ).
thf(2230,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk102 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2227]) ).
thf(848,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(5672,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_lattice4 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(10154,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2905,4295]) ).
thf(10155,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10154]) ).
thf(10167,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10155]) ).
thf(4570,plain,
sk317 @ v6_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(732,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
<=> ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_filter_0) ).
thf(5196,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ( ( ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) ) )
& ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
=> ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(4372,plain,
sk302 @ v3_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
<=> ( C @ ( D @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_nat_lat) ).
thf(2623,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( C @ ( D @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
=> ( C @ ( D @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(9148,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,5001]) ).
thf(9149,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9148]) ).
thf(9162,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk281 ),
inference(simp,[status(thm)],[9149]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(997,axiom,
k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( k5_nat_lat @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_nat_lat) ).
thf(6326,plain,
k1_nat_lat @ ( k2_nat_lat @ ( k5_numbers @ g3_lattices ) ) @ u1_struct_0 @ ( k5_nat_lat @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(21312,plain,
k6_nat_lat @ u1_struct_0 @ ( k5_nat_lat @ m1_subset_1 ),
inference(rewrite,[status(thm)],[6326,3574]) ).
thf(499,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_lattice2) ).
thf(3860,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_binop_1) ).
thf(2983,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(1380,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(4357,plain,
sk301 @ l3_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(3992,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(2003,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(2142,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(2123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(207,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(2218,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(554,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice2) ).
thf(4125,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
=> ( ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(214,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(2258,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(891,axiom,
( ( k6_nat_lat @ l3_lattices )
& ( k6_nat_lat @ v10_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_nat_lat) ).
thf(5852,plain,
( ( k6_nat_lat @ l3_lattices )
& ( k6_nat_lat @ v10_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ g2_lattices ) @ l2_lattices )
& ( B @ ( A @ g2_lattices ) @ v2_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g2_lattices) ).
thf(2374,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ g2_lattices ) @ l2_lattices )
& ( B @ ( A @ g2_lattices ) @ v2_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(11120,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,10678]) ).
thf(11121,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk56 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11120]) ).
thf(11131,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk56 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk56 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[11121]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(2302,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_realset1) ).
thf(2517,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(4794,plain,
k6_nat_lat @ v9_lattices,
inference(cnfConj,[status(thm)],[4793]) ).
thf(5728,plain,
sk411 @ l2_struct_0,
inference(cnfConj,[status(thm)],[5727]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(3705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_2 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_filter_2) ).
thf(4014,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k4_filter_2 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(614,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_binop_1) ).
thf(4472,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( A @ ( B @ v1_binop_1 ) ) )
& ( ( A @ ( B @ v1_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice2) ).
thf(2534,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(2255,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(4356,plain,
sk301 @ v9_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(23744,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,10681]) ).
thf(23745,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23744]) ).
thf(23768,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( k1_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23745]) ).
thf(23820,plain,
( ( k1_nat_lat != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23768]) ).
thf(4254,plain,
sk297 @ v6_lattices,
inference(cnfConj,[status(thm)],[4247]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(4596,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(505,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_0) ).
thf(3892,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(950,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice4) ).
thf(6131,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(3882,plain,
k13_nat_lat @ v6_lattices,
inference(cnfConj,[status(thm)],[3877]) ).
thf(743,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= C ) )
=> ( B
= ( A @ k6_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice2) ).
thf(5232,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= C ) )
=> ( B
= ( A @ k6_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(330,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(2951,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(623,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k10_filter_0 ) @ k3_relat_1 )
= ( A @ u1_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_filter_0) ).
thf(4523,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k10_filter_0 ) @ k3_relat_1 )
= ( A @ u1_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(665,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) )
= ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice4) ).
thf(4843,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) )
= ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(1876,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(2815,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(23698,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,10675]) ).
thf(23699,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk205 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23698]) ).
thf(23782,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk205 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23699]) ).
thf(23835,plain,
( ( sk205 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23782]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_binop_1) ).
thf(2736,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(4841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(92,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
thf(1527,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r3_binop_1 ) ) )
& ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_binop_1) ).
thf(3337,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r3_binop_1 ) ) )
& ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(774,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_lattice4 ) @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(5371,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k3_lattice4 ) @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(810,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k4_filter_0 ) ) )
= ( A @ k6_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_0) ).
thf(5527,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k4_filter_0 ) ) )
= ( A @ k6_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(183,axiom,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( D @ ( C @ k4_tarski ) )
!= B )
& ( A @ ( B @ r2_hidden ) ) ) )
=> ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
thf(2050,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( D @ ( C @ k4_tarski ) )
!= B )
& ( A @ ( B @ r2_hidden ) ) ) )
=> ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(4579,plain,
sk317 @ v10_lattices,
inference(cnfConj,[status(thm)],[4566]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(4885,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_filter_0 ) )
& ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(4367,plain,
sk302 @ v13_lattices,
inference(cnfConj,[status(thm)],[4363]) ).
thf(868,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k2_lattice4 ) )
= ( A @ k6_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattice4) ).
thf(5760,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k2_lattice4 ) )
= ( A @ k6_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(909,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice4) ).
thf(5926,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
= ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(351,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
= ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(3062,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
= ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(853,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_setwiseo ) )
=> ( ( A @ k5_lattices )
= ( A @ u2_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice2) ).
thf(5700,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_setwiseo ) )
=> ( ( A @ k5_lattices )
= ( A @ u2_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_realset1) ).
thf(1859,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(298,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(2800,plain,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(1314,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m2_subset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1056,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1055]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(1197,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(10969,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,7222]) ).
thf(10970,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10969]) ).
thf(11067,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != k10_nat_lat )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10970]) ).
thf(669,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(4865,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(1164,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] : ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(miniscope,[status(thm)],[1163]) ).
thf(1165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) )
| ~ ( B @ ( A @ ( C @ m1_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[1164]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(2549,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(3822,plain,
sk272 @ v7_lattices,
inference(cnfConj,[status(thm)],[3812]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r2_binop_1 ) ) )
& ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_binop_1) ).
thf(3145,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r2_binop_1 ) ) )
& ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(10967,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8931]) ).
thf(10968,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk298 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10967]) ).
thf(11035,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != sk298 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[10968]) ).
thf(11082,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk298 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11035]) ).
thf(17909,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12849,1067]) ).
thf(17910,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( k11_nat_lat @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[17909]) ).
thf(17911,plain,
! [A: $i] : ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ ( k11_nat_lat @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[17910:[bind(A,$thf( k11_nat_lat @ k1_relat_1 )),bind(B,$thf( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) )),bind(C,$thf( C ))]]) ).
