%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT328+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 : n026.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 07:47:16 AM UTC 2026
% Result : Theorem 172.45s 49.04s
% Output : Refutation 178.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1083
% Syntax : Number of formulae : 3431 ( 637 unt; 0 typ; 67 def)
% Number of atoms : 19258 (3174 equ; 0 cnn)
% Maximal formula atoms : 58 ( 5 avg)
% Number of connectives : 64908 (5084 ~;2714 |;6916 &;44796 @)
% ( 240 <=>;5158 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 334 ( 331 usr; 79 con; 0-9 aty)
% Number of variables : 7970 ( 53 ^;7513 !; 337 ?;7970 :)
% ( 0 !>; 0 ?*; 0 @-; 67 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_decl,type,
v10_lattices: $i > $o ).
thf(l3_lattices_decl,type,
l3_lattices: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(r1_filter_2_decl,type,
r1_filter_2: $i > $i > $i > $o ).
thf(k22_filter_2_decl,type,
k22_filter_2: $i > $i > $i > $i ).
thf(k6_domain_1_decl,type,
k6_domain_1: $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(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $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(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(r6_binop_1_decl,type,
r6_binop_1: $i > $i > $i > $o ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $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(v1_xboole_0_decl,type,
v1_xboole_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(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(v3_binop_1_decl,type,
v3_binop_1: $i > $i > $o ).
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(r2_binop_1_decl,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k3_relat_1_decl,type,
k3_relat_1: $i > $i ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(r3_binop_1_decl,type,
r3_binop_1: $i > $i > $i > $o ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(v3_filter_0_decl,type,
v3_filter_0: $i > $o ).
thf(v4_lattices_decl,type,
v4_lattices: $i > $o ).
thf(v5_lattices_decl,type,
v5_lattices: $i > $o ).
thf(v6_lattices_decl,type,
v6_lattices: $i > $o ).
thf(v7_lattices_decl,type,
v7_lattices: $i > $o ).
thf(v8_lattices_decl,type,
v8_lattices: $i > $o ).
thf(v9_lattices_decl,type,
v9_lattices: $i > $o ).
thf(v11_lattices_decl,type,
v11_lattices: $i > $o ).
thf(v12_lattices_decl,type,
v12_lattices: $i > $o ).
thf(k1_lattice2_decl,type,
k1_lattice2: $i > $i ).
thf(v3_lattices_decl,type,
v3_lattices: $i > $o ).
thf(l2_lattices_decl,type,
l2_lattices: $i > $o ).
thf(u2_lattices_decl,type,
u2_lattices: $i > $i ).
thf(l1_lattices_decl,type,
l1_lattices: $i > $o ).
thf(u1_lattices_decl,type,
u1_lattices: $i > $i ).
thf(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $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(v6_group_1_decl,type,
v6_group_1: $i > $o ).
thf(v14_lattices_decl,type,
v14_lattices: $i > $o ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(v13_lattices_decl,type,
v13_lattices: $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(m1_filter_0_decl,type,
m1_filter_0: $i > $i > $o ).
thf(k8_filter_0_decl,type,
k8_filter_0: $i > $i > $i ).
thf(l2_struct_0_decl,type,
l2_struct_0: $i > $o ).
thf(v2_struct_0_decl,type,
v2_struct_0: $i > $o ).
thf(m2_lattice4_decl,type,
m2_lattice4: $i > $i > $o ).
thf(r1_lattice2_decl,type,
r1_lattice2: $i > $i > $i > $o ).
thf(k7_domain_1_decl,type,
k7_domain_1: $i > $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k5_finsub_1_decl,type,
k5_finsub_1: $i > $i ).
thf(v1_lattice2_decl,type,
v1_lattice2: $i > $o ).
thf(k13_nat_lat_decl,type,
k13_nat_lat: $i ).
thf(k3_binop_1_decl,type,
k3_binop_1: $i > $i > $i ).
thf(k2_subset_1_decl,type,
k2_subset_1: $i > $i ).
thf(m2_nat_lat_decl,type,
m2_nat_lat: $i > $i > $o ).
thf(a_2_2_domain_1_decl,type,
a_2_2_domain_1: $i > $i > $i ).
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(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(v15_lattices_decl,type,
v15_lattices: $i > $o ).
thf(v16_lattices_decl,type,
v16_lattices: $i > $o ).
thf(r7_binop_1_decl,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k6_nat_lat_decl,type,
k6_nat_lat: $i ).
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(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(m2_filter_2_decl,type,
m2_filter_2: $i > $i > $o ).
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(k2_lattices_decl,type,
k2_lattices: $i > $i > $i > $i ).
thf(r2_filter_2_decl,type,
r2_filter_2: $i > $i > $o ).
thf(v1_filter_0_decl,type,
v1_filter_0: $i > $i > $o ).
thf(k15_filter_2_decl,type,
k15_filter_2: $i > $i > $i ).
thf(k5_filter_0_decl,type,
k5_filter_0: $i > $i > $i > $i ).
thf(m1_lattice4_decl,type,
m1_lattice4: $i > $i > $i > $o ).
thf(v2_lattice4_decl,type,
v2_lattice4: $i > $i > $i > $o ).
thf(r2_lattice4_decl,type,
r2_lattice4: $i > $i > $i > $o ).
thf(v17_lattices_decl,type,
v17_lattices: $i > $o ).
thf(k17_filter_2_decl,type,
k17_filter_2: $i > $i ).
thf(v1_filter_2_decl,type,
v1_filter_2: $i > $i > $o ).
thf(r4_lattice4_decl,type,
r4_lattice4: $i > $i > $i > $o ).
thf(k4_lattices_decl,type,
k4_lattices: $i > $i > $i > $i ).
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(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(k5_lattices_decl,type,
k5_lattices: $i > $i ).
thf(k6_lattices_decl,type,
k6_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(k3_lattice2_decl,type,
k3_lattice2: $i > $i > $i > $i > $i ).
thf(k1_lattices_decl,type,
k1_lattices: $i > $i > $i > $i ).
thf(r1_lattices_decl,type,
r1_lattices: $i > $i > $i > $o ).
thf(k1_domain_1_decl,type,
k1_domain_1: $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(k13_filter_2_decl,type,
k13_filter_2: $i > $i > $i ).
thf(k3_filter_2_decl,type,
k3_filter_2: $i > $i > $i ).
thf(k7_filter_2_decl,type,
k7_filter_2: $i > $i > $i ).
thf(k19_filter_2_decl,type,
k19_filter_2: $i > $i > $i ).
thf(p1_s2_domain_1_decl,type,
p1_s2_domain_1: $i > $i > $o ).
thf(k5_lattice4_decl,type,
k5_lattice4: $i > $i ).
thf(k7_lattices_decl,type,
k7_lattices: $i > $i > $i ).
thf(k1_lattice4_decl,type,
k1_lattice4: $i > $i > $i ).
thf(k3_lattices_decl,type,
k3_lattices: $i > $i > $i > $i ).
thf(k7_filter_0_decl,type,
k7_filter_0: $i > $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(k8_setwiseo_decl,type,
k8_setwiseo: $i > $i > $i > $i > $i ).
thf(k16_filter_2_decl,type,
k16_filter_2: $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(u2_struct_0_decl,type,
u2_struct_0: $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(k2_lattice4_decl,type,
k2_lattice4: $i > $i > $i ).
thf(k14_filter_2_decl,type,
k14_filter_2: $i > $i > $i ).
thf(r2_lattices_decl,type,
r2_lattices: $i > $i > $i > $o ).
thf(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(r3_lattice4_decl,type,
r3_lattice4: $i > $i > $i > $o ).
thf(k11_filter_0_decl,type,
k11_filter_0: $i > $i > $i ).
thf(a_3_2_domain_1_decl,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(a_2_0_lattice4_decl,type,
a_2_0_lattice4: $i > $i > $i ).
thf(v1_lattice4_decl,type,
v1_lattice4: $i > $i > $i > $o ).
thf(m3_lattice4_decl,type,
m3_lattice4: $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(a_3_5_domain_1_decl,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(k18_filter_2_decl,type,
k18_filter_2: $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(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(v2_filter_0_decl,type,
v2_filter_0: $i > $i > $o ).
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(a_3_0_filter_0_decl,type,
a_3_0_filter_0: $i > $i > $i > $i ).
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(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(k7_funcop_1_decl,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k7_grcat_1_decl,type,
k7_grcat_1: $i > $i ).
thf(k8_domain_1_decl,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(k11_filter_2_decl,type,
k11_filter_2: $i > $i > $i ).
thf(k12_filter_0_decl,type,
k12_filter_0: $i > $i > $i ).
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(r1_filter_0_decl,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(v1_setwiseo_decl,type,
v1_setwiseo: $i > $i > $o ).
thf(a_2_0_filter_0_decl,type,
a_2_0_filter_0: $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(k5_filter_2_decl,type,
k5_filter_2: $i > $i > $i ).
thf(k6_filter_2_decl,type,
k6_filter_2: $i > $i > $i ).
thf(k2_filter_2_decl,type,
k2_filter_2: $i > $i > $i ).
thf(a_3_2_filter_2_decl,type,
a_3_2_filter_2: $i > $i > $i > $i ).
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(r1_filter_1_decl,type,
r1_filter_1: $i > $i > $o ).
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(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(a_2_0_filter_2_decl,type,
a_2_0_filter_2: $i > $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(a_3_0_filter_2_decl,type,
a_3_0_filter_2: $i > $i > $i > $i ).
thf(k23_filter_2_decl,type,
k23_filter_2: $i > $i > $i ).
thf(a_3_1_filter_2_decl,type,
a_3_1_filter_2: $i > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $o ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk25_decl,type,
sk25: $i > $i > $i ).
thf(sk71_decl,type,
sk71: $i ).
thf(sk80_decl,type,
sk80: $i > $i ).
thf(sk81_decl,type,
sk81: $i > $i > $i ).
thf(sk94_decl,type,
sk94: $i ).
thf(sk95_decl,type,
sk95: $i ).
thf(sk110_decl,type,
sk110: $i > $i > $i ).
thf(sk111_decl,type,
sk111: $i > $i > $i ).
thf(sk118_decl,type,
sk118: $i ).
thf(sk138_decl,type,
sk138: $i ).
thf(sk152_decl,type,
sk152: $i ).
thf(sk157_decl,type,
sk157: $i ).
thf(sk187_decl,type,
sk187: $i ).
thf(sk188_decl,type,
sk188: $i ).
thf(sk195_decl,type,
sk195: $i > $i ).
thf(sk196_decl,type,
sk196: $i ).
thf(sk197_decl,type,
sk197: $i ).
thf(sk207_decl,type,
sk207: $i ).
thf(sk216_decl,type,
sk216: $i ).
thf(sk218_decl,type,
sk218: $i ).
thf(sk234_decl,type,
sk234: $i > $i > $i > $o ).
thf(sk235_decl,type,
sk235: $i > $i > $i > $i ).
thf(sk236_decl,type,
sk236: $i > $i > $i > $i ).
thf(sk251_decl,type,
sk251: $i > $i ).
thf(sk279_decl,type,
sk279: $i ).
thf(sk296_decl,type,
sk296: $i ).
thf(sk300_decl,type,
sk300: $i ).
thf(sk315_decl,type,
sk315: $i ).
thf(sk317_decl,type,
sk317: $i ).
thf(sk332_decl,type,
sk332: $o ).
thf(sk333_decl,type,
sk333: $i ).
thf(sk334_decl,type,
sk334: $i ).
thf(sk340_decl,type,
sk340: $o ).
thf(sk341_decl,type,
sk341: $i ).
thf(sk342_decl,type,
sk342: $i ).
thf(sk344_decl,type,
sk344: $i ).
thf(sk347_decl,type,
sk347: $i ).
thf(sk348_decl,type,
sk348: $o ).
thf(sk349_decl,type,
sk349: $i ).
thf(sk350_decl,type,
sk350: $i ).
thf(sk352_decl,type,
sk352: $i > $i ).
thf(sk360_decl,type,
sk360: $i ).
thf(sk361_decl,type,
sk361: $i ).
thf(sk364_decl,type,
sk364: $i ).
thf(sk369_decl,type,
sk369: $i > $i > $i ).
thf(sk370_decl,type,
sk370: $i > $i > $i ).
thf(sk375_decl,type,
sk375: $o ).
thf(sk376_decl,type,
sk376: $i ).
thf(sk377_decl,type,
sk377: $i ).
thf(sk389_decl,type,
sk389: $i > $i ).
thf(sk407_decl,type,
sk407: $i ).
thf(sk421_decl,type,
sk421: $i ).
thf(sk446_decl,type,
sk446: $o ).
thf(sk447_decl,type,
sk447: $i ).
thf(sk448_decl,type,
sk448: $i ).
thf(sk456_decl,type,
sk456: $i ).
thf(sk469_decl,type,
sk469: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[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 @ k6_domain_1 ) @ ( B @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( A @ ( sk1 @ u1_struct_0 @ k6_domain_1 ) @ ( A @ ( A @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [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(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k1_binop_1 ) ) )
= D ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( A @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( E @ ( D @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk8 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [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(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( B @ ( A @ sk10 ) @ r2_hidden ) ) )
=> ( ( ( ( C @ ( A @ k1_funct_1 ) )
= ( B @ ( A @ sk10 ) ) )
=> ( ( B @ ( A @ sk10 ) @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( ( B @ ( A @ sk10 ) @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( B @ ( A @ sk10 ) ) ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( A @ k1_binop_1 ) ) )
= C ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ~ ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [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 ) ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= A )
& ( ( A @ sk18 @ k1_relat_1 )
= A ) )
=> ( ( A @ sk18 )
= B ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [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(sk71_def,definition,
( sk71
= ( @+[A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk80_def,definition,
( sk80
= ( ^ [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(sk81_def,definition,
( sk81
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( B @ sk80 @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk94_def,definition,
( sk94
= ( @+[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(sk95_def,definition,
( sk95
= ( @+[A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk110_def,definition,
( sk110
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).
thf(sk111_def,definition,
( sk111
= ( ^ [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(sk118_def,definition,
( sk118
= ( @+[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(sk138_def,definition,
( sk138
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk152_def,definition,
( sk152
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk157_def,definition,
( sk157
= ( @+[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(sk187_def,definition,
( sk187
= ( @+[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(sk188_def,definition,
( sk188
= ( @+[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(sk195_def,definition,
( sk195
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk196_def,definition,
( sk196
= ( @+[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(sk197_def,definition,
( sk197
= ( @+[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(sk207_def,definition,
( sk207
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk216_def,definition,
( sk216
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk218_def,definition,
( sk218
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk235_def,definition,
( sk235
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk236_def,definition,
( sk236
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ r2_hidden ) ) ) ) ) ).
thf(sk251_def,definition,
( sk251
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk279_def,definition,
( sk279
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk296_def,definition,
( sk296
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk300_def,definition,
( sk300
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk315_def,definition,
( sk315
= ( @+[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(sk317_def,definition,
( sk317
= ( @+[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(sk333_def,definition,
( sk333
= ( @+[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(sk334_def,definition,
( sk334
= ( @+[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(sk341_def,definition,
( sk341
= ( @+[A: $i] :
~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).
thf(sk342_def,definition,
( sk342
= ( @+[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(sk344_def,definition,
( sk344
= ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).
thf(sk347_def,definition,
( sk347
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk349_def,definition,
( sk349
= ( @+[A: $i] :
~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).
thf(sk350_def,definition,
( sk350
= ( @+[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(sk352_def,definition,
( sk352
= ( ^ [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(sk360_def,definition,
( sk360
= ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).
thf(sk361_def,definition,
( sk361
= ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).
thf(sk364_def,definition,
( sk364
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk369_def,definition,
( sk369
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
=> ( C = B ) ) ) ) ).
thf(sk370_def,definition,
( sk370
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk376_def,definition,
( sk376
= ( @+[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(sk377_def,definition,
( sk377
= ( @+[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(sk389_def,definition,
( sk389
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk407_def,definition,
( sk407
= ( @+[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(sk421_def,definition,
( sk421
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk447_def,definition,
( sk447
= ( @+[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(sk448_def,definition,
( sk448
= ( @+[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(sk456_def,definition,
( sk456
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk469_def,definition,
( sk469
= ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).
thf(85,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(1501,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)],[85]) ).
thf(1,conjecture,
! [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 @ k6_domain_1 ) @ ( B @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_2) ).
thf(2,negated_conjecture,
~ ! [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 @ k6_domain_1 ) @ ( B @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1018,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 @ k6_domain_1 ) @ ( B @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1019,plain,
( ~ ( sk2 @ ( sk1 @ u1_struct_0 @ k6_domain_1 ) @ ( sk2 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ u1_struct_0 @ r1_filter_2 ) ) )
& ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
& ( sk1 @ l3_lattices )
& ( sk1 @ v10_lattices )
& ~ ( sk1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1018]) ).
thf(1024,plain,
~ ( sk1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[1019]) ).
thf(631,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(4715,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)],[631]) ).
thf(4716,plain,
( ( sk317 @ v17_lattices )
& ( sk317 @ v16_lattices )
& ( sk317 @ v15_lattices )
& ( sk317 @ v14_lattices )
& ( sk317 @ v13_lattices )
& ( sk317 @ v11_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)],[4715]) ).
thf(4729,plain,
sk317 @ v10_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(342,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(3167,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(953,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(6285,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)],[953]) ).
thf(474,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(3927,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)],[474]) ).
thf(4728,plain,
sk317 @ v5_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(984,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(6387,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)],[984]) ).
thf(331,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(3115,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)],[331]) ).
thf(3116,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)],[3115]) ).
thf(3117,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)],[3116]) ).
thf(3119,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3117]) ).
thf(3121,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3119]) ).
thf(3122,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[3121]) ).
thf(733,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(5315,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(5316,plain,
~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5315]) ).
thf(5317,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5316]) ).
thf(8161,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,5317]) ).
thf(8162,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8161]) ).
thf(8186,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8162]) ).
thf(989,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(6405,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)],[989]) ).
thf(282,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(2732,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)],[282]) ).
thf(2733,plain,
( ( sk157 @ v14_lattices )
& ( sk157 @ v13_lattices )
& ( sk157 @ v12_lattices )
& ( sk157 @ v11_lattices )
& ( sk157 @ v10_lattices )
& ( sk157 @ v9_lattices )
& ( sk157 @ v8_lattices )
& ( sk157 @ v7_lattices )
& ( sk157 @ v6_lattices )
& ( sk157 @ v5_lattices )
& ( sk157 @ v4_lattices )
& ( sk157 @ v3_lattices )
& ~ ( sk157 @ v3_struct_0 )
& ( sk157 @ l3_lattices ) ),
inference(cnf,[status(esa)],[2732]) ).
thf(2744,plain,
sk157 @ v6_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(975,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(6355,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)],[975]) ).
thf(294,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(2889,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)],[294]) ).
thf(211,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(2295,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)],[211]) ).
thf(507,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(4101,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)],[507]) ).
thf(800,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 ) )
=> ( ( ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) )
= ( E @ ( A @ k6_filter_2 ) @ ( D @ ( A @ k6_filter_2 ) @ ( A @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) )
= ( E @ ( A @ k6_filter_2 ) @ ( D @ ( A @ k6_filter_2 ) @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( C @ ( A @ k5_filter_2 ) @ ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( C @ ( A @ k5_filter_2 ) @ ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_2) ).
thf(5593,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 ) )
=> ( ( ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) )
= ( E @ ( A @ k6_filter_2 ) @ ( D @ ( A @ k6_filter_2 ) @ ( A @ k4_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) )
= ( E @ ( A @ k6_filter_2 ) @ ( D @ ( A @ k6_filter_2 ) @ ( A @ k3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= ( C @ ( A @ k5_filter_2 ) @ ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ k4_lattices ) ) )
= ( C @ ( A @ k5_filter_2 ) @ ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(165,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(2031,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)],[165]) ).
thf(1016,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 ) )
=> ( ( ( D @ ( A @ k6_filter_2 ) @ ( E @ ( A @ k6_filter_2 ) @ ( A @ r3_lattices ) ) )
=> ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) )
=> ( D @ ( A @ k6_filter_2 ) @ ( E @ ( A @ k6_filter_2 ) @ ( A @ r3_lattices ) ) ) )
& ( ( B @ ( A @ k5_filter_2 ) @ ( C @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k5_filter_2 ) @ ( C @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_2) ).
thf(6530,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 ) )
=> ( ( ( D @ ( A @ k6_filter_2 ) @ ( E @ ( A @ k6_filter_2 ) @ ( A @ r3_lattices ) ) )
=> ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
& ( ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) )
=> ( D @ ( A @ k6_filter_2 ) @ ( E @ ( A @ k6_filter_2 ) @ ( A @ r3_lattices ) ) ) )
& ( ( B @ ( A @ k5_filter_2 ) @ ( C @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ r3_lattices ) ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) )
& ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k5_filter_2 ) @ ( C @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(864,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(5896,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)],[864]) ).
thf(172,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2072,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(500,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(4062,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(771,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5491,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(5492,plain,
! [A: $i] : ( A @ ( A @ sk389 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[5491]) ).
thf(42,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(1214,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)],[42]) ).
thf(1215,plain,
! [A: $i] :
( ( ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk14 @ ( A @ m1_subset_1 ) ) )
& ~ ( sk14 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1214]) ).
thf(1217,plain,
! [A: $i] :
( ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk14 @ ( A @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1215]) ).
thf(43861,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk389 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5492,1217]) ).
thf(43862,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk389 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43861]) ).
thf(43863,plain,
~ ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[43862:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ sk389 ))]]) ).
thf(475,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_lattices @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_lattices @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ u1_lattices @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u2_lattices @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u2_lattices @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ u2_lattices @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_filter_2) ).
thf(3930,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_lattices @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_lattices @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ u1_lattices @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u2_lattices @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u2_lattices @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ u2_lattices @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(994,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(6431,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)],[994]) ).
thf(284,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(2787,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)],[284]) ).
thf(963,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(6317,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)],[963]) ).
thf(1009,axiom,
? [A: $i] : ( A @ l3_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(6512,plain,
? [A: $i] : ( A @ l3_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(369,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(3320,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(3321,plain,
( ( sk216 @ v1_funct_1 )
& ( sk216 @ v1_xboole_0 )
& ( sk216 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3320]) ).
thf(3324,plain,
sk216 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3321]) ).