thf(17937,plain,
! [A: $i] : ( k7_nat_lat @ ( k7_nat_lat @ k2_zfmisc_1 ) @ ( A @ ( k11_nat_lat @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[17911]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( B @ ( C @ ( A @ k7_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(2201,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( B @ ( C @ ( A @ k7_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(4350,plain,
sk301 @ v10_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(678,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_lattices ) ) )
=> ( D @ ( C @ ( A @ k2_lattices ) ) @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattices) ).
thf(4895,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_lattices ) ) )
=> ( D @ ( C @ ( A @ k2_lattices ) ) @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_lattices ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(3347,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_lattices ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(946,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattice4) ).
thf(6114,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m3_lattice4 ) )
=> ( ( ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(10150,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4005,4295]) ).
thf(10151,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk281 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10150]) ).
thf(10168,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk281 ),
inference(simp,[status(thm)],[10151]) ).
thf(575,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v10_lattices )
<=> ( ( A @ v9_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v8_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattices) ).
thf(4210,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v9_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v8_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices ) )
=> ( A @ v10_lattices ) )
& ( ( A @ v10_lattices )
=> ( ( A @ v9_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v8_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(757,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r8_relat_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_filter_0) ).
thf(5290,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r8_relat_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(532,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(4024,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(468,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
<=> ( ( A @ v14_lattices )
& ( A @ v13_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattices) ).
thf(3716,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v14_lattices )
& ( A @ v13_lattices ) )
=> ( A @ v15_lattices ) )
& ( ( A @ v15_lattices )
=> ( ( A @ v14_lattices )
& ( A @ v13_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(269,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(2572,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(988,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_lattice2) ).
thf(6287,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v14_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(374,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).
thf(3196,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(3426,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(3633,plain,
sk256 @ v7_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m2_filter_2 ) )
& ( A @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k21_filter_2 ) ) )
= ( C @ ( B @ ( A @ k20_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k21_filter_2) ).
thf(5215,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m2_filter_2 ) )
& ( A @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k21_filter_2 ) ) )
= ( C @ ( B @ ( A @ k20_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(426,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( D @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r2_hidden ) )
=> ( D @ ( A @ k3_filter_0 ) @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_0) ).
thf(3506,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( D @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r2_hidden ) )
=> ( D @ ( A @ k3_filter_0 ) @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(10484,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk56 ) ),
inference(paramod_ordered,[status(thm)],[1858,9045]) ).
thf(10485,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk56 ),
inference(pattern_uni,[status(thm)],[10484:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k19_filter_2 ) @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_filter_2) ).
thf(5200,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k19_filter_2 ) @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(718,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v5_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r1_lattices ) ) )
& ( C @ ( B @ ( A @ r1_lattices ) ) ) )
=> ( D @ ( B @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattices) ).
thf(5110,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ( A @ v5_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ r1_lattices ) ) )
& ( C @ ( B @ ( A @ r1_lattices ) ) ) )
=> ( D @ ( B @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(2651,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(880,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( C @ ( B @ ( A @ r4_lattice4 ) ) )
<=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice4) ).
thf(5803,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) )
=> ( C @ ( B @ ( A @ r4_lattice4 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_lattice4 ) ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
= ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(10971,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,8916]) ).
thf(10972,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10971]) ).
thf(11050,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk298 != k10_nat_lat )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k10_nat_lat @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[10972]) ).
thf(552,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) )
=> ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_lattice2) ).
thf(4118,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v14_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( F @ r2_hidden ) )
=> ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) )
=> ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(6369,plain,
( ( ( sk219 @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,3129]) ).
thf(6370,plain,
( ( sk219 @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6369]) ).
thf(6373,plain,
sk219 != sk141,
inference(simp,[status(thm)],[6370]) ).
thf(837,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( B @ ( C @ ( A @ k5_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_0) ).
thf(5623,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( B @ ( C @ ( A @ k5_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(3886,plain,
k13_nat_lat @ v4_lattices,
inference(cnfConj,[status(thm)],[3877]) ).
thf(799,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
<=> ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_0) ).
thf(5473,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
| ( ( B @ k1_relat_1 )
!= k1_xboole_0 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1086]) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ( ( B @ k1_relat_1 )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1089]) ).
thf(156,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(1930,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k7_lattices ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(5275,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k7_lattices ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(916,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_0) ).
thf(5945,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(967,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice2) ).
thf(6190,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u2_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(2127,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(667,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
=> ( ( C @ ( A @ k3_filter_0 ) )
= ( B @ ( A @ k2_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_0) ).
thf(4848,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C
= ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
=> ( ( C @ ( A @ k3_filter_0 ) )
= ( B @ ( A @ k2_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1340,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk21 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1335]) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk21 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1340]) ).
thf(1352,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk21 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1351]) ).
thf(23687,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2145,9821]) ).
thf(23688,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk217 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[23687]) ).
thf(23777,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk2 )
| ( sk217 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23688]) ).
thf(23830,plain,
( ( sk217 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk217 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[23777]) ).
thf(735,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v14_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_0) ).
thf(5204,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v14_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_tarski ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k2_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_1) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_tarski ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k2_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_relset_1) ).
thf(1977,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ g1_lattices ) )
!= ( D @ ( C @ g1_lattices ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1148]) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( B = D )
| ( ( B @ ( A @ g1_lattices ) )
!= ( D @ ( C @ g1_lattices ) ) ) ),
inference(lifteq,[status(thm)],[1150]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(5668,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(4799,plain,
k6_nat_lat @ v10_lattices,
inference(cnfConj,[status(thm)],[4793]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(3772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(21277,plain,
k6_nat_lat @ u1_struct_0 @ ( k4_nat_lat @ m1_subset_1 ),
inference(rewrite,[status(thm)],[3787,3574]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).
thf(4506,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(6468,plain,
( ( ( sk217 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3118,1186]) ).
thf(6469,plain,
( ( sk217 @ v1_xboole_0 )
!= ( sk11 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6468]) ).
thf(6473,plain,
sk217 != sk11,
inference(simp,[status(thm)],[6469]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(4066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(3817,plain,
sk272 @ v8_lattices,
inference(cnfConj,[status(thm)],[3812]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(3965,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice2) ).
thf(2507,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(6082,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D @ ( F @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A
= ( F @ ( E @ ( B @ k4_lattices ) ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(10142,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1869,2914]) ).
thf(10143,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk56 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10142]) ).
thf(10146,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk56 ),
inference(simp,[status(thm)],[10143]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(3939,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(899,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_2 @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_2) ).
thf(5891,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_2 @ m1_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1004,plain,
sk2 @ v17_lattices,
inference(cnfConj,[status(thm)],[1003]) ).
thf(1885,plain,
sk58 @ l1_lattices,
inference(cnfConj,[status(thm)],[1884]) ).
thf(977,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ~ ( ( ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v1_filter_0 ) ) ) )
& ( B != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_0) ).