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(1049,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(1050,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)],[1049]) ).
thf(1051,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)],[1050]) ).
thf(1052,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)],[1051]) ).
thf(1023,plain,
sk1 @ l3_lattices,
inference(cnfConj,[status(thm)],[1019]) ).
thf(6914,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)],[1052,1023]) ).
thf(6915,plain,
! [A: $i] :
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6914:[bind(A,$thf( sk1 ))]]) ).
thf(6969,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)],[6915]) ).
thf(8841,plain,
! [A: $i] :
( ( ( sk216 @ 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)],[3324,6969]) ).
thf(8842,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8841]) ).
thf(8843,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8842:[bind(A,$thf( sk216 ))]]) ).
thf(15,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(1080,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)],[15]) ).
thf(1081,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ~ ( 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 @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ m1_subset_1 ) )
| ~ ( 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 @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ m1_subset_1 ) )
| ~ ( 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 @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ m1_subset_1 ) )
| ~ ( 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 @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_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 ) ) ) )
| ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( 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 @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_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 ) ) ) )
| ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( 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 @ ( 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)],[1080]) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ m1_subset_1 ) )
| ~ ( 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 @ ( 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)],[1081]) ).
thf(230,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(2427,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)],[230]) ).
thf(239,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(2480,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)],[239]) ).
thf(250,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(2559,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)],[250]) ).
thf(491,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(4015,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)],[491]) ).
thf(912,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( A @ ( B @ v1_filter_2 ) )
<=> ! [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 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_filter_2) ).
thf(6074,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ! [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 ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) )
=> ( A @ ( B @ v1_filter_2 ) ) )
& ( ( A @ ( B @ v1_filter_2 ) )
=> ! [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 ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(247,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(2541,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(2542,plain,
( ( sk138 @ v2_funct_1 )
& ( sk138 @ v1_funct_1 )
& ( sk138 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2541]) ).
thf(2544,plain,
sk138 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2542]) ).
thf(893,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(5999,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)],[893]) ).
thf(214,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(2331,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)],[214]) ).
thf(621,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(4680,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)],[621]) ).
thf(4681,plain,
! [A: $i] :
( ( ( ( A @ ( sk315 @ ( 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 @ ( sk315 @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ v1_funct_2 ) ) )
& ( sk315 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[4680]) ).
thf(4682,plain,
sk315 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4681]) ).
thf(147,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1950,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(979,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(6370,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(6371,plain,
( ( sk456 @ v3_lattices )
& ~ ( sk456 @ v3_struct_0 )
& ( sk456 @ l3_lattices ) ),
inference(cnf,[status(esa)],[6370]) ).
thf(6374,plain,
sk456 @ v3_lattices,
inference(cnfConj,[status(thm)],[6371]) ).
thf(686,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(5066,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)],[686]) ).
thf(5067,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)],[5066]) ).
thf(5068,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk352 @ ( E @ r2_hidden ) )
| ( A @ sk352 @ ( E @ r2_tarski ) )
| ~ ( A @ sk352 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk352 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk352 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk352 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk352 @ ( B @ r2_hidden ) ) )
& ( A @ sk352 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[5067]) ).
thf(5069,plain,
! [A: $i] : ( A @ sk352 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[5068]) ).
thf(721,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(5242,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)],[721]) ).
thf(672,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(4960,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)],[672]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(4603,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(182,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(2114,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)],[182]) ).
thf(38,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(1196,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)],[38]) ).
thf(1197,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)],[1196]) ).
thf(1200,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)],[1197]) ).
thf(929,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(6142,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)],[929]) ).
thf(4684,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[4681]) ).
thf(1022,plain,
sk1 @ v10_lattices,
inference(cnfConj,[status(thm)],[1019]) ).
thf(6894,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)],[1052,1022]) ).
thf(6895,plain,
! [A: $i] :
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6894:[bind(A,$thf( sk1 ))]]) ).
thf(7078,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)],[6895]) ).
thf(8829,plain,
! [A: $i] :
( ( ( sk216 @ 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)],[3324,7078]) ).
thf(8830,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8829]) ).
thf(8831,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8830:[bind(A,$thf( sk216 ))]]) ).
thf(12373,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,8831]) ).
thf(12374,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12373]) ).
thf(12458,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12374]) ).
thf(907,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(6057,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)],[907]) ).
thf(345,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(3185,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)],[345]) ).
thf(898,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(6022,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)],[898]) ).
thf(40,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(1206,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)],[40]) ).
thf(1207,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)],[1206]) ).
thf(1209,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)],[1207]) ).
thf(1211,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)],[1209]) ).
thf(324,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(3070,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)],[324]) ).
thf(3071,plain,
( ( sk197 @ v1_lattice2 )
& ( sk197 @ v3_filter_0 )
& ( sk197 @ v13_lattices )
& ( sk197 @ v10_lattices )
& ( sk197 @ v9_lattices )
& ( sk197 @ v8_lattices )
& ( sk197 @ v7_lattices )
& ( sk197 @ v6_lattices )
& ( sk197 @ v5_lattices )
& ( sk197 @ v4_lattices )
& ( sk197 @ v3_lattices )
& ~ ( sk197 @ v3_struct_0 )
& ( sk197 @ l3_lattices ) ),
inference(cnf,[status(esa)],[3070]) ).
thf(3072,plain,
sk197 @ l3_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(197,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(2205,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)],[197]) ).
thf(2206,plain,
( ( sk94 @ v10_lattices )
& ( sk94 @ v9_lattices )
& ( sk94 @ v8_lattices )
& ( sk94 @ v7_lattices )
& ( sk94 @ v6_lattices )
& ( sk94 @ v5_lattices )
& ( sk94 @ v4_lattices )
& ( sk94 @ v3_lattices )
& ~ ( sk94 @ v3_struct_0 )
& ( sk94 @ l3_lattices ) ),
inference(cnf,[status(esa)],[2205]) ).
thf(2210,plain,
sk94 @ v3_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(183,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(2117,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)],[183]) ).
thf(934,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(6177,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)],[934]) ).
thf(303,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(2940,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)],[303]) ).
thf(368,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(3317,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)],[368]) ).
thf(701,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(5168,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)],[701]) ).
thf(468,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(3905,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(442,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(3755,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)],[442]) ).
thf(3756,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)],[3755]) ).
thf(3757,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)],[3756]) ).
thf(3758,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[3757]) ).
thf(3761,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[3758]) ).
thf(3762,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[3761]) ).
thf(450,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(3810,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)],[450]) ).
thf(3811,plain,
! [A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk251 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[3810]) ).
thf(3813,plain,
! [A: $i] : ( A @ sk251 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3811]) ).
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] :
( ( 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(3230,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)],[354]) ).
thf(78,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(1443,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)],[78]) ).
thf(262,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(2657,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(2658,plain,
( ( sk152 @ v1_relat_1 )
& ( sk152 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2657]) ).
thf(2659,plain,
sk152 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[2658]) ).
thf(939,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(6199,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)],[939]) ).
thf(722,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5244,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(5245,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5244]) ).
thf(5246,plain,
~ ( sk364 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5245]) ).
thf(13044,plain,
! [A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( sk364 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,5246]) ).
thf(13045,plain,
! [A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( sk364 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13044]) ).
thf(13062,plain,
! [A: $i] :
( ( A @ sk251 )
!= sk364 ),
inference(simp,[status(thm)],[13045]) ).
thf(338,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(3153,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)],[338]) ).
thf(3323,plain,
sk216 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[3321]) ).
thf(1216,plain,
~ ( sk14 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1215]) ).
thf(8802,plain,
( ( ( sk216 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,1216]) ).
thf(8803,plain,
( ( sk216 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8802]) ).
thf(8811,plain,
sk216 != sk14,
inference(simp,[status(thm)],[8803]) ).
thf(2941,plain,
( ( sk187 @ v15_lattices )
& ( sk187 @ v14_lattices )
& ( sk187 @ v13_lattices )
& ( sk187 @ v10_lattices )
& ( sk187 @ v9_lattices )
& ( sk187 @ v8_lattices )
& ( sk187 @ v7_lattices )
& ( sk187 @ v6_lattices )
& ( sk187 @ v5_lattices )
& ( sk187 @ v4_lattices )
& ( sk187 @ v3_lattices )
& ~ ( sk187 @ v3_struct_0 )
& ( sk187 @ l3_lattices ) ),
inference(cnf,[status(esa)],[2940]) ).
thf(2953,plain,
sk187 @ v15_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(2947,plain,
sk187 @ v13_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(203,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ 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 @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( C
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) ) )
=> ( ( C @ ( D @ ( B @ r1_lattice2 ) ) )
& ( D @ ( C @ ( B @ r1_lattice2 ) ) )
& ( B @ ( D @ v2_binop_1 ) )
& ( B @ ( D @ v1_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_2) ).
thf(2248,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ 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 @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( C
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) ) )
=> ( ( C @ ( D @ ( B @ r1_lattice2 ) ) )
& ( D @ ( C @ ( B @ r1_lattice2 ) ) )
& ( B @ ( D @ v2_binop_1 ) )
& ( B @ ( D @ v1_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(339,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(3156,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)],[339]) ).
thf(3157,plain,
( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(miniscope,[status(thm)],[3156]) ).
thf(3158,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[3157]) ).
thf(3159,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3158]) ).
thf(8212,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)],[3159,6969]) ).
thf(8213,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8212]) ).
thf(8214,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8213:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(204,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(2268,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(2269,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(cnf,[status(esa)],[2268]) ).
thf(16155,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8214,2269]) ).
thf(16156,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16155]) ).
thf(12,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(1071,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)],[12]) ).
thf(1072,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)],[1071]) ).
thf(1073,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)],[1072]) ).
thf(803,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(5625,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)],[803]) ).
thf(168,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(2044,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)],[168]) ).
thf(2045,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(cnf,[status(esa)],[2044]) ).
thf(2046,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
= ( A @ k1_tarski @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[2045]) ).
thf(559,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4386,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(4387,plain,
sk296 @ v1_xboole_0,
inference(cnf,[status(esa)],[4386]) ).
thf(625,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(4696,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(4697,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4696]) ).
thf(4698,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[4697]) ).
thf(9072,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,4698]) ).
thf(9073,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9072]) ).
thf(9086,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk296 ),
inference(simp,[status(thm)],[9073]) ).
thf(26520,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk296 ) ),
inference(paramod_ordered,[status(thm)],[2046,9086]) ).
thf(26521,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk296 ),
inference(pattern_uni,[status(thm)],[26520:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(26562,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk296 ),
inference(simp,[status(thm)],[26521]) ).
thf(3168,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3167]) ).
thf(3170,plain,
k1_xboole_0 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3168]) ).
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(1047,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(1048,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)],[1047]) ).
thf(8251,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)],[3170,1048]) ).
thf(8252,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)],[8251]) ).
thf(8253,plain,
! [A: $i] : ( k1_xboole_0 @ k1_relat_1 @ ( k1_xboole_0 @ k9_relat_1 ) @ ( A @ ( k1_xboole_0 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8252:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(332,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(3123,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(3124,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3123]) ).
thf(3125,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3124]) ).
thf(23581,plain,
k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ),
inference(rewrite,[status(thm)],[8253,3125]) ).
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(1060,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(1061,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)],[1060]) ).
thf(350,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(3206,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(3207,plain,
( ( sk207 @ v1_funct_1 )
& ( sk207 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3206]) ).
thf(3209,plain,
sk207 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3207]) ).
thf(6760,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)],[1052,1024]) ).
thf(6761,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6760:[bind(A,$thf( sk1 ))]]) ).
thf(7014,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)],[6761]) ).
thf(8566,plain,
! [A: $i] :
( ( ( sk207 @ 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)],[3209,7014]) ).
thf(8567,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8566]) ).
thf(8568,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8567:[bind(A,$thf( sk207 ))]]) ).
thf(8609,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1061,8568]) ).
thf(8610,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[8609]) ).
thf(8631,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( B @ k1_relat_1 )
!= sk1 )
| ( B != sk207 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[8610]) ).
thf(8640,plain,
( ( ( sk207 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ r1_tarski ) )
| ~ ( sk207 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[8631]) ).
thf(3208,plain,
sk207 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3207]) ).
thf(42171,plain,
( ( ( sk207 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8640,3208]) ).
thf(42172,plain,
( ( ( sk207 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[42171]) ).
thf(42193,plain,
( ( ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ) ) )
| ( ( sk207 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23581,42172]) ).
thf(42194,plain,
( ( ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ) ) )
| ( ( sk207 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[42193]) ).
thf(42378,plain,
( ( k1_xboole_0 != k1_xboole_0 )
| ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk207 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[42194]) ).
thf(42382,plain,
( ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk207 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[42378]) ).
thf(550,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(4326,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)],[550]) ).
thf(528,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( 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(4215,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)],[528]) ).
thf(150,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(1968,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)],[150]) ).
thf(1969,plain,
( ( sk71 @ v1_xboole_0 )
& ( sk71 @ v2_funct_1 )
& ( sk71 @ v1_funct_1 )
& ( sk71 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1968]) ).
thf(1971,plain,
sk71 @ v1_funct_1,
inference(cnfConj,[status(thm)],[1969]) ).
thf(607,axiom,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(4612,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(4613,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(cnf,[status(esa)],[4612]) ).
thf(4614,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(lifteq,[status(thm)],[4613]) ).
thf(110,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(1692,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)],[110]) ).
thf(609,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(4623,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)],[609]) ).
thf(900,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(6031,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)],[900]) ).
thf(2660,plain,
sk152 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2658]) ).
thf(6710,plain,
! [B: $i,A: $i] :
( ( ( sk152 @ 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)],[2660,1048]) ).
thf(6711,plain,
! [B: $i,A: $i] :
( ( ( sk152 @ 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)],[6710]) ).
thf(6712,plain,
! [A: $i] : ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6711:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).
thf(26,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(1133,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)],[26]) ).
thf(1134,plain,
! [A: $i] :
( ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1133]) ).
thf(1135,plain,
! [A: $i] :
( ~ ( A @ v1_relat_1 )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1134]) ).
thf(15517,plain,
! [A: $i] :
( ( ( sk152 @ 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)],[2660,1135]) ).
thf(15518,plain,
! [A: $i] :
( ( ( sk152 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15517]) ).
thf(15519,plain,
( ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) )
= ( sk152 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15518:[bind(A,$thf( sk152 ))]]) ).
thf(21468,plain,
! [A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6712,15519]) ).
thf(14,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(1077,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)],[14]) ).
thf(1078,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(miniscope,[status(thm)],[1077]) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[1078]) ).
thf(21488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21468,1079]) ).
thf(21489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[21488]) ).
thf(21490,plain,
! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21489:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk152 @ k9_relat_1 ) )),bind(C,$thf( sk152 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(21570,plain,
! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[21490]) ).