thf(6222,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [D: $i] :
( ( A @ ( D @ m1_filter_0 ) )
=> ~ ( ( ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( A @ ( D @ v1_filter_0 ) ) ) )
& ( B != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(842,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_filter_2) ).
thf(5645,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m2_filter_2 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ m1_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(4345,plain,
sk301 @ v13_lattices,
inference(cnfConj,[status(thm)],[4342]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k10_filter_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_0) ).
thf(4501,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_filter_0 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( B @ ( A @ k10_filter_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(1399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(4271,plain,
k5_numbers @ ( k5_numbers @ ( k5_numbers @ k2_zfmisc_1 ) @ ( k1_nat_lat @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[4269]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).
thf(3013,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m2_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(420,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_lattice2) ).
thf(3474,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) )
= ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) ) )
| ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(64,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
thf(1320,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(4719,plain,
! [A: $i] :
( ( ( ( A @ ( sk339 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s13_funct_2 ) )
| ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk337 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk339 @ m2_relset_1 ) ) )
| ~ sk337 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk339 @ v1_funct_2 ) ) )
| ~ sk337 )
& ( ( sk339 @ v1_funct_1 )
| ~ sk337 )
& ( sk337
| ~ ( f2_s13_funct_2 @ ( sk338 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
& ( sk337
| ( f1_s13_funct_2 @ ( sk338 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4718]) ).
thf(4723,plain,
( sk337
| ( f1_s13_funct_2 @ ( sk338 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4719]) ).
thf(749,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
& ( A @ v17_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice4) ).
thf(5261,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v17_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
=> ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
=> ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
& ( A @ v17_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(1848,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(748,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_lattices ) ) )
<=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
thf(5255,plain,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= C )
=> ( C @ ( B @ ( A @ r1_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(936,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice2) ).
thf(6072,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(10949,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4280,9797]) ).
thf(10950,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk298 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk2 @ ( sk205 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[10949]) ).
thf(11048,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk2 != f1_s4_funct_2 )
| ( sk298 != sk205 )
| ~ ( k1_xboole_0 @ ( sk2 @ ( sk205 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[10950]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k3_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k3_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(1917,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k3_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k3_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(1204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4335,plain,
sk300 @ l2_lattices,
inference(cnfConj,[status(thm)],[4331]) ).
thf(915,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice2) ).
thf(5943,plain,
! [A: $i] :
( ( ( A @ l1_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(703,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(5029,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(963,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattices) ).
thf(6173,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(637,axiom,
k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_nat_lat) ).
thf(4642,plain,
k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice2) ).
thf(4627,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(4584,plain,
sk318 @ v1_lattice2,
inference(cnfConj,[status(thm)],[4582]) ).
thf(764,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v6_group_1 )
<=> ( A @ k1_lattice2 @ v6_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_lattice2) ).
thf(5312,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k1_lattice2 @ v6_group_1 )
=> ( A @ v6_group_1 ) )
& ( ( A @ v6_group_1 )
=> ( A @ k1_lattice2 @ v6_group_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(804,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m3_lattice4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(5494,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m3_lattice4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(876,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattices) ).
thf(5789,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( D @ ( B @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( D @ ( B @ ( A @ k4_lattices ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(659,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r1_lattice2 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r1_lattice2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_filter_2) ).
thf(4784,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r1_lattice2 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r1_lattice2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(2866,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(561,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattices) ).
thf(4161,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k1_lattices ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(948,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ ( A @ k5_filter_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
thf(6119,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ ( A @ k5_filter_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(3637,plain,
sk256 @ v4_lattices,
inference(cnfConj,[status(thm)],[3632]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_0 ) @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(6141,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_0 ) @ m1_filter_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(4189,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(863,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( A @ ( B @ v1_filter_0 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_0) ).
thf(5732,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) )
=> ( A @ ( B @ v1_filter_0 ) ) )
& ( ( A @ ( B @ v1_filter_0 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_filter_0 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( B = C )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(514,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ r1_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattices) ).
thf(3933,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ r1_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(3553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(758,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_0) ).
thf(5293,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( D @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
& ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(612,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ k1_filter_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_0) ).
thf(4459,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
& ( A @ l3_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ( ( B @ ( A @ k3_filter_0 ) )
= ( A @ k1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(469,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(3721,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(4174,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(6713,plain,
( ( ( sk353 @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2487,4929]) ).
thf(6714,plain,
( ( sk353 @ v1_xboole_0 )
!= ( sk141 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6713]) ).
thf(6722,plain,
sk353 != sk141,
inference(simp,[status(thm)],[6714]) ).
thf(391,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v3_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_binop_1) ).
thf(3296,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( A @ ( B @ v3_binop_1 ) ) )
& ( ( A @ ( B @ v3_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(940,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k2_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_0) ).
thf(6094,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k2_filter_0 ) )
= ( A @ u1_struct_0 ) )
& ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(689,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) )
= ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_lattice2) ).
thf(4940,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) )
= ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(823,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_lattices ) @ ( A @ k7_lattices ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattices) ).
thf(5574,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_lattices ) @ ( A @ k7_lattices ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).
thf(1912,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m1_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(904,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_lattice4 ) )
= ( A @ k7_grcat_1 @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_setwiseo ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_lattice4) ).