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(1033,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(1034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ sk3 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ sk3 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( C @ v1_funct_1 )
| ~ ( B @ ( A @ ( C @ sk3 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( B @ ( A @ ( C @ sk3 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
| ( ( C @ k1_relat_1 )
!= A )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( B @ ( A @ ( C @ sk3 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ r2_hidden ) )
| ( ( C @ k1_relat_1 )
!= A )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1033]) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk3 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
| ( ( C @ k1_relat_1 )
!= A )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1034]) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk3 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ( ( C @ k1_relat_1 )
!= A ) ),
inference(lifteq,[status(thm)],[1039]) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_relat_1 @ ( B @ sk3 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ ( A @ ( B @ sk4 ) ) @ ( B @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1040]) ).
thf(379,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(3382,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)],[379]) ).
thf(32,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(1162,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)],[32]) ).
thf(1163,plain,
! [B: $i,A: $i] :
( ( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk11 ) ) )
| ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk10 ) ) )
| ( ( 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 @ sk11 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk10 ) ) )
| ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk10 ) ) )
| ( ( 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 @ sk10 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk11 ) ) )
| ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk11 ) ) )
| ( ( 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 @ sk11 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk10 ) ) )
| ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk11 ) ) )
| ( ( 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 @ sk11 ) @ 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 @ sk10 ) @ 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)],[1162]) ).
thf(1167,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
!= ( A @ ( B @ sk11 ) ) )
| ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk10 ) ) )
| ( ( 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)],[1163]) ).
thf(1173,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 @ sk11 ) )
!= ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) ) )
| ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk10 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1167]) ).
thf(957,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 @ k20_filter_2 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_2) ).
thf(6295,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 @ k20_filter_2 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(820,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(5690,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)],[820]) ).
thf(5691,plain,
! [A: $i] :
( ( ( ( A @ ( sk407 @ ( 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 @ ( sk407 @ ( 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 @ ( sk407 @ ( 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 @ ( sk407 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( sk407 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ) ),
inference(cnf,[status(esa)],[5690]) ).
thf(5697,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5691]) ).
thf(5700,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ m2_relset_1 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5697]) ).
thf(24,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(1126,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)],[24]) ).
thf(1127,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)],[1126]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[1127]) ).
thf(14739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ 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)],[5700,1129]) ).
thf(14740,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[14739]) ).
thf(14741,plain,
( ( f2_s11_funct_2 @ ( sk407 @ k2_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[14740:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk407 ))]]) ).
thf(952,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(6278,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)],[952]) ).
thf(924,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(6127,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)],[924]) ).
thf(588,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(4528,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)],[588]) ).
thf(159,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(1999,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)],[159]) ).
thf(57,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(1286,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)],[57]) ).
thf(1287,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
| ( ( A @ sk18 )
!= ( A @ sk19 ) ) )
& ( ( A = k1_xboole_0 )
| ( ( A @ sk19 @ k1_relat_1 )
= A ) )
& ( ( A = k1_xboole_0 )
| ( ( A @ sk18 @ k1_relat_1 )
= A ) )
& ( ( A = k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) )
& ( ( A = k1_xboole_0 )
| ( A @ sk19 @ v1_relat_1 ) )
& ( ( A = k1_xboole_0 )
| ( A @ sk18 @ v1_funct_1 ) )
& ( ( A = k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1286]) ).
thf(1291,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(cnfConj,[status(thm)],[1287]) ).
thf(1296,plain,
! [A: $i] :
( ( A @ sk19 @ v1_funct_1 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1291]) ).
thf(1951,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[1950]) ).
thf(4063,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4062]) ).
thf(4064,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[4063]) ).
thf(8163,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,4064]) ).
thf(8164,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8163]) ).
thf(8182,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8164]) ).
thf(11728,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1951,8182]) ).
thf(11729,plain,
( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[11728:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(31235,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,11729]) ).
thf(31236,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[31235]) ).
thf(31237,plain,
k1_xboole_0 @ k1_tarski @ sk19 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[31236:[bind(A,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(34846,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ sk19 @ 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)],[31237,7014]) ).
thf(34847,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ sk19 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[34846]) ).
thf(34848,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[34847:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ sk19 ))]]) ).
thf(278,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(2712,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)],[278]) ).
thf(654,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(4856,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)],[654]) ).
thf(29739,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,1024]) ).
thf(29740,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk1 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29739:[bind(A,$thf( sk1 ))]]) ).
thf(156,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(1988,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)],[156]) ).
thf(63,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(1342,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)],[63]) ).
thf(840,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_2) ).
thf(5782,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(167,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(2042,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)],[167]) ).
thf(706,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(5192,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)],[706]) ).
thf(371,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(3332,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(3333,plain,
( ( sk218 @ v1_relat_1 )
& ~ ( sk218 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3332]) ).
thf(3334,plain,
~ ( sk218 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3333]) ).
thf(6636,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,3334]) ).
thf(6637,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6636]) ).
thf(6640,plain,
sk218 != sk152,
inference(simp,[status(thm)],[6637]) ).
thf(592,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(4543,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)],[592]) ).
thf(884,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(5967,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)],[884]) ).
thf(613,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(4633,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)],[613]) ).
thf(385,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(3429,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)],[385]) ).
thf(790,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(5565,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)],[790]) ).
thf(166,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(2035,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)],[166]) ).
thf(947,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(6246,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)],[947]) ).
thf(832,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_2) ).
thf(5755,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(4011,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(2740,plain,
sk157 @ v3_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(299,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(2918,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)],[299]) ).
thf(5694,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5691]) ).
thf(5701,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ v1_funct_2 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5694]) ).
thf(541,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(4279,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)],[541]) ).
thf(825,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(5713,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)],[825]) ).
thf(238,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(2469,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)],[238]) ).
thf(2470,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)],[2469]) ).
thf(2476,plain,
k13_nat_lat @ v4_lattices,
inference(cnfConj,[status(thm)],[2470]) ).
thf(699,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(5163,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)],[699]) ).
thf(411,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(3562,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)],[411]) ).
thf(318,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(3027,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)],[318]) ).
thf(3028,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)],[3027]) ).
thf(3029,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk195 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3028]) ).
thf(3030,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3029]) ).
thf(3032,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3030]) ).
thf(3033,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[3032]) ).
thf(17125,plain,
! [B: $i,A: $i] :
( ( ( A @ sk352 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5069,3033]) ).
thf(17126,plain,
! [B: $i,A: $i] :
( ( A @ sk352 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[17125]) ).
thf(17137,plain,
! [B: $i,A: $i] :
( ( ( A @ sk352 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[17126]) ).
thf(17142,plain,
! [A: $i] :
( ( A @ sk352 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[17137]) ).
thf(30821,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk352 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,17142]) ).
thf(30822,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk352 ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[30821]) ).
thf(30823,plain,
! [A: $i] : ( A @ sk352 @ sk19 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[30822:[bind(A,$thf( C @ sk352 )),bind(B,$thf( C ))]]) ).
thf(32700,plain,
! [A: $i] : ( A @ sk352 @ sk19 @ v1_funct_1 ),
inference(simp,[status(thm)],[30823]) ).
thf(920,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
=> ( B @ ( A @ k18_filter_2 ) @ ( C @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_2) ).
thf(6117,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 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
=> ( B @ ( A @ k18_filter_2 ) @ ( C @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
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(1062,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(1063,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)],[1062]) ).
thf(2073,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(cnf,[status(esa)],[2072]) ).
thf(7108,plain,
! [A: $i] :
( ( ( sk138 @ 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)],[2544,6969]) ).
thf(7109,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7108]) ).
thf(7110,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7109:[bind(A,$thf( sk138 ))]]) ).
thf(7646,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1063,7110]) ).
thf(7647,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7646]) ).
thf(7688,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7647]) ).
thf(7703,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk138 @ v1_relat_1 )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7688]) ).
thf(2543,plain,
sk138 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2542]) ).
thf(9511,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ l3_lattices ) ),
inference(rewrite,[status(thm)],[7703,2543]) ).
thf(9512,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[9511]) ).
thf(12984,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ l3_lattices ) ),
inference(paramod_ordered,[status(thm)],[2073,9512]) ).
thf(12985,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12984]) ).
thf(13013,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12985]) ).
thf(13029,plain,
( ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[13013]) ).
thf(361,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(3276,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)],[361]) ).
thf(2216,plain,
sk94 @ v5_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(8572,plain,
! [A: $i] :
( ( ( sk207 @ 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)],[3209,6969]) ).
thf(8573,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8572]) ).
thf(8574,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8573:[bind(A,$thf( sk207 ))]]) ).
thf(16254,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,8574]) ).
thf(16255,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16254]) ).
thf(16279,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16255]) ).
thf(16304,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16279]) ).
thf(192,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(2160,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(2161,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[2160]) ).
thf(13515,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1951,2161]) ).
thf(13516,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[13515:[bind(A,$thf( k1_xboole_0 ))]]) ).
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(1044,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(1045,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)],[1044]) ).
thf(1046,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)],[1045]) ).
thf(1128,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[1127]) ).
thf(14486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ 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)],[5700,1128]) ).
thf(14487,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk407 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[14486]) ).
thf(14488,plain,
( ( f1_s11_funct_2 @ ( sk407 @ k1_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[14487:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk407 ))]]) ).
thf(69,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(1366,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)],[69]) ).
thf(917,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(6102,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)],[917]) ).
thf(619,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(4665,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)],[619]) ).
thf(418,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(3597,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)],[418]) ).
thf(291,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(2869,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)],[291]) ).
thf(667,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(4941,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)],[667]) ).
thf(377,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(3370,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)],[377]) ).
thf(3335,plain,
sk218 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3333]) ).
thf(216,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(2348,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)],[216]) ).
thf(375,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(3350,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)],[375]) ).
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 ) )
=> ! [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(5977,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)],[887]) ).
thf(15797,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s11_funct_2 @ ( sk407 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(paramod_ordered,[status(thm)],[14488,1079]) ).
thf(15798,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s11_funct_2 @ ( sk407 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[15797]) ).
thf(15799,plain,
! [A: $i] :
( ( f1_s11_funct_2 @ ( A @ ( sk407 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[15798:[bind(A,$thf( sk407 @ k1_relat_1 )),bind(B,$thf( f1_s11_funct_2 )),bind(C,$thf( C ))]]) ).
thf(15863,plain,
! [A: $i] :
( ( f1_s11_funct_2 @ ( A @ ( sk407 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[15799]) ).
thf(485,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(3994,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)],[485]) ).
thf(48,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(1236,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)],[48]) ).
thf(1237,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(miniscope,[status(thm)],[1236]) ).
thf(1238,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ k1_tarski @ ( E @ k4_xboole_0 ) @ ( D @ r2_hidden ) )
| ( D = F )
| ~ ( E @ ( D @ r2_hidden ) ) )
& ( ( A != C )
| ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ ( A @ r2_hidden ) )
| ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ) ),
inference(cnf,[status(esa)],[1237]) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[1238]) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
| ( A != C ) ),
inference(lifteq,[status(thm)],[1240]) ).
thf(1243,plain,
! [B: $i,A: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ r2_hidden ) ),
inference(simp,[status(thm)],[1242]) ).
thf(470,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(3915,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)],[470]) ).
thf(949,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(6250,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)],[949]) ).
thf(6251,plain,
( ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk448 @ r2_hidden ) )
| ~ ( sk448 @ p1_s4_subset_1 )
| sk446 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk448 @ p1_s4_subset_1 )
| ~ ( sk448 @ p1_s4_subset_1 )
| sk446 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk448 @ r2_hidden ) )
| ( f3_s4_subset_1 @ ( sk448 @ r2_hidden ) )
| sk446 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk448 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk448 @ r2_hidden ) )
| sk446 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk448 @ m1_subset_1 ) )
| sk446 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk446
| ~ ( f2_s4_subset_1 @ ( sk447 @ r2_hidden ) )
| ~ ( sk447 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk446
| ( sk447 @ p1_s4_subset_1 )
| ~ ( sk447 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk446
| ~ ( f2_s4_subset_1 @ ( sk447 @ r2_hidden ) )
| ( f2_s4_subset_1 @ ( sk447 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk446
| ( sk447 @ p1_s4_subset_1 )
| ( f2_s4_subset_1 @ ( sk447 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk446
| ( f1_s4_subset_1 @ ( sk447 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[6250]) ).
thf(6258,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk448 @ m1_subset_1 ) )
| sk446 ),
inference(cnfConj,[status(thm)],[6251]) ).
thf(6268,plain,
( ( f1_s4_subset_1 @ ( sk448 @ m1_subset_1 ) )
| sk446
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[6258]) ).
thf(248,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(2546,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(2547,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(cnf,[status(esa)],[2546]) ).
thf(2548,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(lifteq,[status(thm)],[2547]) ).
thf(538,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(4266,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)],[538]) ).
thf(982,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 @ k7_filter_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_2) ).
thf(6381,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 @ k7_filter_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(830,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(5745,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)],[830]) ).
thf(707,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(5194,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(5195,plain,
sk361 @ l2_lattices,
inference(cnf,[status(esa)],[5194]) ).
thf(644,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(4803,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)],[644]) ).
thf(511,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(4124,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)],[511]) ).
thf(827,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(5723,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)],[827]) ).
thf(879,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(5938,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(685,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(5056,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)],[685]) ).
thf(7407,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,4064]) ).
thf(7408,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7407]) ).
thf(7413,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk152 ),
inference(simp,[status(thm)],[7408]) ).
thf(11730,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk152 ) ),
inference(paramod_ordered,[status(thm)],[1951,7413]) ).
thf(11731,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk152 ),
inference(pattern_uni,[status(thm)],[11730:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(465,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(3898,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)],[465]) ).
thf(636,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(4760,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)],[636]) ).
thf(90,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(1529,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)],[90]) ).
thf(583,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(4511,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)],[583]) ).
thf(44055,plain,
( ( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,43863]) ).
thf(44056,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44055]) ).
thf(44068,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk216 ),
inference(simp,[status(thm)],[44056]) ).
thf(304,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(2955,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)],[304]) ).
thf(2956,plain,
( ( sk188 @ v3_filter_0 )
& ( sk188 @ v10_lattices )
& ( sk188 @ v9_lattices )
& ( sk188 @ v8_lattices )
& ( sk188 @ v7_lattices )
& ( sk188 @ v6_lattices )
& ( sk188 @ v5_lattices )
& ( sk188 @ v4_lattices )
& ( sk188 @ v3_lattices )
& ~ ( sk188 @ v3_struct_0 )
& ( sk188 @ l3_lattices ) ),
inference(cnf,[status(esa)],[2955]) ).
thf(2957,plain,
sk188 @ v9_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(101,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(1628,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)],[101]) ).
thf(758,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(5429,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)],[758]) ).
thf(904,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(6039,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)],[904]) ).
thf(265,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(2667,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)],[265]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(1871,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(323,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(3054,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)],[323]) ).
thf(3055,plain,
( ( sk196 @ v16_lattices )
& ( sk196 @ v15_lattices )
& ( sk196 @ v14_lattices )
& ( sk196 @ v13_lattices )
& ( sk196 @ v10_lattices )
& ( sk196 @ v9_lattices )
& ( sk196 @ v8_lattices )
& ( sk196 @ v7_lattices )
& ( sk196 @ v6_lattices )
& ( sk196 @ v5_lattices )
& ( sk196 @ v4_lattices )
& ( sk196 @ v3_lattices )
& ~ ( sk196 @ v3_struct_0 )
& ( sk196 @ l3_lattices ) ),
inference(cnf,[status(esa)],[3054]) ).
thf(3061,plain,
~ ( sk196 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3055]) ).
thf(453,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(3821,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)],[453]) ).
thf(909,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(6066,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)],[909]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(3653,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(206,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(2274,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)],[206]) ).
thf(7422,plain,
! [A: $i] :
( ( ( sk71 @ 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)],[1971,7078]) ).
thf(7423,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7422]) ).
thf(7424,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7423:[bind(A,$thf( sk71 ))]]) ).
thf(7684,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1063,7424]) ).
thf(7685,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7684]) ).
thf(7693,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7685]) ).
thf(7708,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk71 @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7693]) ).
thf(1970,plain,
sk71 @ v1_relat_1,
inference(cnfConj,[status(thm)],[1969]) ).
thf(9551,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[7708,1970]) ).
thf(9552,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[9551]) ).
thf(1012,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(6519,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)],[1012]) ).
thf(13050,plain,
! [A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,3334]) ).
thf(13051,plain,
! [A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13050]) ).
thf(13067,plain,
! [A: $i] :
( ( A @ sk251 )
!= sk218 ),
inference(simp,[status(thm)],[13051]) ).
thf(39576,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk352 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5069,1243]) ).
thf(39577,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk352 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[39576]) ).
thf(39633,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk352 )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[39577]) ).
thf(39648,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= ( B @ sk352 ) ),
inference(simp,[status(thm)],[39633]) ).
thf(533,axiom,
! [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(4238,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)],[533]) ).
thf(389,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(3442,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)],[389]) ).
thf(835,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(5765,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)],[835]) ).
thf(359,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(3263,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)],[359]) ).
thf(571,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(4439,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)],[571]) ).
thf(213,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(2328,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)],[213]) ).
thf(586,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(4524,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)],[586]) ).
thf(476,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(3938,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(553,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(4348,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)],[553]) ).
thf(2735,plain,
sk157 @ v10_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(287,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(2814,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)],[287]) ).
thf(8883,plain,
! [B: $i,A: $i] :
( ( ( sk218 @ 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)],[3335,1048]) ).
thf(8884,plain,
! [B: $i,A: $i] :
( ( ( sk218 @ 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)],[8883]) ).
thf(8885,plain,
! [A: $i] : ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8884:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).
thf(15507,plain,
! [A: $i] :
( ( ( sk218 @ 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)],[3335,1135]) ).
thf(15508,plain,
! [A: $i] :
( ( ( sk218 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15507]) ).
thf(15509,plain,
( ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) )
= ( sk218 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15508:[bind(A,$thf( sk218 ))]]) ).
thf(25760,plain,
! [A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[8885,15509]) ).
thf(273,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(2698,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)],[273]) ).
thf(670,axiom,
k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_nat_lat) ).
thf(4956,plain,
k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(8165,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,3334]) ).
thf(8166,plain,
( ( sk218 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8165]) ).
thf(8184,plain,
sk218 != k1_xboole_0,
inference(simp,[status(thm)],[8166]) ).
thf(32581,plain,
! [A: $i] :
( ( A != sk218 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,8184]) ).
thf(32582,plain,
! [A: $i] :
( ( A != sk218 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[32581]) ).
thf(32583,plain,
sk218 @ sk19 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[32582:[bind(A,$thf( sk218 ))]]) ).
thf(34611,plain,
! [A: $i] :
( ( ( sk218 @ sk19 @ 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)],[32583,7014]) ).
thf(34612,plain,
! [A: $i] :
( ( ( sk218 @ sk19 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[34611]) ).
thf(34613,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[34612:[bind(A,$thf( sk218 @ sk19 ))]]) ).
thf(39153,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,34613]) ).
thf(39154,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[39153]) ).
thf(39212,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( ( sk218 @ sk19 )
!= sk315 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[39154]) ).
thf(322,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(3046,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)],[322]) ).
thf(430,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(3689,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)],[430]) ).
thf(567,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(4415,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)],[567]) ).
thf(834,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(5759,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)],[834]) ).
thf(7219,plain,
! [A: $i] :
( ( ( sk71 @ 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)],[1971,7014]) ).
thf(7220,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7219]) ).
thf(7221,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7220:[bind(A,$thf( sk71 ))]]) ).
thf(7486,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1061,7221]) ).
thf(7487,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7486]) ).
thf(7520,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( B @ k1_relat_1 )
!= sk1 )
| ( B != sk71 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7487]) ).
thf(7522,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) )
| ~ ( sk71 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7520]) ).
thf(7593,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7522,1970]) ).
thf(7594,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[7593]) ).
thf(12993,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2073,7594]) ).
thf(12994,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12993]) ).
thf(13014,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12994]) ).
thf(13030,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13014]) ).
thf(9068,plain,
( ( ( sk296 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,3334]) ).
thf(9069,plain,
( ( sk296 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9068]) ).
thf(9084,plain,
sk296 != sk218,
inference(simp,[status(thm)],[9069]) ).
thf(615,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(4654,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)],[615]) ).
thf(421,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(3605,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)],[421]) ).
thf(3606,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ k2_tarski ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_tarski ) ) )
=> ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3605]) ).
thf(3607,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ k2_tarski ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk236 ) ) @ r2_hidden ) )
| ( H @ ( G @ ( F @ sk234 ) ) ) )
& ( ( H
= ( G @ ( F @ k2_tarski ) ) )
| ( ( F @ ( G @ ( H @ sk236 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk236 ) ) )
= F )
| ( H @ ( G @ ( F @ sk234 ) ) ) )
& ( ( H
= ( G @ ( F @ k2_tarski ) ) )
| ~ ( H @ ( G @ ( F @ sk234 ) ) )
| ( ( F @ ( G @ ( H @ sk235 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ k2_tarski ) ) )
| ~ ( H @ ( G @ ( F @ sk234 ) ) )
| ( ( F @ ( G @ ( H @ sk235 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ k2_tarski ) ) )
| ~ ( H @ ( G @ ( F @ sk234 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk235 ) ) @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
| ( E != B )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( C @ ( E @ r2_hidden ) )
| ( E != A )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ r2_hidden ) )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ) ),
inference(cnf,[status(esa)],[3606]) ).
thf(3612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != A )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(cnfConj,[status(thm)],[3607]) ).
thf(3616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != A )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(lifteq,[status(thm)],[3612]) ).
thf(3617,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[3616]) ).
thf(551,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(4334,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)],[551]) ).
thf(973,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(6350,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)],[973]) ).
thf(198,axiom,
? [A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_struct_0) ).
thf(2217,plain,
? [A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(129,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(1826,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)],[129]) ).
thf(512,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(4130,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)],[512]) ).
thf(962,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(6315,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)],[962]) ).
thf(383,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(3410,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)],[383]) ).
thf(231,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(2436,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(2437,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[2436]) ).
thf(2438,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[2437]) ).
thf(7861,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,2438]) ).
thf(7862,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7861]) ).
thf(7867,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk152 ),
inference(simp,[status(thm)],[7862]) ).
thf(80,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(1455,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)],[80]) ).
thf(918,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(6113,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)],[918]) ).
thf(704,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(5182,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)],[704]) ).
thf(295,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(2897,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)],[295]) ).
thf(890,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 @ k18_filter_2 ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_2) ).
thf(5989,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 @ k18_filter_2 ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( B @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
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 ) )
=> ( ( 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(6332,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)],[968]) ).
thf(638,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(4766,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)],[638]) ).
thf(569,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(4428,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)],[569]) ).
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(1053,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(1054,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)],[1053]) ).
thf(1055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E
= ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ ( 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 @ sk5 ) ) ) ) @ 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 @ sk5 ) ) ) ) @ 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)],[1054]) ).
thf(1058,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
= ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ ( 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)],[1055]) ).
thf(1059,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 @ sk5 ) ) ) ) @ ( D @ k1_funct_1 ) )
= E ) ),
inference(lifteq,[status(thm)],[1058]) ).
thf(29743,plain,
! [A: $i] :
( ( A != sk317 )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,4729]) ).
thf(29744,plain,
( ( k1_xboole_0 @ v10_lattices )
| ( sk317 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29743:[bind(A,$thf( sk317 ))]]) ).
thf(25,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(1130,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)],[25]) ).
thf(1131,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)],[1130]) ).
thf(1132,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)],[1131]) ).
thf(2745,plain,
sk157 @ v12_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(8177,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,2438]) ).
thf(8178,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8177]) ).
thf(8179,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8178]) ).
thf(32586,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k4_tarski ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,8179]) ).
thf(32587,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k4_tarski ) ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[32586]) ).
thf(32588,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk19 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[32587:[bind(A,$thf( E @ ( D @ k4_tarski ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(33138,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk19 @ v1_funct_1 ),
inference(simp,[status(thm)],[32588]) ).
thf(896,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( C @ ( B @ ( A @ k21_filter_2 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_2) ).
thf(6010,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( C @ ( B @ ( A @ k21_filter_2 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(905,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(6049,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)],[905]) ).
thf(486,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(3998,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)],[486]) ).
thf(112,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(1704,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)],[112]) ).
thf(191,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(2158,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)],[191]) ).
thf(828,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 ) )
<=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v17_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_2) ).
thf(5727,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v17_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) )
=> ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v17_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(558,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(4383,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)],[558]) ).
thf(310,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(2989,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)],[310]) ).
thf(18,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(1100,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
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 ) )
=> ! [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(6071,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)],[911]) ).
thf(228,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(2413,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)],[228]) ).
thf(2414,plain,
( ( sk118 @ v1_lattice2 )
& ( sk118 @ v10_lattices )
& ( sk118 @ v9_lattices )
& ( sk118 @ v8_lattices )
& ( sk118 @ v7_lattices )
& ( sk118 @ v6_lattices )
& ( sk118 @ v5_lattices )
& ( sk118 @ v4_lattices )
& ~ ( sk118 @ v3_struct_0 )
& ( sk118 @ l3_lattices ) ),
inference(cnf,[status(esa)],[2413]) ).
thf(2420,plain,
sk118 @ v5_lattices,
inference(cnfConj,[status(thm)],[2414]) ).
thf(742,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(5355,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)],[742]) ).
thf(392,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(3463,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)],[392]) ).
thf(289,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(2857,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)],[289]) ).
thf(802,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(5605,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)],[802]) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ m1_subset_1 ) )
| ~ ( 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 @ ( 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)],[1081]) ).
thf(88,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(1514,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)],[88]) ).
thf(9122,plain,
! [A: $i] :
( ( ( sk315 @ 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)],[4682,6969]) ).
thf(9123,plain,
! [A: $i] :
( ( ( sk315 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9122]) ).
thf(9124,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9123:[bind(A,$thf( sk315 ))]]) ).
thf(16259,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,9124]) ).
thf(16260,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16259]) ).
thf(16275,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk315 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16260]) ).
thf(16300,plain,
( ( sk315 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16275]) ).
thf(709,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(5199,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)],[709]) ).
thf(522,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(4194,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(8173,plain,
( ( ( sk14 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,1216]) ).
thf(8174,plain,
( ( sk14 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8173]) ).
thf(8181,plain,
sk14 != k1_xboole_0,
inference(simp,[status(thm)],[8174]) ).
thf(30651,plain,
! [A: $i] :
( ( A != sk14 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,8181]) ).
thf(30652,plain,
! [A: $i] :
( ( A != sk14 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[30651]) ).
thf(30653,plain,
sk14 @ sk19 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[30652:[bind(A,$thf( sk14 ))]]) ).
thf(34149,plain,
! [A: $i] :
( ( ( sk14 @ sk19 @ 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)],[30653,7014]) ).
thf(34150,plain,
! [A: $i] :
( ( ( sk14 @ sk19 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[34149]) ).
thf(34151,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[34150:[bind(A,$thf( sk14 @ sk19 ))]]) ).
thf(36811,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,34151]) ).
thf(36812,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[36811]) ).
thf(36908,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( ( sk14 @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[36812]) ).
thf(36923,plain,
( ( ( sk14 @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[36908]) ).
thf(29868,plain,
! [A: $i] :
( ( A != sk187 )
| ( k1_xboole_0 @ v13_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,2947]) ).
thf(29869,plain,
( ( k1_xboole_0 @ v13_lattices )
| ( sk187 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29868:[bind(A,$thf( sk187 ))]]) ).
thf(577,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(4492,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)],[577]) ).
thf(735,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(5323,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)],[735]) ).
thf(950,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(6272,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)],[950]) ).
thf(3084,plain,
sk197 @ v5_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(20,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(1108,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)],[20]) ).
thf(1109,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)],[1108]) ).
thf(1111,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)],[1109]) ).
thf(1115,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)],[1111]) ).
thf(393,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(3470,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)],[393]) ).
thf(593,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(4551,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)],[593]) ).
thf(143,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(1931,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)],[143]) ).
thf(880,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(5942,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)],[880]) ).
thf(513,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(4141,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(669,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(4952,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)],[669]) ).
thf(344,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(3174,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)],[344]) ).
thf(3175,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)],[3174]) ).
thf(3180,plain,
k6_nat_lat @ v8_lattices,
inference(cnfConj,[status(thm)],[3175]) ).
thf(561,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(4390,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)],[561]) ).
thf(690,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(5091,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)],[690]) ).
thf(575,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v17_lattices )
& ( A @ k1_lattice2 @ v16_lattices )
& ( A @ k1_lattice2 @ v15_lattices )
& ( A @ k1_lattice2 @ v14_lattices )
& ( A @ k1_lattice2 @ v13_lattices )
& ( A @ k1_lattice2 @ v12_lattices )
& ( A @ k1_lattice2 @ v11_lattices )
& ( 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',fc4_filter_2) ).
thf(4471,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v17_lattices )
& ( A @ k1_lattice2 @ v16_lattices )
& ( A @ k1_lattice2 @ v15_lattices )
& ( A @ k1_lattice2 @ v14_lattices )
& ( A @ k1_lattice2 @ v13_lattices )
& ( A @ k1_lattice2 @ v12_lattices )
& ( A @ k1_lattice2 @ v11_lattices )
& ( 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)],[575]) ).
thf(642,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(4793,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)],[642]) ).
thf(420,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(3602,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)],[420]) ).
thf(772,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(5493,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)],[772]) ).
thf(978,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(6364,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)],[978]) ).
thf(6707,plain,
! [B: $i,A: $i] :
( ( ( sk71 @ 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)],[1970,1048]) ).
thf(6708,plain,
! [B: $i,A: $i] :
( ( ( sk71 @ 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)],[6707]) ).
thf(6709,plain,
! [A: $i] : ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6708:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).
thf(15522,plain,
! [A: $i] :
( ( ( sk71 @ 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)],[1970,1135]) ).
thf(15523,plain,
! [A: $i] :
( ( ( sk71 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15522]) ).
thf(15524,plain,
( ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) )
= ( sk71 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15523:[bind(A,$thf( sk71 ))]]) ).
thf(19484,plain,
! [A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6709,15524]) ).
thf(19504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19484,1079]) ).
thf(19505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[19504]) ).
thf(19506,plain,
! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[19505:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk71 @ k9_relat_1 ) )),bind(C,$thf( sk71 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(19578,plain,
! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[19506]) ).
thf(566,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(4411,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)],[566]) ).
thf(58,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(1302,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)],[58]) ).
thf(7658,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1063,7221]) ).
thf(7659,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7658]) ).
thf(7696,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk71 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7659]) ).
thf(7711,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk71 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7696]) ).
thf(9881,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7711,1970]) ).
thf(9882,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[9881]) ).
thf(178,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(2090,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)],[178]) ).
thf(436,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(3724,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(844,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(5804,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)],[844]) ).
thf(871,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(5914,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)],[871]) ).
thf(29,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(1144,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)],[29]) ).
thf(1145,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ( F
!= ( B @ ( D @ k1_realset1 ) ) )
| ( E
!= ( B @ ( C @ k1_realset1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( 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 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ( F
!= ( B @ ( D @ k1_realset1 ) ) )
| ( E
!= ( B @ ( C @ k1_realset1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( 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 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1144]) ).
thf(1147,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ( F
!= ( B @ ( D @ k1_realset1 ) ) )
| ( E
!= ( B @ ( C @ k1_realset1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( 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 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1145]) ).
thf(1150,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( 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 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 )
| ( F
!= ( B @ ( D @ k1_realset1 ) ) )
| ( E
!= ( B @ ( C @ k1_realset1 ) ) ) ),
inference(lifteq,[status(thm)],[1147]) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ k1_realset1 ) @ ( B @ ( C @ k1_realset1 ) @ ( B @ r5_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( D @ k1_realset1 ) @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( D @ k1_realset1 ) @ v1_funct_2 ) ) )
| ~ ( B @ ( D @ k1_realset1 ) @ v1_funct_1 )
| ~ ( 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 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( 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 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1150]) ).
thf(743,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(5360,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)],[743]) ).
thf(444,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(3771,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)],[444]) ).
thf(184,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(2119,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)],[184]) ).
thf(2120,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)],[2119]) ).
thf(2121,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk80 @ ( F @ r2_hidden ) )
| ( A @ sk80 @ ( F @ r2_tarski ) )
| ~ ( A @ sk80 @ ( F @ r1_tarski ) ) )
& ( ( A @ ( D @ sk81 ) @ ( E @ r2_hidden ) )
| ~ ( D @ ( E @ r1_tarski ) )
| ~ ( A @ sk80 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk80 @ ( A @ ( D @ sk81 ) @ r2_hidden ) )
| ~ ( A @ sk80 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk80 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk80 @ ( B @ r2_hidden ) ) )
& ( A @ sk80 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[2120]) ).
thf(2123,plain,
! [A: $i] : ( A @ sk80 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2121]) ).
thf(15417,plain,
! [B: $i,A: $i] :
( ( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2123,3033]) ).
thf(15418,plain,
! [B: $i,A: $i] :
( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[15417]) ).
thf(15429,plain,
! [B: $i,A: $i] :
( ( ( A @ sk80 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[15418]) ).
thf(15436,plain,
! [A: $i] :
( ( A @ sk80 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15429]) ).
thf(32184,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk80 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,15436]) ).
thf(32185,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk80 ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[32184]) ).
thf(32186,plain,
! [A: $i] : ( A @ sk80 @ sk19 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[32185:[bind(A,$thf( C @ sk80 )),bind(B,$thf( C ))]]) ).
thf(33023,plain,
! [A: $i] : ( A @ sk80 @ sk19 @ v1_funct_1 ),
inference(simp,[status(thm)],[32186]) ).
thf(160,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(2007,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)],[160]) ).
thf(2950,plain,
sk187 @ v7_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(881,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(5957,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)],[881]) ).
thf(36851,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,34151]) ).
thf(36852,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[36851]) ).
thf(36909,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( ( sk14 @ sk19 )
!= sk315 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk14 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[36852]) ).
thf(727,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(5264,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)],[727]) ).
thf(894,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(6002,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)],[894]) ).
thf(3322,plain,
sk216 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3321]) ).
thf(145,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(1946,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)],[145]) ).
thf(563,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(4396,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)],[563]) ).
thf(81,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(1465,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)],[81]) ).
thf(573,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 @ m2_filter_2 ) )
=> ( ( C
= ( B @ ( A @ k19_filter_2 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ m2_filter_2 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_2) ).
thf(4443,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 @ m2_filter_2 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ m2_filter_2 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ k19_filter_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k19_filter_2 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m2_filter_2 ) )
=> ( ( D @ ( B @ r1_tarski ) )
=> ( D @ ( C @ r1_tarski ) ) ) )
& ( C @ ( B @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(180,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(2105,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(3075,plain,
sk197 @ v1_lattice2,
inference(cnfConj,[status(thm)],[3071]) ).
thf(546,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 @ m2_filter_2 ) )
=> ~ ( ( C @ ( A @ r2_filter_2 ) )
& ( C @ ( B @ r2_hidden ) ) ) )
& ( B
!= ( A @ k6_lattices ) )
& ( A @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_filter_2) ).
thf(4297,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 @ m2_filter_2 ) )
=> ~ ( ( C @ ( A @ r2_filter_2 ) )
& ( C @ ( B @ r2_hidden ) ) ) )
& ( B
!= ( A @ k6_lattices ) )
& ( A @ v14_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(632,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(4733,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)],[632]) ).
thf(16380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( sk407 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(paramod_ordered,[status(thm)],[14741,1079]) ).
thf(16381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( sk407 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[16380]) ).
thf(16382,plain,
! [A: $i] :
( ( f2_s11_funct_2 @ ( A @ ( sk407 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[16381:[bind(A,$thf( sk407 @ k2_relat_1 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( C ))]]) ).
thf(16448,plain,
! [A: $i] :
( ( f2_s11_funct_2 @ ( A @ ( sk407 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[16382]) ).
thf(73,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(1418,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)],[73]) ).
thf(390,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(3453,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)],[390]) ).
thf(394,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(3473,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)],[394]) ).
thf(7474,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1061,7110]) ).
thf(7475,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7474]) ).
thf(7514,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( B @ k1_relat_1 )
!= sk1 )
| ( B != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7475]) ).
thf(7534,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) )
| ~ ( sk138 @ v1_relat_1 )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7514]) ).
thf(7774,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ l3_lattices ) ),
inference(rewrite,[status(thm)],[7534,2543]) ).
thf(7775,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7774]) ).
thf(935,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(6189,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)],[935]) ).
thf(109,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(1682,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)],[109]) ).
thf(27,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(1136,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)],[27]) ).
thf(817,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(5680,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)],[817]) ).
thf(647,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(4815,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)],[647]) ).
thf(4724,plain,
sk317 @ v3_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(810,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(5650,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)],[810]) ).
thf(1020,plain,
~ ( sk2 @ ( sk1 @ u1_struct_0 @ k6_domain_1 ) @ ( sk2 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ u1_struct_0 @ r1_filter_2 ) ) ),
inference(cnfConj,[status(thm)],[1019]) ).
thf(246,axiom,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(2539,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(2540,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[2539]) ).
thf(888,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(5985,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)],[888]) ).
thf(473,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(3923,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)],[473]) ).
thf(327,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(3091,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(3092,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3091]) ).
thf(3093,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3092]) ).
thf(96,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(1581,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)],[96]) ).
thf(997,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(6438,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)],[997]) ).
thf(4718,plain,
sk317 @ v4_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(998,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(6451,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)],[998]) ).
thf(8560,plain,
! [A: $i] :
( ( ( sk207 @ 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)],[3209,7078]) ).
thf(8561,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8560]) ).
thf(8562,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8561:[bind(A,$thf( sk207 ))]]) ).
thf(12355,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,8562]) ).
thf(12356,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12355]) ).
thf(12430,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12356]) ).
thf(319,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(3036,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)],[319]) ).
thf(665,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(4924,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)],[665]) ).
thf(649,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(4825,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)],[649]) ).
thf(770,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(5489,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)],[770]) ).
thf(39,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(1201,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)],[39]) ).
thf(8206,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)],[3159,7014]) ).
thf(8207,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8206]) ).
thf(8208,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8207:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(8320,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1063,8208]) ).
thf(8321,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[8320]) ).
thf(8348,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[8321]) ).
thf(8357,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ k1_relat_1 @ r1_tarski ) )
| ~ ( k1_xboole_0 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[8348]) ).
thf(11086,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8357,3170]) ).
thf(11087,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11086]) ).
thf(19,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(1102,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)],[19]) ).
thf(1103,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1102]) ).
thf(1104,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[1103]) ).
thf(1106,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1104]) ).
thf(11298,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) ) ),
inference(rewrite,[status(thm)],[11087,1106]) ).
thf(1105,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[1103]) ).
thf(1107,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1105]) ).
thf(11672,plain,
( ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) ) ),
inference(rewrite,[status(thm)],[11298,1107]) ).
thf(11673,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11672]) ).
thf(12965,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[11673,2073]) ).
thf(12966,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12965]) ).
thf(849,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(5824,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)],[849]) ).
thf(1001,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 @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k7_lattices ) )
= ( B @ ( A @ k7_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l70_filter_2) ).
thf(6474,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 @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k7_lattices ) )
= ( B @ ( A @ k7_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(683,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(5043,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(5044,plain,
( ( sk347 @ v3_lattices )
& ( sk347 @ l3_lattices ) ),
inference(cnf,[status(esa)],[5043]) ).
thf(5045,plain,
sk347 @ l3_lattices,
inference(cnfConj,[status(thm)],[5044]) ).
thf(793,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(5572,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)],[793]) ).
thf(2964,plain,
~ ( sk188 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2956]) ).
thf(1973,plain,
sk71 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[1969]) ).
thf(6589,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,3334]) ).
thf(6590,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6589]) ).
thf(6591,plain,
sk218 != sk71,
inference(simp,[status(thm)],[6590]) ).
thf(482,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(3986,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)],[482]) ).
thf(3068,plain,
sk196 @ v10_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(760,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(5448,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(494,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 @ 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 @ ( C @ m1_filter_2 ) )
=> ( B @ ( C @ m1_filter_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_filter_2) ).
thf(4033,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ 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 @ ( C @ m1_filter_2 ) )
=> ( B @ ( C @ m1_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(208,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(2281,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)],[208]) ).
thf(807,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(5643,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)],[807]) ).
thf(196,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(2190,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)],[196]) ).
thf(384,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(3412,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)],[384]) ).
thf(3413,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 ) ) )
& ! [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 ) ) ) ),
inference(miniscope,[status(thm)],[3412]) ).
thf(3414,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ k2_tarski ) @ ( D @ r1_tarski ) )
| ( D
!= ( F @ ( E @ k2_tarski ) ) ) )
& ( ( F @ ( E @ k2_tarski ) @ ( D @ r1_tarski ) )
| ( D
!= ( F @ k1_tarski ) ) )
& ( ( F @ ( E @ k2_tarski ) @ ( D @ r1_tarski ) )
| ( D
!= ( E @ k1_tarski ) ) )
& ( ( F @ ( E @ k2_tarski ) @ ( D @ r1_tarski ) )
| ( D != k1_xboole_0 ) )
& ( ( A
= ( C @ ( B @ k2_tarski ) ) )
| ( A
= ( C @ k1_tarski ) )
| ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ~ ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) ) ) ),
inference(cnf,[status(esa)],[3413]) ).
thf(3417,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[3414]) ).
thf(3420,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[3417]) ).
thf(3421,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[3420]) ).
thf(748,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(5375,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)],[748]) ).
thf(435,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(3712,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)],[435]) ).
thf(16157,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,8843]) ).
thf(16158,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16157]) ).
thf(16286,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16158]) ).
thf(16312,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16286]) ).
thf(809,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(5648,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)],[809]) ).
thf(21,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(1117,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1118,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[1117]) ).
thf(1119,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[1118]) ).
thf(99,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(1622,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)],[99]) ).
thf(2424,plain,
sk118 @ v6_lattices,
inference(cnfConj,[status(thm)],[2414]) ).
thf(730,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_2) ).
thf(5296,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( C @ r1_tarski ) )
& ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(1005,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(6498,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)],[1005]) ).
thf(740,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(5343,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)],[740]) ).
thf(428,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(3676,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)],[428]) ).
thf(856,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(5846,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)],[856]) ).