thf(5911,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_lattice4 ) )
= ( A @ k7_grcat_1 @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_setwiseo ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v3_struct_0 )
<=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
thf(3575,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( ( A @ u1_struct_0 @ v1_xboole_0 )
=> ( A @ v3_struct_0 ) )
& ( ( A @ v3_struct_0 )
=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1014,plain,
sk1 @ v17_lattices,
inference(cnfConj,[status(thm)],[1003]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(1870,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(460,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(3669,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(30458,plain,
$false,
inference(e,[status(thm)],[1633,4262,3399,3666,2876,3477,4852,2499,1083,6121,5999,3927,6042,8887,6014,6374,5810,5437,5509,1036,2822,2094,5365,3883,5116,5088,10166,1168,4571,4005,5857,23595,5593,2031,3798,1105,2280,4904,5454,9163,4311,3813,6219,5242,3912,5224,8928,4592,1041,1173,1855,4043,3534,3990,6063,4714,4037,1158,2512,4376,3072,1005,11043,23846,1068,2908,5842,11090,10912,4391,9045,1401,2953,23825,3460,1422,2947,1569,1939,23810,5173,6338,4711,4603,3012,2837,1142,23601,5265,5383,10463,1305,9818,3120,5589,5316,3781,6078,4058,4435,2146,3848,1497,1078,1788,6278,5814,3794,1608,4575,5906,6246,3367,3648,4097,4011,17988,4884,3365,3044,5288,11058,1867,2184,4638,6416,1872,1233,4279,5674,3253,6241,1761,5161,1640,23821,10170,5782,6336,5708,11055,3895,5192,4762,1458,3370,4343,5301,2082,8911,6138,4047,6236,4792,1835,2046,2972,3634,1243,5486,4371,4266,4618,3777,6009,5921,1935,4803,1650,7326,1921,5056,4137,1724,2173,4607,26434,2516,4760,4963,2819,3880,3878,2136,5750,7043,4467,1228,1623,1482,10501,7993,4249,5797,5342,1887,4386,2957,6707,3221,4563,6034,4070,3046,2269,6723,3821,1907,2274,3820,3891,2654,3248,1055,5953,4348,11068,2698,3131,4956,4224,3574,4654,3617,1330,4334,1323,3612,3148,11178,12065,6315,4349,3280,5160,1577,3845,2562,5640,2488,1832,1191,6332,11051,5706,4568,23817,8022,2466,5108,4766,1462,1059,1132,6208,2745,3713,5461,4243,11040,2691,3638,1147,4358,1479,3084,4383,1362,3557,4669,3374,9800,4788,4353,11463,4179,6310,2373,3919,1013,4270,6365,1115,4675,3312,3657,4368,2520,2730,4390,4471,4771,3231,4302,2388,3866,1100,11495,4253,4008,3258,6364,10497,10025,3788,4595,5792,5787,5663,4258,4001,6176,2925,4798,1183,1489,4205,3887,2324,26571,4583,11064,3199,5888,4443,12069,4578,3075,5027,3393,9832,4600,2782,1109,2893,3702,6189,2880,4847,1858,1864,3438,6187,5914,5032,5156,1151,10786,1020,3357,3569,2540,4871,4115,23839,5457,2777,3152,1051,6204,11036,2964,5379,6110,1886,6327,2718,6210,10029,1843,5929,4718,1169,10799,4660,2437,1928,1377,5448,10145,5643,2190,5772,2523,4087,6347,2371,4364,1119,23814,1394,5246,5846,7194,4924,3361,23570,2242,2286,23829,25144,2103,1405,3226,4643,1600,5137,1104,4892,3906,4588,6474,3378,23845,3503,4531,9797,2047,2641,9048,3435,7197,2922,3011,1206,4604,2204,3303,5530,4589,4629,2574,4888,5411,4480,6047,1199,3635,2364,1153,5697,5545,26414,9164,4076,4370,1311,5862,2232,4576,3054,5540,2083,1067,26428,2496,2905,1868,7999,4999,2000,1047,1730,1057,1163,2409,6343,5611,3827,1042,1355,4375,1666,3884,4449,3889,1274,5206,23828,5049,3735,2733,5670,2805,3867,5002,1123,25594,4989,5044,1751,4252,5956,3742,4344,4521,3239,5754,4284,6107,3816,1619,5893,3814,5396,3471,1883,4295,4280,4585,2565,4385,6708,5534,6143,2179,2211,1106,1032,5937,3269,5983,4140,5465,6163,4155,3314,3499,3065,27188,3349,1159,4746,1656,12849,6060,1079,1027,4740,6168,11042,1128,2492,3727,5729,8031,3595,1012,4316,5285,2840,3862,5615,4636,23837,4883,3650,6148,4123,2245,1936,5189,5626,23832,2300,3909,3782,5904,1983,6324,5714,5053,2515,1851,12404,2990,23822,2801,5238,1017,11056,4248,6133,1064,1111,5577,12063,3218,4048,1856,2694,8931,1425,1096,8014,5362,5583,4930,1719,5919,5978,2858,2537,3119,5373,7222,1118,8916,18039,10678,4219,11877,3018,25879,4333,3775,8017,5496,6116,23850,4406,5865,1039,3573,1028,2023,10946,10708,5818,1942,4276,6720,1182,3094,4425,3596,26954,4389,2080,5337,11046,3032,1937,1810,1791,2551,1016,3671,3723,3643,23599,10487,1155,1744,11248,3935,10720,4846,5149,10026,2851,5683,2862,2766,4953,2272,3201,1825,2504,1114,5947,3654,1099,5726,4384,6097,3787,1530,1456,3059,2487,23818,4068,1231,1131,3743,2505,3819,10148,6239,2566,5058,4717,1002,2813,4347,3628,1874,23833,3115,5305,11061,4259,3109,1979,4689,4069,2370,5479,3802,4352,14008,3856,1563,1170,5434,1071,11065,2221,5126,4004,2909,26307,1333,11031,3755,1857,5557,5747,5112,2749,1991,3834,2546,2761,4567,4081,2883,27268,3592,1054,3999,2368,4906,3639,2915,23823,3508,1895,5513,2995,5909,3841,2617,1732,4572,23813,4921,10703,6026,4354,2033,3042,5230,4256,4359,9049,4365,3396,5598,2260,12628,2144,6192,1251,5483,3130,5722,5524,4470,11033,4685,4594,12813,5451,9821,3890,5508,3491,13135,6243,4393,6001,5608,4797,2028,1301,3839,3523,4503,4577,11063,5647,4017,5698,2225,5065,2489,10700,6344,1154,4943,3547,4662,4341,4268,2727,3636,2048