thf(186,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(2137,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)],[186]) ).
thf(590,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(4536,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)],[590]) ).
thf(479,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(3955,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)],[479]) ).
thf(356,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(3243,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)],[356]) ).
thf(966,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(6327,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)],[966]) ).
thf(2965,plain,
sk188 @ l3_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(7216,plain,
! [A: $i] :
( ( ( sk138 @ 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)],[2544,7014]) ).
thf(7217,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7216]) ).
thf(7218,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7217:[bind(A,$thf( sk138 ))]]) ).
thf(7662,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1063,7218]) ).
thf(7663,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7662]) ).
thf(7687,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk138 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7663]) ).
thf(7702,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk138 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7687]) ).
thf(8442,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7702,2543]) ).
thf(8443,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[8442]) ).
thf(611,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(4628,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)],[611]) ).
thf(527,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(4211,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)],[527]) ).
thf(885,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(5970,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)],[885]) ).
thf(941,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(6210,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)],[941]) ).
thf(111,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(1696,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)],[111]) ).
thf(867,axiom,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(5907,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(5908,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[5907]) ).
thf(43891,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5908,1217]) ).
thf(43892,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43891]) ).
thf(43893,plain,
~ ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[43892:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ k8_subset_1 ))]]) ).
thf(44110,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,43893]) ).
thf(44111,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44110]) ).
thf(44148,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk71 ),
inference(simp,[status(thm)],[44111]) ).
thf(3184,plain,
k6_nat_lat @ v10_lattices,
inference(cnfConj,[status(thm)],[3175]) ).
thf(308,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(2982,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)],[308]) ).
thf(504,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(4082,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)],[504]) ).
thf(7419,plain,
! [A: $i] :
( ( ( sk138 @ 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)],[2544,7078]) ).
thf(7420,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7419]) ).
thf(7421,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7420:[bind(A,$thf( sk138 ))]]) ).
thf(7653,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1063,7421]) ).
thf(7654,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7653]) ).
thf(7694,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7654]) ).
thf(7709,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk138 @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7694]) ).
thf(9841,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[7709,2543]) ).
thf(9842,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[9841]) ).
thf(11703,plain,
( ( ( sk138 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[1107,9842]) ).
thf(11704,plain,
( ( ( sk138 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11703]) ).
thf(11710,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11704]) ).
thf(15868,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[2073,11710]) ).
thf(15869,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15868]) ).
thf(15912,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15869]) ).
thf(15922,plain,
( ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15912]) ).
thf(15932,plain,
( ( ( sk138 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[1106,15922]) ).
thf(15933,plain,
( ( ( sk138 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15932]) ).
thf(15955,plain,
( ( sk138 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15933]) ).
thf(15958,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15955]) ).
thf(400,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(3510,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)],[400]) ).
thf(501,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(4065,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(387,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(3435,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)],[387]) ).
thf(2954,plain,
sk187 @ v8_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(702,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(5174,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(754,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(5406,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)],[754]) ).
thf(860,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(5875,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)],[860]) ).
thf(39615,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2123,1243]) ).
thf(39616,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[39615]) ).
thf(39635,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk80 )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[39616]) ).
thf(39650,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= ( B @ sk80 ) ),
inference(simp,[status(thm)],[39635]) ).
thf(7111,plain,
! [A: $i] :
( ( ( sk71 @ 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)],[1971,6969]) ).
thf(7112,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7111]) ).
thf(7113,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7112:[bind(A,$thf( sk71 ))]]) ).
thf(12379,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,7113]) ).
thf(12380,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12379]) ).
thf(12457,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12380]) ).
thf(786,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 ) )
=> ( ! [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 ) ) ) ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_filter_2) ).
thf(5545,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 @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m2_lattice4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(12402,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,9124]) ).
thf(12403,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12402]) ).
thf(12428,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk315 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12403]) ).
thf(12474,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12428]) ).
thf(140,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(1915,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)],[140]) ).
thf(2737,plain,
sk157 @ l3_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(103,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(1636,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)],[103]) ).
thf(13,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(1074,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)],[13]) ).
thf(300,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(2922,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)],[300]) ).
thf(33269,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ 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
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[29740,7014]) ).
thf(33270,plain,
! [A: $i] :
( ( ( sk1 @ sk19 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[33269]) ).
thf(33271,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ m2_relset_1 ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(pattern_uni,[status(thm)],[33270:[bind(A,$thf( sk1 @ sk19 ))]]) ).
thf(35046,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[4684,33271]) ).
thf(35047,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[35046]) ).
thf(35105,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( ( sk1 @ sk19 )
!= sk315 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[35047]) ).
thf(314,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(3011,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)],[314]) ).
thf(673,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(4962,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)],[673]) ).
thf(781,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(5530,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)],[781]) ).
thf(2473,plain,
k13_nat_lat @ v10_lattices,
inference(cnfConj,[status(thm)],[2470]) ).
thf(7567,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1061,7424]) ).
thf(7568,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7567]) ).
thf(7585,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( B @ k1_relat_1 )
!= sk1 )
| ( B != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7568]) ).
thf(7586,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) )
| ~ ( sk71 @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7585]) ).
thf(8045,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[7586,1970]) ).
thf(8046,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[8045]) ).
thf(59,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(1306,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)],[59]) ).
thf(680,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(5017,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(8159,plain,
( ( ( sk364 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,5246]) ).
thf(8160,plain,
( ( sk364 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8159]) ).
thf(8183,plain,
sk364 != k1_xboole_0,
inference(simp,[status(thm)],[8160]) ).
thf(32129,plain,
! [A: $i] :
( ( A != sk364 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,8183]) ).
thf(32130,plain,
! [A: $i] :
( ( A != sk364 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[32129]) ).
thf(32131,plain,
sk364 @ sk19 @ v1_funct_1,
inference(pattern_uni,[status(thm)],[32130:[bind(A,$thf( sk364 ))]]) ).
thf(34380,plain,
! [A: $i] :
( ( ( sk364 @ sk19 @ 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)],[32131,7014]) ).
thf(34381,plain,
! [A: $i] :
( ( ( sk364 @ sk19 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[34380]) ).
thf(34382,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[34381:[bind(A,$thf( sk364 @ sk19 ))]]) ).
thf(589,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(4531,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)],[589]) ).
thf(1199,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)],[1197]) ).
thf(219,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(2361,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)],[219]) ).
thf(2362,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk110 ) @ v1_funct_1 )
& ( A @ ( B @ sk110 ) @ v1_relat_1 )
& ( B @ ( A @ ( A @ ( B @ sk110 ) @ m1_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[2361]) ).
thf(2364,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2362]) ).
thf(194,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(2164,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)],[194]) ).
thf(928,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(6139,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)],[928]) ).
thf(3812,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk251 @ m1_subset_1 ) ),
inference(cnfConj,[status(thm)],[3811]) ).
thf(18851,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( A @ sk251 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1951,3812]) ).
thf(18852,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ sk251 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[18851:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(12325,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,8568]) ).
thf(12326,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12325]) ).
thf(12446,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk207 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12326]) ).
thf(169,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(2047,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)],[169]) ).
thf(695,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(5117,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)],[695]) ).
thf(443,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(3767,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)],[443]) ).
thf(201,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(2232,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)],[201]) ).
thf(784,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(5540,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)],[784]) ).
thf(11,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(1064,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)],[11]) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk6 ) ) ) )
| ~ ( 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 @ ( B @ m1_subset_1 ) ) )
& ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk6 ) ) @ m1_subset_1 ) )
| ~ ( 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 @ ( B @ m1_subset_1 ) ) )
& ( ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ~ ( 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 @ ( B @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[1064]) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk6 ) ) @ m1_subset_1 ) )
| ~ ( 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 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1065]) ).
thf(118,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(1736,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)],[118]) ).
thf(499,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(4059,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)],[499]) ).
thf(222,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(2382,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)],[222]) ).
thf(11681,plain,
( ( ( sk138 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1107,8443]) ).
thf(11682,plain,
( ( ( sk138 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11681]) ).
thf(11707,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11682]) ).
thf(13419,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2073,11707]) ).
thf(13420,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13419]) ).
thf(13453,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13420]) ).
thf(13460,plain,
( ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13453]) ).
thf(13615,plain,
( ( ( sk138 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1106,13460]) ).
thf(13616,plain,
( ( ( sk138 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13615]) ).
thf(13638,plain,
( ( sk138 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13616]) ).
thf(13644,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13638]) ).
thf(447,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(3795,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)],[447]) ).
thf(1057,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ 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)],[1055]) ).
thf(253,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(2589,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)],[253]) ).
thf(16,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(1091,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)],[16]) ).
thf(816,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(5670,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)],[816]) ).
thf(1021,plain,
sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[1019]) ).
thf(40081,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( A @ k1_tarski @ k1_zfmisc_1 @ ( B @ k1_tarski @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[2046,3421]) ).
thf(40082,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[40081:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(40160,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[40082]) ).
thf(40661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40160,1079]) ).
thf(40662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[40661]) ).
thf(40663,plain,
! [B: $i,A: $i] : ( B @ k1_tarski @ k1_zfmisc_1 @ ( A @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[40662:[bind(A,$thf( G )),bind(B,$thf( k1_xboole_0 @ k1_tarski )),bind(C,$thf( G @ k1_tarski @ k1_zfmisc_1 )),bind(D,$thf( D ))]]) ).
thf(40735,plain,
! [B: $i,A: $i] : ( B @ k1_tarski @ k1_zfmisc_1 @ ( A @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[40663]) ).
thf(663,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(4920,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)],[663]) ).
thf(50,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(1253,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)],[50]) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1253]) ).
thf(1255,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1254]) ).
thf(128,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(1824,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)],[128]) ).
thf(1008,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 @ k5_filter_2 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
thf(6509,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 @ k5_filter_2 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(617,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(4661,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)],[617]) ).
thf(9104,plain,
! [A: $i] :
( ( ( sk315 @ 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)],[4682,7078]) ).
thf(9105,plain,
! [A: $i] :
( ( ( sk315 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9104]) ).
thf(9106,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9105:[bind(A,$thf( sk315 ))]]) ).
thf(16237,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,9106]) ).
thf(16238,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16237]) ).
thf(16282,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk315 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[16238]) ).
thf(16307,plain,
( ( sk315 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[16282]) ).
thf(233,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(2441,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)],[233]) ).
thf(712,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(5206,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)],[712]) ).
thf(267,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(2673,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)],[267]) ).
thf(137,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(1900,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)],[137]) ).
thf(115,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(1723,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)],[115]) ).
thf(358,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(3261,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)],[358]) ).
thf(970,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(6343,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)],[970]) ).
thf(256,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(2601,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)],[256]) ).
thf(922,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(6122,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)],[922]) ).
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(1123,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(659,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(4878,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)],[659]) ).
thf(795,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(5579,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)],[795]) ).
thf(1015,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(6528,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)],[1015]) ).
thf(676,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(4989,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)],[676]) ).
thf(741,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(5346,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)],[741]) ).
thf(5347,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk377 @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) )
| ~ ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk375 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk377 @ m2_relset_1 ) ) )
| ~ sk375 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk377 @ v1_funct_2 ) ) )
| ~ sk375 )
& ( ( sk377 @ v1_funct_1 )
| ~ sk375 )
& ( sk375
| ~ ( A @ ( sk376 @ p1_s3_funct_2 ) )
| ~ ( f2_s3_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk375
| ( f1_s3_funct_2 @ ( sk376 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[5346]) ).
thf(5349,plain,
( sk375
| ( f1_s3_funct_2 @ ( sk376 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[5347]) ).
thf(189,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(2147,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)],[189]) ).
thf(585,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(4521,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)],[585]) ).
thf(483,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(3989,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)],[483]) ).
thf(3069,plain,
sk196 @ v16_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(764,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(5470,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)],[764]) ).
thf(302,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(2937,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)],[302]) ).
thf(580,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(4499,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)],[580]) ).
thf(29860,plain,
! [A: $i] :
( ( A != sk197 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,3072]) ).
thf(29861,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk197 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29860:[bind(A,$thf( sk197 ))]]) ).
thf(776,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(5507,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)],[776]) ).
thf(451,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(3814,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)],[451]) ).
thf(750,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(5396,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)],[750]) ).
thf(496,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(4044,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)],[496]) ).
thf(363,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(3286,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)],[363]) ).
thf(2958,plain,
sk188 @ v3_filter_0,
inference(cnfConj,[status(thm)],[2956]) ).
thf(812,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(5655,plain,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(367,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(3314,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)],[367]) ).
thf(419,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(3600,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)],[419]) ).
thf(333,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(3126,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(3127,plain,
~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[3126]) ).
thf(3128,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[3127]) ).
thf(8175,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,3128]) ).
thf(8176,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8175]) ).
thf(8180,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8176]) ).
thf(31850,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( B @ k1_funct_2 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,8180]) ).
thf(31851,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( B @ k1_funct_2 ) ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[31850]) ).
thf(31852,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk19 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[31851:[bind(A,$thf( D @ ( D @ k1_funct_2 ) )),bind(B,$thf( D ))]]) ).
thf(32904,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk19 @ v1_funct_1 ),
inference(simp,[status(thm)],[31852]) ).
thf(1208,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)],[1207]) ).
thf(1210,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)],[1208]) ).
thf(29892,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,8182]) ).
thf(29893,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[29892]) ).
thf(29894,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ sk19 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[29893:[bind(A,$thf( C @ k1_zfmisc_1 )),bind(B,$thf( C ))]]) ).
thf(32946,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ sk19 @ v1_funct_1 ),
inference(simp,[status(thm)],[29894]) ).
thf(503,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(4080,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)],[503]) ).
thf(3264,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)],[3263]) ).
thf(3265,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)],[3264]) ).
thf(3267,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3265]) ).
thf(3270,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3267]) ).
thf(3271,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3270]) ).
thf(545,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(4295,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)],[545]) ).
thf(960,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(6303,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)],[960]) ).
thf(8794,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,4064]) ).
thf(8795,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8794]) ).
thf(8810,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk216 ),
inference(simp,[status(thm)],[8795]) ).
thf(8029,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,4698]) ).
thf(8030,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8029]) ).
thf(8039,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk152 ),
inference(simp,[status(thm)],[8030]) ).
thf(26522,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk152 ) ),
inference(paramod_ordered,[status(thm)],[2046,8039]) ).
thf(26523,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk152 ),
inference(pattern_uni,[status(thm)],[26522:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(26563,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk152 ),
inference(simp,[status(thm)],[26523]) ).
thf(5693,plain,
( ( ( f4_s11_funct_2 @ ( sk407 @ ( 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)],[5691]) ).
thf(5702,plain,
( ( ( f4_s11_funct_2 @ ( sk407 @ ( 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)],[5693]) ).
thf(292,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(2873,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)],[292]) ).
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(1025,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(1026,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)],[1025]) ).
thf(1028,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)],[1026]) ).
thf(1031,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)],[1028]) ).
thf(1032,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)],[1031]) ).
thf(481,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(3980,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)],[481]) ).
thf(14730,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,1129]) ).
thf(14731,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14730]) ).
thf(14732,plain,
f2_s4_funct_2 @ ( sk315 @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[14731:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk315 ))]]) ).
thf(1092,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)],[1091]) ).
thf(1093,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)],[1092]) ).
thf(14783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk315 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14732,1093]) ).
thf(14784,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk315 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14783]) ).
thf(14785,plain,
! [A: $i] : ( sk315 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14784:[bind(A,$thf( sk315 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14804,plain,
! [A: $i] : ( sk315 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14785]) ).
thf(14215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,1128]) ).
thf(14216,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14215]) ).
thf(14217,plain,
f1_s4_funct_2 @ ( sk315 @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[14216:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk315 ))]]) ).
thf(521,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(4192,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)],[521]) ).
thf(266,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(2670,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)],[266]) ).
thf(763,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(5465,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)],[763]) ).
thf(606,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(4608,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)],[606]) ).
thf(8020,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,3128]) ).
thf(8021,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8020]) ).
thf(8026,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk152 ),
inference(simp,[status(thm)],[8021]) ).
thf(2477,plain,
k13_nat_lat @ v3_lattices,
inference(cnfConj,[status(thm)],[2470]) ).
thf(380,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(3403,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(4725,plain,
sk317 @ v11_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(3065,plain,
sk196 @ v8_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(409,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(3556,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ 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)],[409]) ).
thf(34,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(1178,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)],[34]) ).
thf(956,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(6292,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)],[956]) ).
thf(12319,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,8843]) ).
thf(12320,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12319]) ).
thf(12461,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12320]) ).
thf(195,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(2179,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)],[195]) ).
thf(130,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(1836,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)],[130]) ).
thf(694,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( A @ ( B @ v1_filter_2 ) )
<=> ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v2_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_2) ).
thf(5113,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v2_filter_0 ) )
=> ( A @ ( B @ v1_filter_2 ) ) )
& ( ( A @ ( B @ v1_filter_2 ) )
=> ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v2_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(44133,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,43893]) ).
thf(44134,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44133]) ).
thf(44149,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk216 ),
inference(simp,[status(thm)],[44134]) ).
thf(2213,plain,
sk94 @ l3_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(27236,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( A @ k1_tarski @ k1_zfmisc_1 @ ( B @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[2046,3617]) ).
thf(27237,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[27236:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(27277,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[27237]) ).
thf(37,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(1189,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)],[37]) ).
thf(1190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ v3_binop_1 ) )
| ( ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk12 ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ sk12 ) ) )
| ~ ( 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 ) )
| ( A @ ( A @ ( B @ sk12 ) @ m1_subset_1 ) )
| ~ ( 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 @ ( B @ k1_binop_1 ) ) )
= C )
| ~ ( A @ ( C @ m1_subset_1 ) )
| ~ ( A @ ( B @ v3_binop_1 ) )
| ~ ( 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)],[1189]) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ v3_binop_1 ) )
| ( ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk12 ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ sk12 ) ) )
| ~ ( 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)],[1190]) ).
thf(1195,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ v3_binop_1 ) )
| ~ ( 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 @ sk12 ) @ ( A @ ( B @ sk12 ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ sk12 ) ) ) ),
inference(lifteq,[status(thm)],[1193]) ).
thf(2211,plain,
sk94 @ v7_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(6255,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk448 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk448 @ r2_hidden ) )
| sk446 ),
inference(cnfConj,[status(thm)],[6251]) ).
thf(6267,plain,
( ( sk448 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk448 @ r2_hidden ) )
| sk446
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[6255]) ).
thf(29979,plain,
! [A: $i] :
( ( A != sk207 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,16304]) ).
thf(29980,plain,
! [A: $i] :
( ( A != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[29979]) ).
thf(29981,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( sk207 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29980:[bind(A,$thf( sk207 ))]]) ).
thf(437,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(3727,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)],[437]) ).
thf(2741,plain,
sk157 @ v11_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(9076,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,3128]) ).
thf(9077,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9076]) ).
thf(9080,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk296 ),
inference(simp,[status(thm)],[9077]) ).
thf(102,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(1634,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)],[102]) ).
thf(4732,plain,
sk317 @ v17_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(878,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(5936,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)],[878]) ).
thf(779,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(5515,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)],[779]) ).
thf(13054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,4698]) ).
thf(13055,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13054]) ).
thf(13063,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk251 )
!= ( C @ ( B @ k2_tarski ) ) ),
inference(simp,[status(thm)],[13055]) ).
thf(857,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( B @ ( A @ r2_filter_2 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_filter_2) ).
thf(5854,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) )
=> ( B @ ( A @ r2_filter_2 ) ) )
& ( ( B @ ( A @ r2_filter_2 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
| ( C
= ( A @ u1_struct_0 ) ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(446,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(3784,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)],[446]) ).
thf(671,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(4957,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)],[671]) ).
thf(271,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(2692,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)],[271]) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1201]) ).
thf(1203,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1202]) ).
thf(1204,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1203]) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
= A ),
inference(cnf,[status(esa)],[1204]) ).
thf(40565,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
= A ),
inference(lifteq,[status(thm)],[1205]) ).
thf(796,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 @ k18_filter_2 ) )
= ( A @ u1_struct_0 ) )
& ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_filter_2) ).
thf(5583,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 @ k18_filter_2 ) )
= ( A @ u1_struct_0 ) )
& ~ ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(422,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(3632,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)],[422]) ).
thf(3078,plain,
sk197 @ v4_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(7490,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1061,7218]) ).
thf(7491,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7490]) ).
thf(7518,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( B @ k1_relat_1 )
!= sk1 )
| ( B != sk138 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7491]) ).
thf(7538,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) )
| ~ ( sk138 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7518]) ).
thf(7873,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7538,2543]) ).
thf(7874,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[7873]) ).
thf(1085,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( 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 ) ) ) )
| ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( 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 @ ( 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)],[1081]) ).
thf(1089,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( 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 @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_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(lifteq,[status(thm)],[1085]) ).
thf(469,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(3909,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)],[469]) ).
thf(47,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(1234,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)],[47]) ).
thf(969,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(6339,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)],[969]) ).
thf(455,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(3831,plain,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(28,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(1141,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)],[28]) ).
thf(1142,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)],[1141]) ).
thf(1143,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)],[1142]) ).
thf(2946,plain,
sk187 @ l3_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(27242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( C @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3617,3033]) ).
thf(27243,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[27242]) ).
thf(27273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) )
!= k1_xboole_0 )
| ( A != C ) ),
inference(simp,[status(thm)],[27243]) ).
thf(27282,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k2_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[27273]) ).
thf(52,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(1259,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)],[52]) ).
thf(92,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(1534,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)],[92]) ).
thf(932,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(6153,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)],[932]) ).
thf(980,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(6375,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)],[980]) ).
thf(937,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(6195,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)],[937]) ).
thf(1002,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(6477,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)],[1002]) ).
thf(307,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(2973,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)],[307]) ).
thf(252,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(2577,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)],[252]) ).
thf(277,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(2709,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)],[277]) ).
thf(45,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(1227,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)],[45]) ).
thf(134,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(1878,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)],[134]) ).
thf(280,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(2726,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1137,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)],[1136]) ).
thf(1138,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)],[1137]) ).
thf(532,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(4227,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)],[532]) ).
thf(29749,plain,
! [A: $i] :
( ( A != sk317 )
| ( k1_xboole_0 @ v5_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,4728]) ).
thf(29750,plain,
( ( k1_xboole_0 @ v5_lattices )
| ( sk317 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29749:[bind(A,$thf( sk317 ))]]) ).
thf(355,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(3237,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)],[355]) ).
thf(8800,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,4698]) ).
thf(8801,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8800]) ).
thf(8815,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk216 ),
inference(simp,[status(thm)],[8801]) ).
thf(773,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(5497,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)],[773]) ).
thf(312,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(3001,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)],[312]) ).
thf(3060,plain,
sk196 @ l3_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(3176,plain,
k6_nat_lat @ v3_lattices,
inference(cnfConj,[status(thm)],[3175]) ).
thf(326,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(3087,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)],[326]) ).
thf(317,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(3018,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)],[317]) ).
thf(648,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(4817,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)],[648]) ).
thf(35006,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[2269,33271]) ).
thf(35007,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[35006]) ).
thf(35102,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( ( sk1 @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[35007]) ).
thf(35111,plain,
( ( ( sk1 @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk1 @ sk19 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 ) ),
inference(simp,[status(thm)],[35102]) ).
thf(236,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(2460,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)],[236]) ).
thf(5939,plain,
( ~ ( sk421 @ v3_struct_0 )
& ( sk421 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[5938]) ).
thf(5941,plain,
~ ( sk421 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5939]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ 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 @ k8_filter_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_filter_2) ).
thf(6175,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_lattice2 @ 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 @ k8_filter_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(3179,plain,
k6_nat_lat @ v7_lattices,
inference(cnfConj,[status(thm)],[3175]) ).
thf(675,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(4983,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)],[675]) ).
thf(35,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(1182,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)],[35]) ).
thf(2419,plain,
sk118 @ v1_lattice2,
inference(cnfConj,[status(thm)],[2414]) ).
thf(74,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(1424,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)],[74]) ).
thf(31,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(1157,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)],[31]) ).
thf(1158,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)],[1157]) ).
thf(1160,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)],[1158]) ).
thf(478,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(3952,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)],[478]) ).
thf(293,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(2877,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)],[293]) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ m1_subset_1 ) )
| ~ ( 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 @ ( 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)],[1081]) ).
thf(163,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(2023,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)],[163]) ).
thf(687,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(5075,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)],[687]) ).
thf(7554,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,5317]) ).
thf(7555,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7554]) ).
thf(7559,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk71 ),
inference(simp,[status(thm)],[7555]) ).
thf(847,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(5818,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)],[847]) ).
thf(30579,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,1021]) ).
thf(30580,plain,
( ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
| ( sk1 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[30579:[bind(A,$thf( sk1 ))]]) ).
thf(106,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(1659,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)],[106]) ).
thf(382,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(3407,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(351,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(3210,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)],[351]) ).
thf(328,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(3094,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)],[328]) ).
thf(4721,plain,
~ ( sk317 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4716]) ).
thf(725,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(5253,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)],[725]) ).
thf(738,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(5337,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(841,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(5786,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)],[841]) ).
thf(13058,plain,
! [B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,3128]) ).
thf(13059,plain,
! [B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13058]) ).
thf(13066,plain,
! [B: $i,A: $i] :
( ( A @ sk251 )
!= ( B @ ( B @ k1_funct_2 ) ) ),
inference(simp,[status(thm)],[13059]) ).
thf(97,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(1584,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)],[97]) ).
thf(798,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(5588,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)],[798]) ).
thf(121,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(1791,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)],[121]) ).
thf(656,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(4861,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)],[656]) ).
thf(3415,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( C @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[3414]) ).
thf(3427,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( C @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[3415]) ).
thf(3428,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[3427]) ).
thf(9064,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,5317]) ).
thf(9065,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9064]) ).
thf(9085,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk296 ),
inference(simp,[status(thm)],[9065]) ).
thf(986,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(6395,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)],[986]) ).
thf(1006,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(6501,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)],[1006]) ).
thf(364,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(3296,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(3297,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(cnf,[status(esa)],[3296]) ).
thf(3298,plain,
! [A: $i] :
( ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) )
= ( A @ k2_subset_1 ) ),
inference(lifteq,[status(thm)],[3297]) ).
thf(40042,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_subset_1 ) )
= A ),
inference(rewrite,[status(thm)],[3298,2548,3093]) ).
thf(181,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(2108,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)],[181]) ).
thf(6713,plain,
! [B: $i,A: $i] :
( ( ( sk138 @ 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)],[2543,1048]) ).
thf(6714,plain,
! [B: $i,A: $i] :
( ( ( sk138 @ 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)],[6713]) ).
thf(6715,plain,
! [A: $i] : ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6714:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).
thf(15537,plain,
! [A: $i] :
( ( ( sk138 @ 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)],[2543,1135]) ).
thf(15538,plain,
! [A: $i] :
( ( ( sk138 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15537]) ).
thf(15539,plain,
( ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) )
= ( sk138 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15538:[bind(A,$thf( sk138 ))]]) ).
thf(21572,plain,
! [A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6715,15539]) ).
thf(866,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(5905,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)],[866]) ).
thf(574,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(4457,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)],[574]) ).
thf(951,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(6275,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)],[951]) ).
thf(2472,plain,
k13_nat_lat @ v8_lattices,
inference(cnfConj,[status(thm)],[2470]) ).
thf(261,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(2649,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)],[261]) ).
thf(8653,plain,
! [B: $i,A: $i] :
( ( ( sk216 @ 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)],[3322,1048]) ).
thf(8654,plain,
! [B: $i,A: $i] :
( ( ( sk216 @ 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)],[8653]) ).
thf(8655,plain,
! [A: $i] : ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8654:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).
thf(15514,plain,
! [A: $i] :
( ( ( sk216 @ 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)],[3322,1135]) ).
thf(15515,plain,
! [A: $i] :
( ( ( sk216 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15514]) ).
thf(15516,plain,
( ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) )
= ( sk216 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15515:[bind(A,$thf( sk216 ))]]) ).
thf(23769,plain,
! [A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[8655,15516]) ).
thf(23789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23769,1079]) ).
thf(23790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[23789]) ).
thf(23791,plain,
! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[23790:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk216 @ k9_relat_1 ) )),bind(C,$thf( sk216 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(23874,plain,
! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[23791]) ).
thf(30,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(1152,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)],[30]) ).
thf(1153,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)],[1152]) ).
thf(1155,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)],[1153]) ).
thf(633,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(4736,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)],[633]) ).
thf(901,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 ) )
=> ( B @ ( C @ ( A @ k20_filter_2 ) ) @ ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_2) ).
thf(6033,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 ) )
=> ( B @ ( C @ ( A @ k20_filter_2 ) ) @ ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(53,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(1266,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)],[53]) ).
thf(806,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(5639,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)],[806]) ).
thf(4717,plain,
sk317 @ v15_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(155,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(1984,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)],[155]) ).
thf(49,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(1246,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)],[49]) ).
thf(472,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(3920,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)],[472]) ).
thf(305,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(2968,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)],[305]) ).
thf(242,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(2504,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)],[242]) ).
thf(425,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(3656,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)],[425]) ).
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 @ 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(6134,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)],[926]) ).
thf(396,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(3486,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)],[396]) ).
thf(17,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(1094,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)],[17]) ).
thf(1095,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)],[1094]) ).
thf(1097,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)],[1095]) ).
thf(1099,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)],[1097]) ).
thf(83,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(1478,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)],[83]) ).
thf(767,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(5481,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)],[767]) ).
thf(915,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(6097,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)],[915]) ).
thf(245,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(2536,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)],[245]) ).
thf(270,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(2681,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)],[270]) ).
thf(582,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 @ 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 @ ( C @ m2_filter_2 ) )
=> ( B @ ( C @ m2_filter_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_filter_2) ).
thf(4508,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ( A @ 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 @ ( C @ m2_filter_2 ) )
=> ( B @ ( C @ m2_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1367,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)],[1366]) ).
thf(1368,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) )
& ( ( B
= ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( B @ sk25 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( B @ sk25 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) )
& ( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) )
& ( ( B
= ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
| ( A = k1_xboole_0 ) )
& ( ( A @ ( B @ sk25 ) @ v1_funct_1 )
| ( A = k1_xboole_0 ) )
& ( ( A @ ( B @ sk25 ) @ v1_relat_1 )
| ( A = k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1367]) ).
thf(1375,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1368]) ).
thf(1381,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk25 ) @ k1_relat_1 )
= B )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1375]) ).
thf(1382,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk25 ) @ k1_relat_1 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1381]) ).
thf(12397,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,8574]) ).
thf(12398,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12397]) ).
thf(12429,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12398]) ).
thf(3059,plain,
sk196 @ v7_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(151,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(1974,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)],[151]) ).
thf(995,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(6433,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)],[995]) ).
thf(940,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(6207,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)],[940]) ).
thf(925,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(6129,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)],[925]) ).
thf(886,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(5973,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)],[886]) ).
thf(1192,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ v3_binop_1 ) )
| ( A @ ( A @ ( B @ sk12 ) @ m1_subset_1 ) )
| ~ ( 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)],[1190]) ).
thf(7481,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1061,7421]) ).
thf(7482,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7481]) ).
thf(7521,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( B @ k1_relat_1 )
!= sk1 )
| ( B != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7482]) ).
thf(7523,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) )
| ~ ( sk138 @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7521]) ).
thf(7737,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[7523,2543]) ).
thf(7738,plain,
( ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7737]) ).
thf(839,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 @ k1_lattice2 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k6_filter_2 ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k1_lattice2 @ k7_lattices ) ) )
& ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k7_lattices ) )
= ( B @ ( A @ k7_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_2) ).
thf(5776,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 @ k1_lattice2 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k6_filter_2 ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k1_lattice2 @ k7_lattices ) ) )
& ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k7_lattices ) )
= ( B @ ( A @ k7_lattices ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(818,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(5683,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)],[818]) ).
thf(133,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(1874,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)],[133]) ).
thf(732,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(5305,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)],[732]) ).
thf(75,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(1429,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)],[75]) ).
thf(716,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
<=> ( A @ k1_lattice2 @ ( B @ m1_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_filter_2) ).
thf(5217,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ k1_lattice2 @ ( B @ m1_filter_2 ) )
=> ( A @ ( B @ m2_filter_2 ) ) )
& ( ( A @ ( B @ m2_filter_2 ) )
=> ( A @ k1_lattice2 @ ( B @ m1_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(3064,plain,
sk196 @ v13_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(801,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(5603,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)],[801]) ).
thf(746,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(5369,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)],[746]) ).
thf(153,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(1979,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)],[153]) ).
thf(3074,plain,
sk197 @ v13_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(502,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(4069,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)],[502]) ).
thf(3083,plain,
sk197 @ v3_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(348,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(3201,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)],[348]) ).
thf(531,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(4223,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)],[531]) ).
thf(220,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(2366,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)],[220]) ).
thf(2367,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk111 ) @ v1_funct_2 ) ) )
& ( A @ ( B @ sk111 ) @ v1_funct_1 )
& ( A @ ( B @ sk111 ) @ v1_relat_1 )
& ( B @ ( A @ ( A @ ( B @ sk111 ) @ m1_relset_1 ) ) ) ),
inference(cnf,[status(esa)],[2366]) ).
thf(2370,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2367]) ).
thf(352,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(3215,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)],[352]) ).
thf(457,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(3834,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)],[457]) ).
thf(9066,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,4064]) ).
thf(9067,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9066]) ).
thf(9081,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk296 ),
inference(simp,[status(thm)],[9067]) ).
thf(126,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(1814,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)],[126]) ).
thf(2208,plain,
sk94 @ v9_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(12974,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[2073,9552]) ).
thf(12975,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12974]) ).
thf(13010,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk71 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12975]) ).
thf(13026,plain,
( ( ( sk71 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13010]) ).
thf(852,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
=> ( A @ k6_lattices @ ( A @ k18_filter_2 ) @ ( A @ k17_filter_2 @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_2) ).
thf(5833,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
=> ( A @ k6_lattices @ ( A @ k18_filter_2 ) @ ( A @ k17_filter_2 @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(868,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(5909,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)],[868]) ).
thf(1183,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)],[1182]) ).
thf(1184,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)],[1183]) ).
thf(1185,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)],[1184]) ).
thf(859,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(5872,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)],[859]) ).
thf(117,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(1732,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)],[117]) ).
thf(296,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(2909,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)],[296]) ).
thf(1010,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_2) ).
thf(6514,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(467,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(3903,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)],[467]) ).
thf(788,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(5557,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)],[788]) ).
thf(831,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(5747,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)],[831]) ).
thf(824,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(5711,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)],[824]) ).
thf(753,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(5402,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)],[753]) ).
thf(610,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(4625,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)],[610]) ).
thf(417,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(3587,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)],[417]) ).
thf(3183,plain,
~ ( k6_nat_lat @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3175]) ).
thf(462,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 @ ( 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 ) ) ) ) )
=> ( A @ ( B @ m2_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_2) ).
thf(3856,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 @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m2_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(43854,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
!= ( sk14 @ ( A @ m1_subset_1 ) ) )
| ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1021,1217]) ).
thf(43855,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
!= ( sk14 @ ( A @ m1_subset_1 ) ) )
| ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43854]) ).
thf(43961,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ( sk2 != A )
| ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43855]) ).
thf(43991,plain,
( ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[43961]) ).
thf(44556,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,43991]) ).
thf(44557,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[44556]) ).
thf(44599,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= k1_xboole_0 )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[44557]) ).
thf(11686,plain,
( ( ( sk138 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(paramod_ordered,[status(thm)],[1107,9512]) ).
thf(11687,plain,
( ( ( sk138 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[11686]) ).
thf(11709,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[11687]) ).
thf(14657,plain,
( ( ( sk138 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(paramod_ordered,[status(thm)],[1106,11709]) ).
thf(14688,plain,
( ( sk138 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[14657]) ).
thf(14695,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[14688]) ).
thf(14707,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ l3_lattices ) ),
inference(rewrite,[status(thm)],[14695,2073]) ).
thf(14708,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[14707]) ).
thf(366,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(3306,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)],[366]) ).
thf(7409,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,4064]) ).
thf(7410,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7409]) ).
thf(7414,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk71 ),
inference(simp,[status(thm)],[7410]) ).
thf(174,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(2076,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)],[174]) ).
thf(283,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(2748,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)],[283]) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( A @ k1_relat_1 @ ( A @ ( B @ sk10 ) @ 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)],[1163]) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( A @ k1_relat_1 @ ( A @ ( B @ sk10 ) @ 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)],[1168]) ).
thf(2963,plain,
sk188 @ v7_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(298,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(2915,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(232,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(2439,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(2440,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(cnf,[status(esa)],[2439]) ).
thf(226,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(2408,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)],[226]) ).
thf(285,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(2793,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)],[285]) ).
thf(713,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(5209,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)],[713]) ).
thf(199,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(2221,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)],[199]) ).
thf(495,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(4036,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)],[495]) ).
thf(14760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk315 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14732,1079]) ).
thf(14761,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk315 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14760]) ).
thf(14762,plain,
! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk315 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14761:[bind(A,$thf( sk315 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14806,plain,
! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk315 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14762]) ).
thf(15296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( A @ ( sk315 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14806,1079]) ).
thf(15297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( A @ ( sk315 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[15296]) ).
thf(15298,plain,
! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk315 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[15297:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk315 @ k2_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f2_s4_funct_2 )),bind(D,$thf( D ))]]) ).
thf(15344,plain,
! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk315 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[15298]) ).
thf(778,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ( A @ ( A @ k5_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_2) ).
thf(5513,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
=> ( A @ ( A @ k5_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(2423,plain,
sk118 @ l3_lattices,
inference(cnfConj,[status(thm)],[2414]) ).
thf(44045,plain,
( ( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,43863]) ).
thf(44046,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44045]) ).
thf(44066,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk296 ),
inference(simp,[status(thm)],[44046]) ).
thf(1013,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 @ k20_filter_2 ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_filter_2) ).
thf(6524,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 @ k20_filter_2 ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(55,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(1278,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)],[55]) ).
thf(629,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(4708,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)],[629]) ).
thf(223,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(2391,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)],[223]) ).
thf(321,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(3042,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)],[321]) ).
thf(761,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(5451,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(16165,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,8568]) ).
thf(16166,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16165]) ).
thf(16285,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16166]) ).
thf(16311,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16285]) ).
thf(562,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(4393,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(876,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(5928,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)],[876]) ).
thf(991,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(6422,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)],[991]) ).
thf(752,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(5400,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)],[752]) ).
thf(373,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(3343,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)],[373]) ).
thf(433,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(3707,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)],[433]) ).
thf(815,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(5666,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)],[815]) ).
thf(86,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(1510,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)],[86]) ).
thf(768,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(5483,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)],[768]) ).
thf(892,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(5996,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)],[892]) ).
thf(906,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(6053,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)],[906]) ).
thf(780,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(5524,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)],[780]) ).
thf(397,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(3491,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)],[397]) ).
thf(8033,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,4698]) ).
thf(8034,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8033]) ).
thf(8040,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk71 ),
inference(simp,[status(thm)],[8034]) ).
thf(3079,plain,
~ ( sk197 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3071]) ).
thf(251,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(2570,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)],[251]) ).
thf(11736,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk71 ) ),
inference(paramod_ordered,[status(thm)],[1951,7414]) ).
thf(11737,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk71 ),
inference(pattern_uni,[status(thm)],[11736:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(616,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(4657,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)],[616]) ).
thf(882,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 @ k18_filter_2 ) )
= ( B @ ( A @ a_2_0_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
thf(5960,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 @ k18_filter_2 ) )
= ( B @ ( A @ a_2_0_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(439,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(3738,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)],[439]) ).