,4283,13972,3811,5395,2791,23812,4309,3758,5940,23827,2016,2514,1388,4801,4605,5099,5876,1795,3590,4328,3604,4381,4590,3868,2817,4758,26804,3599,4251,3796,5427,3118,2326,2293,3646,5282,1092,3579,6261,5580,3532,4796,1271,13730,12067,4645,11060,23593,1058,6302,4573,5086,3340,3594,3700,5703,5449,7465,1897,3641,4273,6248,6334,5997,9803,5784,1464,2474,11053,5432,11038,4433,1356,2510,4716,2361,3101,4337,4929,3631,5848,4586,6196,4509,2119,5071,5671,23848,4498,3251,4369,2229,3815,2084,9161,6179,4305,1117,10675,23816,3779,2906,1048,6112,1349,5303,9047,1933,23831,6321,5222,1144,4958,5407,2945,4073,1043,6289,3138,4176,6154,1122,4300,5381,2378,5795,4374,12064,5267,1307,2065,6216,4388,2182,5816,4569,2446,4208,3006,4296,7066,5563,4203,5035,5202,3747,5730,10810,4833,2780,11073,5335,1909,4897,1162,6414,4332,3192,5392,3614,2874,5318,6080,1460,6044,11095,5459,5838,1061,5780,2710,2911,1112,2578,1171,2365,5931,23834,5377,4373,1176,2931,1435,1102,4890,2506,10147,2418,10793,5340,6345,11041,1044,1245,5218,3917,9841,3159,2369,4362,1015,3953,3241,1477,6100,3142,5299,6325,3876,8922,10499,4158,5548,5424,3193,1166,1208,11062,4598,4879,2449,2629,6170,4581,1181,4168,5414,2005,1413,5812,1076,3881,5661,5463,3009,2914,1583,4690,5538,5587,1662,4394,4260,6185,4580,12368,2271,5757,9826,2037,4688,1145,1018,23819,4113,2564,4355,5763,6719,4336,4255,5452,3640,1647,3659,4200,3129,4469,4377,4593,6012,2942,6069,3391,5716,3737,7087,1961,4035,6472,1025,5602,1070,3112,1225,4272,5399,4366,8890,1566,1753,1267,2882,5018,7228,10027,2831,6146,1711,3448,23597,1038,3344,10144,13634,5001,5767,6280,24749,3642,4346,2092,12071,4092,1790,1987,2224,3818,3885,1637,3334,1188,1186,5015,4020,13694,4222,1869,3823,5560,5995,3127,4351,3544,2322,6313,1085,5543,4800,4982,3564,11049,4737,2044,5638,1579,1218,5450,3853,5277,5062,4164,2354,4802,3970,1802,3388,3024,2939,13076,4257,4111,4392,10714,8893,23826,6188,3488,6415,5223,1141,4133,2543,4246,5240,5504,2145,1485,1972,1052,6213,10028,4143,3224,4046,4932,1094,5226,3117,1008,6161,4795,3520,5596,7089,1084,25045,2885,1949,1157,6137,2347,4185,6284,3168,3284,6706,4278,9046,5873,5490,5981,16277,4606,4727,5917,8028,4587,4945,1180,5536,1817,6721,3171,2960,5510,10796,5934,4780,1126,4078,3725,5308,2997,4006,2110,1010,1575,3056,2226,5860,5332,1866,2658,3929,1734,5184,1108,23811,20126,4574,3797,11076,4913,1721,2273,5724,2853,2406,2554,1062,7996,1854,2764,4881,11091,4900,25823,13959,10169,3709,4250,1101,7219,4495,2130,3662,4527,2416,3780,4261,9160,4451,5600,3978,4293,3879,4591,4387,1077,2183,6166,11071,5128,6198,2421,4182,5828,1030,2956,3694,2786,4602,4197,3324,6305,5532,2912,2399,3598,5040,8721,2230,5672,10167,4570,5196,4372,2623,9162,1994,4927,21312,3860,2983,8908,1380,4357,3992,2003,2142,2123,2218,4125,2258,1133,5852,2374,11131,7216,2302,2517,4794,6326,5728,3705,4014,4472,10681,2534,2255,4356,23820,4254,1097,4596,3892,6131,3882,5232,2951,4523,4843,1876,2815,23835,2736,2008,4841,1527,3337,5371,5527,2050,4579,4885,4367,5760,5926,3062,5700,1859,2800,1314,4968,1056,1197,11067,4865,1065,1165,2549,3822,3145,11082,17937,2201,4565,5159,4350,4895,3347,6114,10168,4210,5290,4024,3716,2572,2366,6287,3196,3426,3633,5215,3506,10485,5200,5110,5440,2651,5803,11050,4118,6373,13171,5623,3886,1120,5473,1093,1930,5275,2502,5945,6190,2127,4848,1352,23830,5204,1829,1977,1152,5668,3057,4799,2898,2485,3772,21277,4506,6473,4066,3817,3965,2507,6082,7088,10146,4330,3939,5891,3740,1004,1885,6222,5645,4345,4501,1399,4271,3013,3474,1320,4723,1184,8741,5261,1848,5255,6072,11048,1917,1204,4335,9838,5943,5029,6173,10723,4642,10813,4627,4584,5312,5494,5789,4784,2866,4161,6119,3637,6141,4189,5732,3933,3553,5293,4459,3721,4174,6722,3296,6094,4940,5574,1912,5911,3575,1014,1870,3669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT296+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n009.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 20:34:14 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.58/1.74 % [INFO] Parsing done (737ms).
% 3.58/1.75 % [INFO] Running in sequential loop mode.
% 4.81/2.14 % [INFO] eprover registered as external prover.
% 4.81/2.15 % [INFO] Scanning for conjecture ...
% 5.71/2.48 % [INFO] Found a conjecture (or negated_conjecture) and 2927 axioms. Running axiom selection ...
% 8.55/3.31 % [INFO] Axiom selection finished. Selected 999 axioms (removed 1928 axioms).
% 11.11/4.11 % [INFO] Problem is first-order (TPTP FOF).
% 11.45/4.18 % [INFO] Type checking passed.
% 11.45/4.19 % [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 ...
% 124.41/30.81 % External prover 'e' found a proof!
% 124.41/30.81 % [INFO] Killing All external provers ...
% 124.41/30.81 % Time passed: 30273ms (effective reasoning time: 29053ms)
% 124.41/30.81 % 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)>