thf(2734,plain,
sk157 @ v14_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(863,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(5882,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)],[863]) ).
thf(691,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(5095,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)],[691]) ).
thf(945,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 @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k18_filter_2 ) )
= ( B @ ( A @ k2_filter_2 ) ) )
& ( ( B @ ( A @ k18_filter_2 ) )
= ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k2_filter_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_2) ).
thf(6228,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 @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k18_filter_2 ) )
= ( B @ ( A @ k2_filter_2 ) ) )
& ( ( B @ ( A @ k18_filter_2 ) )
= ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k2_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(360,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(3274,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(539,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(4269,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)],[539]) ).
thf(429,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(3686,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)],[429]) ).
thf(30141,plain,
! [A: $i] :
( ( A != sk315 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,16300]) ).
thf(30142,plain,
! [A: $i] :
( ( A != sk315 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[30141]) ).
thf(30143,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( sk315 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[30142:[bind(A,$thf( sk315 ))]]) ).
thf(492,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(4017,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)],[492]) ).
thf(826,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(5715,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)],[826]) ).
thf(576,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(4489,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)],[576]) ).
thf(70,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(1389,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)],[70]) ).
thf(1124,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)],[1123]) ).
thf(1125,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)],[1124]) ).
thf(16228,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,8831]) ).
thf(16229,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16228]) ).
thf(16277,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[16229]) ).
thf(16302,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[16277]) ).
thf(696,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(5121,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)],[696]) ).
thf(1372,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1368]) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1372]) ).
thf(1388,plain,
! [A: $i] : ( A @ ( A @ ( k1_xboole_0 @ sk25 ) @ k2_relat_1 @ r1_tarski ) ),
inference(simp,[status(thm)],[1387]) ).
thf(851,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(5831,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)],[851]) ).
thf(8022,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,3128]) ).
thf(8023,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8022]) ).
thf(8027,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk71 ),
inference(simp,[status(thm)],[8023]) ).
thf(720,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(5239,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)],[720]) ).
thf(2959,plain,
sk188 @ v5_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(406,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ( A @ ( B @ v1_filter_2 ) )
& ( B
!= ( A @ k17_filter_2 ) ) )
<=> ( B @ ( A @ r2_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_2) ).
thf(3536,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ( B @ ( A @ r2_filter_2 ) )
=> ( ( A @ ( B @ v1_filter_2 ) )
& ( B
!= ( A @ k17_filter_2 ) ) ) )
& ( ( ( A @ ( B @ v1_filter_2 ) )
& ( B
!= ( A @ k17_filter_2 ) ) )
=> ( B @ ( A @ r2_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(668,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(4943,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)],[668]) ).
thf(5696,plain,
( ( ( f3_s11_funct_2 @ ( sk407 @ ( 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)],[5691]) ).
thf(5698,plain,
( ( ( f3_s11_funct_2 @ ( sk407 @ ( 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)],[5696]) ).
thf(4142,plain,
( ~ ( sk279 @ v3_struct_0 )
& ( sk279 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[4141]) ).
thf(4144,plain,
~ ( sk279 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4142]) ).
thf(946,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(6234,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)],[946]) ).
thf(12353,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,7421]) ).
thf(12354,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12353]) ).
thf(12441,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12354]) ).
thf(677,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(4998,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)],[677]) ).
thf(999,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(6468,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)],[999]) ).
thf(1004,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(6493,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)],[1004]) ).
thf(29736,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_tarski ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,8186]) ).
thf(29737,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_tarski ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[29736]) ).
thf(29738,plain,
! [A: $i] : ( A @ k1_tarski @ sk19 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[29737:[bind(A,$thf( C @ k1_tarski )),bind(B,$thf( C ))]]) ).
thf(32888,plain,
! [A: $i] : ( A @ k1_tarski @ sk19 @ v1_funct_1 ),
inference(simp,[status(thm)],[29738]) ).
thf(243,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(2525,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)],[243]) ).
thf(855,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(5844,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)],[855]) ).
thf(8792,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,5317]) ).
thf(8793,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8792]) ).
thf(8814,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk216 ),
inference(simp,[status(thm)],[8793]) ).
thf(438,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(3736,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)],[438]) ).
thf(3081,plain,
sk197 @ v3_filter_0,
inference(cnfConj,[status(thm)],[3071]) ).
thf(5940,plain,
sk421 @ l2_struct_0,
inference(cnfConj,[status(thm)],[5939]) ).
thf(362,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(3283,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)],[362]) ).
thf(620,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(4677,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)],[620]) ).
thf(8790,plain,
( ( ( sk364 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,5246]) ).
thf(8791,plain,
( ( sk364 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8790]) ).
thf(8809,plain,
sk364 != sk216,
inference(simp,[status(thm)],[8791]) ).
thf(605,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(4605,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)],[605]) ).
thf(601,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(4590,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)],[601]) ).
thf(381,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(3404,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)],[381]) ).
thf(464,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 @ m2_filter_2 ) )
<=> ( ! [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 ) ) )
& ( 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 @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_2) ).
thf(3868,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 ) )
=> ( ( ( C @ ( D @ ( 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 @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m2_filter_2 ) ) )
& ( ( A @ ( B @ m2_filter_2 ) )
=> ( ! [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 ) ) )
& ( 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 @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(639,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(4769,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)],[639]) ).
thf(635,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 @ k19_filter_2 ) @ ( B @ ( A @ k18_filter_2 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_2) ).
thf(4758,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 @ k19_filter_2 ) @ ( B @ ( A @ k18_filter_2 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(30885,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ k2_tarski ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,27282]) ).
thf(30886,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ k2_tarski ) ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[30885]) ).
thf(30887,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk19 @ v1_funct_1 ),
inference(pattern_uni,[status(thm)],[30886:[bind(A,$thf( E @ ( D @ k2_tarski ) )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).
thf(32713,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk19 @ v1_funct_1 ),
inference(simp,[status(thm)],[30887]) ).
thf(774,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(5503,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)],[774]) ).
thf(4944,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk334 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
| ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk332 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk334 @ m2_relset_1 ) ) )
| ~ sk332 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk334 @ v1_funct_2 ) ) )
| ~ sk332 )
& ( ( sk334 @ v1_funct_1 )
| ~ sk332 )
& ( sk332
| ~ ( A @ ( sk333 @ p1_s14_funct_2 ) )
| ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk332
| ( f1_s14_funct_2 @ ( sk333 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4943]) ).
thf(4946,plain,
( sk332
| ( f1_s14_funct_2 @ ( sk333 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4944]) ).
thf(272,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(2695,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)],[272]) ).
thf(51,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(1256,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)],[51]) ).
thf(595,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(4558,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)],[595]) ).
thf(519,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(4186,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)],[519]) ).
thf(3077,plain,
sk197 @ v9_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(158,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(1997,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)],[158]) ).
thf(705,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(5190,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)],[705]) ).
thf(229,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(2425,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(948,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(6248,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)],[948]) ).
thf(6547,plain,
( ( ( sk71 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,1216]) ).
thf(6548,plain,
( ( sk71 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6547]) ).
thf(6549,plain,
sk71 != sk14,
inference(simp,[status(thm)],[6548]) ).
thf(6372,plain,
sk456 @ l3_lattices,
inference(cnfConj,[status(thm)],[6371]) ).
thf(405,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(3532,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)],[405]) ).
thf(587,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(4526,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)],[587]) ).
thf(1139,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)],[1137]) ).
thf(441,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(3751,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)],[441]) ).
thf(2218,plain,
( ( sk95 @ v2_struct_0 )
& ( sk95 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[2217]) ).
thf(2220,plain,
sk95 @ v2_struct_0,
inference(cnfConj,[status(thm)],[2218]) ).
thf(113,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(1707,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)],[113]) ).
thf(210,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(2293,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)],[210]) ).
thf(506,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(4099,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)],[506]) ).
thf(2738,plain,
~ ( sk157 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2733]) ).
thf(637,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( A @ v13_lattices )
=> ( B @ ( A @ k5_lattices @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_filter_2) ).
thf(4764,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( A @ v13_lattices )
=> ( B @ ( A @ k5_lattices @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(456,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(3832,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)],[456]) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ~ ( 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 @ ( 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)],[1081]) ).
thf(1090,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( 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 @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_1 )
| ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
| ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ),
inference(lifteq,[status(thm)],[1084]) ).
thf(415,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(3579,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)],[415]) ).
thf(653,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(4854,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)],[653]) ).
thf(423,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(3641,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)],[423]) ).
thf(2474,plain,
k13_nat_lat @ v5_lattices,
inference(cnfConj,[status(thm)],[2470]) ).
thf(104,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(1638,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)],[104]) ).
thf(535,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(4245,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)],[535]) ).
thf(44,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(1221,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)],[44]) ).
thf(1222,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(miniscope,[status(thm)],[1221]) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
| ( ( A @ ( B @ sk15 ) )
!= ( C @ ( B @ k1_funct_1 ) ) )
| ~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) )
& ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
| ( A @ ( A @ ( B @ sk15 ) @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1222]) ).
thf(1224,plain,
! [B: $i,A: $i] :
( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
| ( A @ ( A @ ( B @ sk15 ) @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1223]) ).
thf(218,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(2358,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(67,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(1356,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)],[67]) ).
thf(8526,plain,
! [B: $i,A: $i] :
( ( ( sk207 @ 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)],[3208,1048]) ).
thf(8527,plain,
! [B: $i,A: $i] :
( ( ( sk207 @ 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)],[8526]) ).
thf(8528,plain,
! [A: $i] : ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8527:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).
thf(15527,plain,
! [A: $i] :
( ( ( sk207 @ 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)],[3208,1135]) ).
thf(15528,plain,
! [A: $i] :
( ( ( sk207 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15527]) ).
thf(15529,plain,
( ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) )
= ( sk207 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15528:[bind(A,$thf( sk207 ))]]) ).
thf(23659,plain,
! [A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[8528,15529]) ).
thf(23679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23659,1079]) ).
thf(23680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[23679]) ).
thf(23681,plain,
! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[23680:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk207 @ k9_relat_1 ) )),bind(C,$thf( sk207 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(23751,plain,
! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[23681]) ).
thf(908,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(6061,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)],[908]) ).
thf(190,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(2151,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)],[190]) ).
thf(29866,plain,
! [A: $i] :
( ( A != sk187 )
| ( k1_xboole_0 @ v15_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,2953]) ).
thf(29867,plain,
( ( k1_xboole_0 @ v15_lattices )
| ( sk187 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29866:[bind(A,$thf( sk187 ))]]) ).
thf(21592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21572,1079]) ).
thf(21593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[21592]) ).
thf(21594,plain,
! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21593:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk138 @ k9_relat_1 ) )),bind(C,$thf( sk138 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(21667,plain,
! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[21594]) ).
thf(286,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(2802,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)],[286]) ).
thf(640,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(4773,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)],[640]) ).
thf(1191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C )
| ~ ( A @ ( C @ m1_subset_1 ) )
| ~ ( A @ ( B @ v3_binop_1 ) )
| ~ ( 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)],[1190]) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ m1_subset_1 ) )
| ~ ( A @ ( B @ v3_binop_1 ) )
| ~ ( 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 @ ( B @ k1_binop_1 ) ) )
= C ) ),
inference(lifteq,[status(thm)],[1191]) ).
thf(12340,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,7110]) ).
thf(12341,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12340]) ).
thf(12445,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12341]) ).
thf(175,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(2079,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)],[175]) ).
thf(2478,plain,
~ ( k13_nat_lat @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2470]) ).
thf(357,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(3251,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)],[357]) ).
thf(557,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(4369,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)],[557]) ).
thf(176,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(2084,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)],[176]) ).
thf(2214,plain,
sk94 @ v6_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(2415,plain,
~ ( sk118 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2414]) ).
thf(309,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(2987,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)],[309]) ).
thf(320,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(3038,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)],[320]) ).
thf(2422,plain,
sk118 @ v9_lattices,
inference(cnfConj,[status(thm)],[2414]) ).
thf(547,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(4305,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)],[547]) ).
thf(123,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(1806,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)],[123]) ).
thf(9116,plain,
! [A: $i] :
( ( ( sk315 @ 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)],[4682,7014]) ).
thf(9117,plain,
! [A: $i] :
( ( ( sk315 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9116]) ).
thf(9118,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9117:[bind(A,$thf( sk315 ))]]) ).
thf(16230,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,9118]) ).
thf(16231,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16230]) ).
thf(16281,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk315 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16231]) ).
thf(16306,plain,
( ( sk315 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16281]) ).
thf(13046,plain,
! [B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,5317]) ).
thf(13047,plain,
! [B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13046]) ).
thf(13064,plain,
! [B: $i,A: $i] :
( ( A @ sk251 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[13047]) ).
thf(931,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(6147,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)],[931]) ).
thf(480,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(3957,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)],[480]) ).
thf(11676,plain,
( ( ( sk71 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[1107,9552]) ).
thf(11677,plain,
( ( ( sk71 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11676]) ).
thf(11708,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11677]) ).
thf(13718,plain,
( ( ( sk71 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[1106,11708]) ).
thf(13747,plain,
( ( sk71 != k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13718]) ).
thf(13757,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13747]) ).
thf(14192,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[13757,2073]) ).
thf(14193,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[14192]) ).
thf(938,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(6197,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)],[938]) ).
thf(626,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(4699,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(65,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(1349,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)],[65]) ).
thf(6318,plain,
( ( k13_nat_lat @ l3_lattices )
& ( k13_nat_lat @ v10_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[6317]) ).
thf(6321,plain,
k13_nat_lat @ l3_lattices,
inference(cnfConj,[status(thm)],[6318]) ).
thf(11734,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk296 ) ),
inference(paramod_ordered,[status(thm)],[1951,9081]) ).
thf(11735,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk296 ),
inference(pattern_uni,[status(thm)],[11734:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(12361,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,7221]) ).
thf(12362,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12361]) ).
thf(12413,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk71 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12362]) ).
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 @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) )
<=> ( C @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_2) ).
thf(5901,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 ) ) )
=> ( C @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) )
=> ( C @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(862,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(5880,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)],[862]) ).
thf(11732,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk216 ) ),
inference(paramod_ordered,[status(thm)],[1951,8810]) ).
thf(11733,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk216 ),
inference(pattern_uni,[status(thm)],[11732:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(684,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(5047,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)],[684]) ).
thf(5048,plain,
! [A: $i] :
( ( ( ( A @ ( sk350 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s13_funct_2 ) )
| ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk348 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk350 @ m2_relset_1 ) ) )
| ~ sk348 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk350 @ v1_funct_2 ) ) )
| ~ sk348 )
& ( ( sk350 @ v1_funct_1 )
| ~ sk348 )
& ( sk348
| ~ ( f2_s13_funct_2 @ ( sk349 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
& ( sk348
| ( f1_s13_funct_2 @ ( sk349 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[5047]) ).
thf(5054,plain,
( sk348
| ( f1_s13_funct_2 @ ( sk349 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[5048]) ).
thf(2943,plain,
sk187 @ v4_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(434,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(3710,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)],[434]) ).
thf(2945,plain,
~ ( sk187 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2941]) ).
thf(347,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(3197,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)],[347]) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk3 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ r2_hidden ) )
| ( ( C @ k1_relat_1 )
!= A )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1034]) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk3 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ( ( C @ k1_relat_1 )
!= A ) ),
inference(lifteq,[status(thm)],[1035]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_relat_1 @ ( B @ sk3 ) ) )
| ( B @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ ( B @ sk4 ) ) @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1042]) ).
thf(22,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(1120,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)],[22]) ).
thf(1121,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1120]) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1121]) ).
thf(749,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(5381,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)],[749]) ).
thf(3182,plain,
k6_nat_lat @ v5_lattices,
inference(cnfConj,[status(thm)],[3175]) ).
thf(3066,plain,
sk196 @ v15_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(560,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(4388,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)],[560]) ).
thf(1165,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk10 ) ) )
| ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
= ( A @ ( B @ sk11 ) ) )
| ( ( 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)],[1163]) ).
thf(1175,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 @ sk11 ) @ ( B @ k1_funct_1 ) )
= ( A @ ( B @ sk10 ) ) )
| ( ( A @ ( B @ sk11 ) )
= ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1165]) ).
thf(44022,plain,
( ( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,43863]) ).
thf(44023,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44022]) ).
thf(44073,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[44023]) ).
thf(710,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(5202,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)],[710]) ).
thf(660,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(4882,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)],[660]) ).
thf(597,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(4569,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)],[597]) ).
thf(540,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(4277,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)],[540]) ).
thf(227,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(2410,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)],[227]) ).
thf(993,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(6429,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)],[993]) ).
thf(416,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 @ 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] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ! [F: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ~ ( F @ v1_xboole_0 ) )
=> ( ( ( D = F )
& ( C = E )
& ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) ) )
=> ( ( D @ ( C @ ( A @ k5_filter_0 ) ) )
= ( F @ ( E @ ( B @ k5_filter_0 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l59_filter_2) ).
thf(3583,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 @ 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] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ! [F: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ~ ( F @ v1_xboole_0 ) )
=> ( ( ( D = F )
& ( C = E )
& ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
= ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) ) )
=> ( ( D @ ( C @ ( A @ k5_filter_0 ) ) )
= ( F @ ( E @ ( B @ k5_filter_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(27804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( D @ ( C @ k2_tarski ) ) )
| ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( B @ sk251 ) ) ),
inference(paramod_ordered,[status(thm)],[2046,13063]) ).
thf(27805,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ k1_zfmisc_1 )
!= ( A @ sk251 ) ),
inference(pattern_uni,[status(thm)],[27804:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 )),bind(D,$thf( E @ k1_tarski ))]]) ).
thf(27834,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ k1_zfmisc_1 )
!= ( A @ sk251 ) ),
inference(simp,[status(thm)],[27805]) ).
thf(33,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(1176,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)],[33]) ).
thf(1177,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)],[1176]) ).
thf(889,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(5987,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)],[889]) ).
thf(107,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(1667,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)],[107]) ).
thf(789,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(5563,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)],[789]) ).
thf(288,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(2824,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)],[288]) ).
thf(624,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(4694,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)],[624]) ).
thf(525,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(4203,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)],[525]) ).
thf(614,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(4635,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)],[614]) ).
thf(745,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(5367,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)],[745]) ).
thf(777,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(5511,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)],[777]) ).
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 ) )
=> ( ( 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(6004,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)],[895]) ).
thf(260,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(2632,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)],[260]) ).
thf(591,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(4541,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)],[591]) ).
thf(2742,plain,
sk157 @ v5_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(873,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(5920,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)],[873]) ).