% 124.41/30.82 % Axioms used in derivation (999): t31_lattice2, dt_k4_filter_2, t45_lattice4, t2_filter_0, t21_zfmisc_1, t11_filter_2, t13_relset_1, dt_k7_filter_0, d13_filter_0, rc1_lattice2, d1_lattices, t119_funct_2, t66_nat_lat, t7_filter_0, t158_relat_1, t17_lattice4, rc5_lattices, t1_filter_2, dt_k9_filter_2, t50_lattice4, redefinition_m2_relset_1, fraenkel_a_1_0_domain_1, t51_partfun1, t24_filter_0, fc1_lattices, t10_lattice2, fraenkel_a_3_2_domain_1, d12_nat_lat, cc5_lattice2, t31_filter_0, t37_lattice2, t78_filter_0, t43_lattice2, dt_m1_lattice4, fc1_zfmisc_1, t35_subset_1, t135_zfmisc_1, t25_relset_1, t30_relat_1, d4_funct_1, t53_subset_1, t20_lattice4, t39_lattices, t76_lattice2, d10_lattices, t20_zfmisc_1, d1_tarski, dt_k2_lattice2, d20_binop_1, t66_funct_2, t62_filter_0, t66_partfun1, dt_k1_filter_2, t80_filter_0, d6_filter_0, d5_relat_1, t109_xboole_1, redefinition_k16_filter_2, t25_lattice2, d10_binop_1, t10_filter_2, t36_lattice4, t29_filter_0, fc2_filter_0, t81_filter_0, t24_lattice4, d13_lattices, cc3_lattice2, d14_binop_1, dt_k9_domain_1, d6_lattice2, t7_subset_1, t30_lattice2, t32_funct_2, d11_binop_1, t2_realset1, t3_xboole_1, d4_lattice4, t3_realset1, d3_subset_1, fc1_xboole_0, rc12_lattices, dt_k7_domain_1, t34_xboole_1, t29_lattice2, d1_lattice2, t56_partfun1, t59_partfun1, s12_funct_2, t43_lattices, s3_funct_2, t42_filter_0, cc6_lattices, t57_lattice2, t33_lattice2, t16_funct_2, d16_lattices, t113_zfmisc_1, t67_lattice2, t7_lattice2, t48_domain_1, t111_zfmisc_1, dt_k2_subset_1, t8_subset_1, t80_lattice2, t9_filter_2, existence_l1_lattices, t32_lattice4, d5_tarski, t15_funct_1, dt_k11_domain_1, t26_lattices, fc4_relat_1, t19_lattices, t4_ordinal1, t1_subset, dt_k1_lattice4, t147_relat_1, t10_partfun1, t47_lattice2, d5_xboole_0, t4_lattice4, t9_lattice2, fc4_subset_1, t168_funct_2, t10_relset_1, dt_k15_filter_2, fc3_relat_1, d8_funct_1, t69_filter_0, t144_relat_1, t57_domain_1, existence_l3_lattices, dt_k6_nat_lat, t53_lattices, t70_nat_lat, fc1_numbers, dt_k3_funct_2, dt_k5_lattices, t7_funct_2, t87_filter_0, fc4_lattice2, t42_zfmisc_1, t21_lattice2, t14_binop_1, dt_k1_subset_1, t19_relat_1, dt_k16_filter_2, t28_binop_1, dt_k1_nat_lat, dt_k13_domain_1, fc1_lattice2, dt_g2_struct_0, t72_lattice2, t117_zfmisc_1, free_g1_lattices, dt_k4_subset_1, t83_filter_0, t35_lattice4, t23_filter_0, redefinition_k12_filter_2, t16_lattice4, abstractness_v2_struct_0, t46_lattice4, dt_m2_nat_lat, d7_binop_1, existence_m3_lattice4, existence_m1_struct_0, dt_k3_lattice4, t35_zfmisc_1, t18_filter_0, rc2_struct_0, dt_k1_lattice2, t32_relat_1, dt_m1_nat_lat, t62_nat_lat, t65_partfun1, t44_funct_2, fraenkel_a_2_0_lattice4, t117_funct_1, d10_filter_0, cc4_lattice2, dt_k1_struct_0, t26_lattice4, cc2_lattice2, t85_filter_0, dt_m1_realset1, t110_zfmisc_1, t103_zfmisc_1, dt_k19_filter_2, dt_u2_struct_0, t63_partfun1, t15_relset_1, t29_numbers, t14_filter_0, fraenkel_a_2_0_filter_0, rc2_partfun1, t18_relat_1, rc3_funct_1, fc1_filter_0, t48_filter_0, d9_lattice4, t49_funct_2, t41_lattice2, fraenkel_a_3_3_domain_1, t50_funct_2, t70_zfmisc_1, t69_zfmisc_1, cc4_lattices, redefinition_k11_filter_0, dt_k5_filter_0, dt_k3_filter_0, t52_nat_lat, d1_struct_0, t27_zfmisc_1, t37_xboole_1, t17_funct_1, t61_nat_lat, t41_zfmisc_1, fc2_lattice2, dt_m2_relset_1, cc1_relat_1, dt_k7_funct_2, redefinition_k2_funct_2, dt_k5_filter_2, t59_lattice2, dt_k12_nat_lat, t70_partfun1, fc3_lattice2, t26_filter_0, t56_relat_1, t83_lattice2, t2_funct_1, t36_subset_1, t29_partfun1, t33_lattice4, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, t32_filter_0, commutativity_k7_domain_1, t46_lattice2, free_g2_lattices, fraenkel_a_2_0_domain_1, d2_tarski, dt_k2_binop_1, involutiveness_k3_subset_1, rc1_funct_1, t53_filter_0, d5_lattices, t17_binop_1, t25_funct_2, t15_binop_1, dt_m2_realset1, redefinition_k13_filter_2, redefinition_k6_filter_0, dt_k1_filter_0, dt_k6_filter_2, t115_zfmisc_1, t66_lattice2, t62_funct_1, t65_funct_2, t69_nat_lat, t19_funct_1, dt_m2_lattice4, d11_filter_0, t31_lattices, s13_funct_2, fraenkel_a_2_2_domain_1, t129_zfmisc_1, d4_subset_1, t2_binop_1, t31_relat_1, t63_nat_lat, d6_binop_1, dt_m1_filter_2, t27_lattices, t64_funct_2, reflexivity_r3_lattices, d1_xboole_0, rc8_lattices, d9_lattices, t56_filter_0, t72_filter_0, fraenkel_a_3_0_filter_0, t130_zfmisc_1, t3_filter_2, t175_partfun1, t15_relat_1, t48_funct_2, fraenkel_a_3_7_domain_1, d16_lattice4, t70_filter_0, t46_filter_0, t40_lattice2, t64_relat_1, t138_zfmisc_1, t25_subset_1, t37_filter_0, rc11_lattices, rc3_lattices, t52_filter_0, t108_zfmisc_1, t165_funct_2, t57_filter_0, dt_l1_lattices, dt_k12_filter_2, dt_k4_lattice4, t60_partfun1, existence_m1_realset1, dt_k11_filter_2, t31_partfun1, dt_k7_lattices, dt_k2_nat_lat, t3_funct_2, rc2_subset_1, existence_l2_lattices, t27_relset_1, t52_domain_1, t118_zfmisc_1, t55_partfun1, t8_funct_2, rc2_lattices, s4_subset_1, t118_funct_2, t29_lattice4, t76_nat_lat, t14_relset_1, t39_lattice4, t16_relset_1, t38_lattice4, d13_relat_1, t28_lattice2, t164_funct_2, d15_lattice4, fc2_funct_2, t6_boole, t12_funct_1, dt_k6_subset_1, t10_relat_1, d1_relat_1, t59_filter_0, t1_xboole_1, redefinition_k12_filter_0, dt_k4_nat_lat, cc6_lattice2, t64_partfun1, t47_lattice4, existence_l2_struct_0, t32_lattices, t34_filter_0, t5_lattice4, t19_filter_0, t44_lattice4, t49_filter_0, t5_subset, redefinition_m1_nat_lat, t26_relset_1, t29_relat_1, d14_lattice4, t77_funct_2, t59_domain_1, t22_lattices, t32_partfun1, d6_tarski, t4_relat_1, t26_binop_1, t28_subset_1, d12_lattices, d17_lattice4, fc3_subset_1, t128_zfmisc_1, t39_partfun1, t75_zfmisc_1, redefinition_k4_filter_2, t8_lattice4, rc1_filter_0, d2_realset1, d16_nat_lat, dt_g2_lattices, fc2_subset_1, t45_funct_2, t25_zfmisc_1, d4_relat_1, d7_lattices, t6_lattice2, t23_binop_1, t150_relat_1, existence_m1_relset_1, t1_zfmisc_1, dt_m2_filter_2, t50_lattices, s8_domain_1, dt_l3_lattices, t48_lattice2, rc1_lattices, t79_zfmisc_1, t12_lattice2, t5_funct_2, dt_k8_funct_2, d12_lattice4, t167_funct_2, dt_m1_struct_0, t17_lattices, t11_funct_2, abstractness_v2_lattices, d13_nat_lat, t40_funct_2, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t40_filter_0, t24_binop_1, dt_k3_nat_lat, t27_lattice4, t75_lattice2, t4_filter_0, t89_filter_0, dt_l2_lattices, redefinition_k7_domain_1, t72_partfun1, t8_funct_1, t2_tarski, t16_funct_1, t28_zfmisc_1, t72_zfmisc_1, t82_funct_2, dt_k4_filter_0, t33_xboole_1, s9_domain_1, t84_lattice2, t47_lattices, d20_lattices, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t38_filter_0, d3_lattices, t23_zfmisc_1, t34_lattice4, cc5_lattices, t4_subset, t38_subset_1, d18_lattices, t169_funct_2, t44_lattices, dt_k2_funct_1, cc1_funct_2, d8_filter_0, t32_xboole_1, t56_lattice2, t52_subset_1, t60_filter_0, t5_ordinal1, rc13_lattices, t4_boole, t71_lattice2, d2_funct_2, t22_lattice2, t8_filter_2, t70_lattice2, dt_k8_domain_1, dt_k17_filter_2, t15_lattice4, t74_zfmisc_1, t39_subset_1, t64_nat_lat, dt_k8_filter_0, t14_funct_1, t5_filter_2, t9_zfmisc_1, d7_filter_0, existence_m2_realset1, existence_m3_realset1, t56_subset_1, dt_k1_domain_1, t17_funct_2, redefinition_k14_filter_2, t75_filter_0, t13_lattice2, fc1_realset1, t45_lattices, t49_lattice4, t51_funct_2, d12_binop_1, t21_lattices, t12_zfmisc_1, t85_lattice2, rc4_lattices, d2_lattice4, t38_lattice2, rc7_lattices, t132_funct_2, t139_zfmisc_1, t16_lattice2, cc1_funct_1, t4_funct_2, redefinition_k1_filter_2, d10_lattice4, s11_funct_2, d3_relat_2, s2_domain_1, rc3_struct_0, t3_ordinal1, t9_domain_1, t25_lattices, t7_boole, dt_k14_filter_2, dt_k5_lattice4, t11_binop_1, t55_filter_0, t143_relat_1, d2_subset_1, t27_lattice2, commutativity_k4_lattices, redefinition_k9_filter_2, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, rc2_lattice2, commutativity_k2_struct_0, t7_filter_2, dt_k6_domain_1, t157_funct_1, t31_lattice4, fc5_lattice2, d17_lattices, dt_k2_partfun1, dt_k11_nat_lat, rc2_funct_1, t158_funct_2, t90_filter_0, redefinition_k15_filter_2, t4_subset_1, redefinition_k1_domain_1, rc1_funct_2, t26_zfmisc_1, t6_filter_2, t69_partfun1, t7_ordinal1, dt_k10_filter_2, t9_funct_2, t31_funct_2, rc1_subset_1, d8_nat_lat, dt_k9_filter_0, t48_lattice4, t68_filter_0, fc6_lattice2, t8_lattice2, t18_lattices, cc1_lattices, t5_filter_0, t64_zfmisc_1, fc5_relat_1, dt_k3_lattice2, t30_filter_0, t40_lattice4, redefinition_r3_lattices, t40_lattices, t65_funct_1, t4_filter_2, t113_funct_2, t71_partfun1, d21_lattices, t41_lattices, t159_funct_2, t116_zfmisc_1, d4_lattices, existence_m1_filter_0, t2_lattice2, redefinition_m1_filter_2, dt_k2_struct_0, t49_lattices, t14_funct_2, t27_binop_1, t48_lattices, dt_k2_lattice4, t9_filter_0, fc1_nat_lat, fraenkel_a_3_1_domain_1, t60_funct_2, t7_lattice4, cc2_funct_1, t5_realset1, cc1_relset_1, s4_funct_2, t41_lattice4, rc9_lattices, dt_k7_filter_2, d2_zfmisc_1, t48_nat_lat, t56_nat_lat, cc1_filter_0, t169_partfun1, fraenkel_a_2_1_lattice4, t26_lattice2, dt_k24_filter_2, t17_lattice2, t18_funct_1, d3_lattice2, t4_relset_1, t10_filter_0, t31_subset_1, t2_filter_2, t3_subset, t25_binop_1, d2_binop_1, d6_lattice4, t30_lattice4, s1_domain_1, t12_filter_0, t124_funct_1, t50_lattice2, t55_subset_1, t79_funct_2, dt_u1_lattices, fraenkel_a_2_1_domain_1, existence_m1_subset_1, t22_lattice4, existence_m1_filter_2, commutativity_k2_tarski, t3_relat_1, t22_filter_0, t24_relat_1, t8_relset_1, t106_zfmisc_1, t125_zfmisc_1, t73_filter_0, t11_relset_1, t155_relat_1, t19_numbers, t44_filter_0, t118_funct_1, t19_lattice2, t146_relat_1, existence_m2_subset_1, t35_xboole_1, t49_domain_1, d17_binop_1, dt_k2_filter_0, dt_k2_funct_2, d2_filter_0, rc1_nat_lat, t65_nat_lat, t15_subset_1, t5_lattice2, free_g2_struct_0, dt_k20_filter_2, t17_relset_1, d15_nat_lat, d9_binop_1, cc3_lattices, d5_subset_1, t99_partfun1, t107_zfmisc_1, t9_realset1, t121_funct_2, t114_zfmisc_1, dt_k23_filter_2, t58_partfun1, d1_zfmisc_1, t27_filter_0, t11_lattice4, rc2_relat_1, t36_lattice2, existence_m2_relset_1, d4_binop_1, t64_filter_0, t38_zfmisc_1, t75_nat_lat, t9_lattice4, t69_enumset1, t82_lattice2, t22_zfmisc_1, d1_filter_0, redefinition_k7_filter_0, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, fc2_lattices, t62_lattice2, t39_filter_0, t74_lattice2, t11_filter_0, existence_m2_lattice4, t23_lattice4, d4_lattice2, t116_funct_2, fraenkel_a_3_6_domain_1, t168_partfun1, s14_funct_2, t51_filter_0, t14_lattice4, t37_lattice4, redefinition_k2_binop_1, t74_filter_0, t65_lattice2, d5_filter_0, t60_nat_lat, t61_lattice2, t6_funct_2, redefinition_k24_filter_2, t44_lattice2, t41_subset_1, fc3_nat_lat, d3_lattice4, t157_relat_1, cc3_finsub_1, t51_subset_1, t21_subset_1, existence_m1_lattice4, t36_zfmisc_1, d4_filter_0, reflexivity_r1_filter_2, t45_lattice2, t8_realset1, dt_m3_lattice4, d3_tarski, cc6_funct_2, redefinition_k1_struct_0, t25_lattice4, d8_realset1, rc1_relat_1, t54_funct_1, t40_subset_1, t17_subset_1, t6_relset_1, d1_relset_1, redefinition_k11_filter_2, fc1_struct_0, t52_lattice2, t18_binop_1, redefinition_k3_lattices, t78_lattice2, fraenkel_a_3_1_filter_0, t39_zfmisc_1, d1_realset1, d15_lattices, t131_funct_2, dt_k22_filter_2, t119_zfmisc_1, dt_k4_lattices, t60_relat_1, rc1_lattice4, t77_lattice2, fraenkel_a_3_4_domain_1, t24_lattice2, t19_lattice4, reflexivity_r1_tarski, t9_funct_1, t6_zfmisc_1, t18_funct_2, dt_l2_struct_0, t52_lattices, t1_realset1, t2_xboole_1, t35_lattice2, t57_partfun1, t9_mcart_1, t34_funct_2, t67_filter_0, symmetry_r1_filter_2, t27_finsub_1, redefinition_m1_struct_0, t10_subset_1, t41_filter_0, existence_m2_nat_lat, d12_funct_1, d2_lattices, t9_relset_1, dt_g3_lattices, fc6_relat_1, d15_binop_1, rc6_lattices, free_g3_lattices, t77_filter_0, cc7_lattices, d14_lattices, dt_k10_filter_0, t54_lattice2, t21_lattice4, t36_xboole_1, dt_k8_subset_1, dt_k3_filter_2, d7_lattice4, existence_m1_nat_lat, t58_filter_0, redefinition_k2_filter_2, d4_xboole_0, t47_filter_0, t39_lattice2, t20_relat_1, dt_k1_lattices, t73_zfmisc_1, t69_lattice2, dt_k12_domain_1, d14_nat_lat, t18_lattice4, d5_binop_1, t54_subset_1, t123_funct_1, t29_lattices, t88_filter_0, d1_relat_2, t82_filter_0, redefinition_k2_struct_0, t54_filter_0, t15_filter_0, dt_k2_filter_2, t68_zfmisc_1, dt_m2_subset_1, dt_k5_numbers, t12_funct_2, d16_binop_1, t20_filter_0, t28_finsub_1, t32_lattice2, d8_binop_1, abstractness_v3_lattices, t26_finsub_1, t51_lattice2, t136_zfmisc_1, t8_boole, rc1_xboole_0, t24_partfun1, redefinition_k8_funct_2, t34_zfmisc_1, t80_zfmisc_1, t5_relat_1, t24_zfmisc_1, t55_lattice2, t120_funct_2, t59_funct_2, fc7_relat_1, t60_funct_1, dt_k5_nat_lat, t37_zfmisc_1, t23_finsub_1, t30_finsub_1, dt_k21_filter_2, fc8_relat_1, t10_realset1, dt_k3_binop_1, rc5_struct_0, t23_relat_1, t10_zfmisc_1, t2_subset, redefinition_k21_filter_2, d9_filter_0, t38_funct_2, t33_partfun1, t34_finsub_1, d3_relat_1, t85_funct_2, t65_relat_1, t21_relat_1, dt_k6_filter_0, t156_relat_1, t109_zfmisc_1, fraenkel_a_2_3_domain_1, t60_domain_1, t152_relat_1, dt_k6_lattices, t134_zfmisc_1, d3_nat_lat, t25_partfun1, dt_m1_filter_0, d18_binop_1, redefinition_k10_filter_2, t115_funct_2, d6_lattices, t9_tarski, t51_lattices, commutativity_k3_lattices, t149_relat_1, d13_lattice4, t32_finsub_1, t48_subset_1, d1_lattice4, d8_lattices, t28_relat_1, d1_funct_1, d1_filter_2, t81_lattice2, t34_lattices, d12_filter_0, t42_lattice4, t50_subset_1, t65_filter_0, d10_xboole_0, d2_lattice2, dt_k10_nat_lat, fc2_realset1, t68_nat_lat, t34_lattice2, dt_k2_lattices, d19_lattices, t67_partfun1, t3_boole, t49_nat_lat, dt_u2_lattices, d8_relat_2, t25_relat_1, dt_k8_filter_2, t13_binop_1, t53_lattice2, existence_l1_struct_0, abstractness_v1_lattices, t45_filter_0, t49_subset_1, t7_tarski, rc1_partfun1, t71_filter_0, redefinition_r1_filter_2, t28_lattice4, t79_lattice2, d5_funct_1, t6_ordinal1, dt_k18_filter_2, redefinition_k6_subset_1, rc10_lattices, t12_relset_1, cc1_lattice2, cc5_funct_2, fc1_lattice4, redefinition_m2_subset_1, t60_lattice2, t50_filter_0, t43_lattice4, dt_g1_lattices, dt_k7_nat_lat, t58_lattice2, d3_filter_0, d1_binop_1, rc2_xboole_0, fraenkel_a_3_5_domain_1, s7_domain_1, dt_m3_realset1, dt_k13_nat_lat, t30_zfmisc_1, rc4_struct_0, dt_k10_domain_1, t49_lattice2, fraenkel_a_0_1_domain_1, t16_binop_1, t66_filter_0, t6_filter_0, redefinition_k3_filter_2, d13_binop_1, idempotence_k4_subset_1, t40_zfmisc_1, d11_lattices, t63_filter_0, t63_lattice2, t174_partfun1, t55_funct_2, t18_lattice2, t112_zfmisc_1, t73_lattice2, existence_m2_filter_2, d3_binop_1, d5_nat_lat, t6_lattice4, t14_lattice2, dt_k13_filter_2, d2_relat_1, dt_k3_lattices, t68_lattice2, d19_binop_1, cc2_lattices, redefinition_k4_lattices, t61_funct_2, fc3_lattices, dt_k3_subset_1, fraenkel_a_0_2_domain_1, fc1_funct_2, cc1_binop_1, t6_relat_1, t172_partfun1, t33_subset_1, t30_partfun1, t65_zfmisc_1, t63_subset_1, t112_partfun1, t13_filter_0, d4_nat_lat, t38_xboole_1, fraenkel_a_4_1_domain_1, t23_lattices, t3_filter_0, t10_lattice4, antisymmetry_r2_hidden, d5_lattice4, d8_lattice4, t67_nat_lat, t64_lattice2, t22_subset_1, redefinition_k6_domain_1
% 124.41/30.82 % No. of inferences in proof: 3206
% 124.41/30.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 30273 ms resp. 29053 ms w/o parsing
% 130.09/32.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 130.09/32.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------