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_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(4833,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)],[650]) ).
thf(891,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(5994,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)],[891]) ).
thf(3073,plain,
sk197 @ v10_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(5175,plain,
sk360 @ l2_struct_0,
inference(cnf,[status(esa)],[5174]) ).
thf(4731,plain,
sk317 @ v6_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(737,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(5335,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)],[737]) ).
thf(413,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(3572,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)],[413]) ).
thf(341,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(3165,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)],[341]) ).
thf(526,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(4208,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)],[526]) ).
thf(518,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(4181,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)],[518]) ).
thf(346,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(3192,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)],[346]) ).
thf(11678,plain,
( ( ( sk71 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1107,9882]) ).
thf(11679,plain,
( ( ( sk71 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11678]) ).
thf(11715,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11679]) ).
thf(14813,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2073,11715]) ).
thf(14814,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[14813]) ).
thf(14855,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk71 @ k1_relat_1 )
!= k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[14814]) ).
thf(14862,plain,
( ( ( sk71 @ k1_relat_1 )
!= k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[14855]) ).
thf(14875,plain,
( ( ( sk71 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1106,14862]) ).
thf(14876,plain,
( ( ( sk71 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[14875]) ).
thf(14901,plain,
( ( sk71 != k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[14876]) ).
thf(14910,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[14901]) ).
thf(813,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( A @ v14_lattices ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
& ( A @ k17_filter_2 @ ( B @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_2) ).
thf(5656,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
& ( A @ v14_lattices ) )
=> ( ( B
= ( A @ u1_struct_0 ) )
& ( A @ k17_filter_2 @ ( B @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1146,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ( F
!= ( B @ ( D @ k1_realset1 ) ) )
| ( E
!= ( B @ ( C @ k1_realset1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( 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 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1145]) ).
thf(1148,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( 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 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 )
| ( F
!= ( B @ ( D @ k1_realset1 ) ) )
| ( E
!= ( B @ ( C @ k1_realset1 ) ) ) ),
inference(lifteq,[status(thm)],[1146]) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ k1_realset1 ) @ ( B @ ( C @ k1_realset1 ) @ ( B @ r4_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( D @ k1_realset1 ) @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( D @ k1_realset1 ) @ v1_funct_2 ) ) )
| ~ ( B @ ( D @ k1_realset1 ) @ v1_funct_1 )
| ~ ( 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 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( 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 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[1148]) ).
thf(734,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(5318,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)],[734]) ).
thf(4726,plain,
sk317 @ v8_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(264,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(2664,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)],[264]) ).
thf(4990,plain,
! [A: $i] :
( ( ( ( A @ ( sk342 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s12_funct_2 ) )
| ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk340 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk342 @ m2_relset_1 ) ) )
| ~ sk340 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk342 @ v1_funct_2 ) ) )
| ~ sk340 )
& ( ( sk342 @ v1_funct_1 )
| ~ sk340 )
& ( sk340
| ~ ( f2_s12_funct_2 @ ( sk341 @ f3_s12_funct_2 @ r2_hidden ) ) )
& ( sk340
| ( f1_s12_funct_2 @ ( sk341 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4989]) ).
thf(4993,plain,
( sk340
| ( f1_s12_funct_2 @ ( sk341 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4990]) ).
thf(207,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(2278,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)],[207]) ).
thf(13060,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,2438]) ).
thf(13061,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13060]) ).
thf(13069,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk251 )
!= ( C @ ( B @ k4_tarski ) ) ),
inference(simp,[status(thm)],[13061]) ).
thf(854,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(5838,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)],[854]) ).
thf(148,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(1952,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)],[148]) ).
thf(2418,plain,
sk118 @ v7_lattices,
inference(cnfConj,[status(thm)],[2414]) ).
thf(981,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(6377,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)],[981]) ).
thf(2212,plain,
sk94 @ v10_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(41,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(1212,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)],[41]) ).
thf(1213,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)],[1212]) ).
thf(258,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(2620,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)],[258]) ).
thf(177,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(2086,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)],[177]) ).
thf(581,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(4502,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)],[581]) ).
thf(954,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(6288,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)],[954]) ).
thf(449,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 @ k20_filter_2 ) ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( E @ ( D @ ( A @ k20_filter_2 ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_2) ).
thf(3806,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 @ k20_filter_2 ) ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
& ( E @ ( D @ ( A @ k20_filter_2 ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(794,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(5575,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)],[794]) ).
thf(179,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(2101,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)],[179]) ).
thf(689,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(5089,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)],[689]) ).
thf(899,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(6029,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)],[899]) ).
thf(739,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(5340,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)],[739]) ).
thf(1198,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)],[1197]) ).
thf(971,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(6345,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)],[971]) ).
thf(4720,plain,
sk317 @ v13_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(142,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(1926,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)],[142]) ).
thf(2962,plain,
sk188 @ v10_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(2365,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2362]) ).
thf(82,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(1474,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)],[82]) ).
thf(16201,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,8562]) ).
thf(16202,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16201]) ).
thf(16284,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[16202]) ).
thf(16310,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[16284]) ).
thf(505,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(4085,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)],[505]) ).
thf(2369,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2367]) ).
thf(254,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(2592,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)],[254]) ).
thf(8171,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,4698]) ).
thf(8172,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8171]) ).
thf(8185,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8172]) ).
thf(26524,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2046,8185]) ).
thf(26525,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[26524:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(26564,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[26525]) ).
thf(77,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(1435,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)],[77]) ).
thf(662,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(4918,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)],[662]) ).
thf(376,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(3363,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)],[376]) ).
thf(370,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(3325,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)],[370]) ).
thf(916,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(6100,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)],[916]) ).
thf(116,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(1726,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)],[116]) ).
thf(7552,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,5317]) ).
thf(7553,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7552]) ).
thf(7558,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk152 ),
inference(simp,[status(thm)],[7553]) ).
thf(2967,plain,
sk188 @ v4_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(523,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(4196,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)],[523]) ).
thf(965,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(6325,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)],[965]) ).
thf(401,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( B @ ( A @ r2_filter_2 ) )
<=> ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v1_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_2) ).
thf(3512,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v1_filter_0 ) )
=> ( B @ ( A @ r2_filter_2 ) ) )
& ( ( B @ ( A @ r2_filter_2 ) )
=> ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v1_filter_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(3178,plain,
k6_nat_lat @ v6_lattices,
inference(cnfConj,[status(thm)],[3175]) ).
thf(579,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(4497,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)],[579]) ).
thf(7496,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1061,7113]) ).
thf(7497,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7496]) ).
thf(7519,plain,
! [B: $i,A: $i] :
( ( A != k1_xboole_0 )
| ( ( B @ k1_relat_1 )
!= sk1 )
| ( B != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7497]) ).
thf(7539,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) )
| ~ ( sk71 @ v1_relat_1 )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7519]) ).
thf(7915,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ l3_lattices ) ),
inference(rewrite,[status(thm)],[7539,1970]) ).
thf(7916,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7915]) ).
thf(2207,plain,
~ ( sk94 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2206]) ).
thf(736,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(5326,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)],[736]) ).
thf(44008,plain,
( ( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,43863]) ).
thf(44009,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44008]) ).
thf(44070,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk152 ),
inference(simp,[status(thm)],[44009]) ).
thf(942,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(6212,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)],[942]) ).
thf(6695,plain,
( ( ( sk364 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,5246]) ).
thf(6696,plain,
( ( sk364 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6695]) ).
thf(6698,plain,
sk364 != sk71,
inference(simp,[status(thm)],[6696]) ).
thf(5452,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(cnf,[status(esa)],[5451]) ).
thf(19147,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1951,5452]) ).
thf(19148,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[19147:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(19409,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ),
inference(rewrite,[status(thm)],[19148,2540]) ).
thf(572,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4441,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(2471,plain,
k13_nat_lat @ v6_lattices,
inference(cnfConj,[status(thm)],[2470]) ).
thf(340,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(3161,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)],[340]) ).
thf(833,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( B @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_2) ).
thf(5757,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( B @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(598,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(4581,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)],[598]) ).
thf(919,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(6115,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)],[919]) ).
thf(95,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(1551,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)],[95]) ).
thf(6638,plain,
( ( ( sk152 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,1216]) ).
thf(6639,plain,
( ( sk152 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6638]) ).
thf(6641,plain,
sk152 != sk14,
inference(simp,[status(thm)],[6639]) ).
thf(1075,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)],[1074]) ).
thf(1076,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)],[1075]) ).
thf(814,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 @ ( A @ k22_filter_2 ) ) @ ( D @ r2_hidden ) )
<=> ( ( C @ ( D @ ( A @ r3_lattices ) ) )
& ( D @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_filter_2) ).
thf(5661,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 @ ( D @ ( A @ r3_lattices ) ) )
& ( D @ ( B @ ( A @ r3_lattices ) ) ) )
=> ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( D @ r2_hidden ) )
=> ( ( C @ ( D @ ( A @ r3_lattices ) ) )
& ( D @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(313,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(3009,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)],[313]) ).
thf(568,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(4426,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)],[568]) ).
thf(146,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(1948,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(819,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(5688,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)],[819]) ).
thf(202,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(2239,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)],[202]) ).
thf(13056,plain,
! [A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,1216]) ).
thf(13057,plain,
! [A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13056]) ).
thf(13065,plain,
! [A: $i] :
( ( A @ sk251 )
!= sk14 ),
inference(simp,[status(thm)],[13057]) ).
thf(565,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(4405,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)],[565]) ).
thf(623,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( B @ ( A @ r2_filter_2 ) )
=> ! [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_2) ).
thf(4690,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( B @ ( A @ r2_filter_2 ) )
=> ! [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)],[623]) ).
thf(124,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(1809,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)],[124]) ).
thf(2952,plain,
sk187 @ v5_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(1872,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1871]) ).
thf(1873,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1872]) ).
thf(490,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(4013,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)],[490]) ).
thf(14244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk315 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14217,1079]) ).
thf(14245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk315 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14244]) ).
thf(14246,plain,
! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk315 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14245:[bind(A,$thf( sk315 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14289,plain,
! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk315 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14246]) ).
thf(15217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( A @ ( sk315 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14289,1079]) ).
thf(15218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( A @ ( sk315 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[15217]) ).
thf(15219,plain,
! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk315 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[15218:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk315 @ k1_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f1_s4_funct_2 )),bind(D,$thf( D ))]]) ).
thf(15276,plain,
! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk315 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[15219]) ).
thf(661,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(4886,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)],[661]) ).
thf(936,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 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k19_filter_2 ) @ ( B @ ( A @ k19_filter_2 ) @ ( A @ k19_filter_2 ) @ r1_tarski ) )
& ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( A @ k19_filter_2 ) @ ( C @ ( A @ k19_filter_2 ) @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_2) ).
thf(6191,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 ) )
=> ! [D: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k19_filter_2 ) @ ( B @ ( A @ k19_filter_2 ) @ ( A @ k19_filter_2 ) @ r1_tarski ) )
& ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( A @ k19_filter_2 ) @ ( C @ ( A @ k19_filter_2 ) @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(548,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(4319,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)],[548]) ).
thf(517,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(4177,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)],[517]) ).
thf(259,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(2629,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(157,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(1990,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)],[157]) ).
thf(700,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(5165,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)],[700]) ).
thf(1011,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(6517,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)],[1011]) ).
thf(62,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(1340,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)],[62]) ).
thf(811,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(5652,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)],[811]) ).
thf(5760,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)],[5759]) ).
thf(5763,plain,
k6_nat_lat @ v13_lattices,
inference(cnfConj,[status(thm)],[5760]) ).
thf(845,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(5807,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)],[845]) ).
thf(4722,plain,
sk317 @ v14_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(1179,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)],[1178]) ).
thf(1181,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)],[1179]) ).
thf(12991,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[2073,7738]) ).
thf(12992,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12991]) ).
thf(13011,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12992]) ).
thf(13027,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13011]) ).
thf(910,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(6069,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)],[910]) ).
thf(3611,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != B )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(cnfConj,[status(thm)],[3607]) ).
thf(3622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != B )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(lifteq,[status(thm)],[3611]) ).
thf(3623,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ r2_hidden ) ),
inference(simp,[status(thm)],[3622]) ).
thf(27547,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( A @ k1_tarski @ k1_zfmisc_1 @ ( C @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[2046,3623]) ).
thf(27548,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[27547:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(27595,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[27548]) ).
thf(1000,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(6472,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)],[1000]) ).
thf(664,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(4922,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)],[664]) ).
thf(426,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(3659,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)],[426]) ).
thf(334,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(3129,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)],[334]) ).
thf(353,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(3228,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)],[353]) ).
thf(602,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(4593,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)],[602]) ).
thf(897,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(6012,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)],[897]) ).
thf(2942,plain,
sk187 @ v10_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(44123,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,43893]) ).
thf(44124,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44123]) ).
thf(44146,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk296 ),
inference(simp,[status(thm)],[44124]) ).
thf(792,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(5570,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)],[792]) ).
thf(89,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(1516,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)],[89]) ).
thf(12375,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,9118]) ).
thf(12376,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12375]) ).
thf(12412,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk315 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12376]) ).
thf(12502,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12412]) ).
thf(555,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(4360,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)],[555]) ).
thf(657,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(4864,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)],[657]) ).
thf(988,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 @ k1_lattice2 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k6_filter_2 ) @ ( A @ k5_filter_2 ) )
= C )
& ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k6_filter_2 ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_2) ).
thf(6399,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 @ k1_lattice2 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k6_filter_2 ) @ ( A @ k5_filter_2 ) )
= C )
& ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k6_filter_2 ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk6 ) ) ) )
| ~ ( 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 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1065]) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ~ ( 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 @ ( B @ m1_subset_1 ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
!= ( A @ ( B @ ( C @ sk6 ) ) ) ) ),
inference(lifteq,[status(thm)],[1068]) ).
thf(724,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(5250,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)],[724]) ).
thf(459,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(3842,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)],[459]) ).
thf(263,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(2661,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)],[263]) ).
thf(697,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(5125,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)],[697]) ).
thf(3082,plain,
sk197 @ v8_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(40576,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk13 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1873,40565]) ).
thf(40577,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk13 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[40576:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(524,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(4200,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)],[524]) ).
thf(269,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(2678,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)],[269]) ).
thf(542,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(4287,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(8200,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)],[3159,7078]) ).
thf(8201,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8200]) ).
thf(8202,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8201:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(8286,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1063,8202]) ).
thf(8287,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[8286]) ).
thf(8311,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[8287]) ).
thf(8319,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ k1_relat_1 @ r1_tarski ) )
| ~ ( k1_xboole_0 @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[8311]) ).
thf(10281,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ k1_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[8319,3170]) ).
thf(10282,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[10281]) ).
thf(11297,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[10282,1106]) ).
thf(11670,plain,
( ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[11297,1107]) ).
thf(11671,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11670]) ).
thf(12967,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[11671,2073]) ).
thf(12968,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12967]) ).
thf(3058,plain,
sk196 @ v4_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(674,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(4971,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)],[674]) ).
thf(279,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(2720,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)],[279]) ).
thf(91,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(1531,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)],[91]) ).
thf(612,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(4630,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)],[612]) ).
thf(8804,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,3128]) ).
thf(8805,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8804]) ).
thf(8813,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk216 ),
inference(simp,[status(thm)],[8805]) ).
thf(843,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 @ m2_filter_2 ) )
=> ~ ( ( ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( D @ ( A @ r2_filter_2 ) ) ) )
& ( B != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_2) ).
thf(5790,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 @ m2_filter_2 ) )
=> ~ ( ( ( ( D @ ( C @ r2_hidden ) )
& ~ ( D @ ( B @ r2_hidden ) ) )
| ( ~ ( D @ ( C @ r2_hidden ) )
& ( D @ ( B @ r2_hidden ) ) ) )
& ( D @ ( A @ r2_filter_2 ) ) ) )
& ( B != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(5018,plain,
sk344 @ l1_lattices,
inference(cnf,[status(esa)],[5017]) ).
thf(985,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(6389,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)],[985]) ).
thf(452,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(3818,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)],[452]) ).
thf(3063,plain,
sk196 @ v6_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(6513,plain,
sk469 @ l3_lattices,
inference(cnf,[status(esa)],[6512]) ).
thf(445,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 @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( A @ k1_lattice2 @ k3_filter_2 ) )
= ( C @ ( A @ k8_filter_2 ) @ ( A @ k19_filter_2 ) ) )
& ( ( C @ ( A @ k8_filter_2 ) @ ( A @ k3_filter_2 ) )
= ( C @ ( A @ k1_lattice2 @ k19_filter_2 ) ) )
& ( ( B @ ( A @ k3_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k19_filter_2 ) ) )
& ( ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k3_filter_2 ) )
= ( B @ ( A @ k19_filter_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_2) ).
thf(3774,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 @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( A @ k1_lattice2 @ k3_filter_2 ) )
= ( C @ ( A @ k8_filter_2 ) @ ( A @ k19_filter_2 ) ) )
& ( ( C @ ( A @ k8_filter_2 ) @ ( A @ k3_filter_2 ) )
= ( C @ ( A @ k1_lattice2 @ k19_filter_2 ) ) )
& ( ( B @ ( A @ k3_filter_2 ) )
= ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k19_filter_2 ) ) )
& ( ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k3_filter_2 ) )
= ( B @ ( A @ k19_filter_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(43,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(1218,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)],[43]) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= C )
| ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ( B @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1218]) ).
thf(1220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= C ) ),
inference(lifteq,[status(thm)],[1219]) ).
thf(3080,plain,
sk197 @ v6_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(2747,plain,
sk157 @ v7_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(84,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(1499,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)],[84]) ).
thf(596,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ~ ( ( C @ ( A @ r2_filter_2 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_2) ).
thf(4561,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ~ ( ( C @ ( A @ r2_filter_2 ) )
& ( C @ ( B @ r1_tarski ) ) ) )
& ( B
!= ( A @ u1_struct_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(552,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(4346,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)],[552]) ).
thf(757,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(5420,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)],[757]) ).
thf(114,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(1716,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)],[114]) ).
thf(477,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( B @ ( A @ r2_filter_2 ) )
<=> ( ! [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_2) ).
thf(3940,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ( ( ( ! [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 ) ) )
=> ( B @ ( A @ r2_filter_2 ) ) )
& ( ( B @ ( A @ r2_filter_2 ) )
=> ( ! [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)],[477]) ).
thf(31725,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,1022]) ).
thf(31726,plain,
( ( k1_xboole_0 @ v10_lattices )
| ( sk1 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[31725:[bind(A,$thf( sk1 ))]]) ).
thf(756,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(5418,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)],[756]) ).
thf(79,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(1452,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)],[79]) ).
thf(3268,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3265]) ).
thf(3272,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3268]) ).
thf(3273,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3272]) ).
thf(903,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(6037,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)],[903]) ).
thf(36,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(1186,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)],[36]) ).
thf(1187,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)],[1186]) ).
thf(1188,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)],[1187]) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( B @ ( A @ ( C @ sk3 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1034]) ).
thf(870,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(5912,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)],[870]) ).
thf(12989,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2073,7874]) ).
thf(12990,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12989]) ).
thf(13016,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12990]) ).
thf(13032,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13016]) ).
thf(44032,plain,
( ( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,43863]) ).
thf(44033,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44032]) ).
thf(44065,plain,
( ( sk14 @ sk389 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk71 ),
inference(simp,[status(thm)],[44033]) ).
thf(8796,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,3334]) ).
thf(8797,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8796]) ).
thf(8808,plain,
sk218 != sk216,
inference(simp,[status(thm)],[8797]) ).
thf(530,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(4221,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(4222,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(cnf,[status(esa)],[4221]) ).
thf(514,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 @ k3_lattices ) ) ) ) ) ) )
& ( D @ ( C @ ( A @ k20_filter_2 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_2) ).
thf(4145,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 @ k3_lattices ) ) ) ) ) ) )
& ( D @ ( C @ ( A @ k20_filter_2 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(454,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(3823,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)],[454]) ).
thf(958,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k8_filter_2 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_2) ).
thf(6298,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k8_filter_2 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(215,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(2337,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)],[215]) ).
thf(9074,plain,
( ( ( sk296 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,1216]) ).
thf(9075,plain,
( ( sk296 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9074]) ).
thf(9082,plain,
sk296 != sk14,
inference(simp,[status(thm)],[9075]) ).
thf(923,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(6125,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)],[923]) ).
thf(2219,plain,
sk95 @ l2_struct_0,
inference(cnfConj,[status(thm)],[2218]) ).
thf(974,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_filter_2 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_filter_2) ).
thf(6352,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_filter_2 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(407,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(3544,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)],[407]) ).
thf(2630,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(cnf,[status(esa)],[2629]) ).
thf(2631,plain,
! [A: $i] :
( ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) )
= ( A @ k1_subset_1 ) ),
inference(lifteq,[status(thm)],[2630]) ).
thf(40026,plain,
! [A: $i] :
( ( A @ ( A @ k3_subset_1 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[2631,2548,3093]) ).
thf(785,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(5543,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)],[785]) ).
thf(212,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(2322,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)],[212]) ).
thf(93,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(1538,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)],[93]) ).
thf(274,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(2701,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)],[274]) ).
thf(996,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(6436,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)],[996]) ).
thf(2545,plain,
sk138 @ v2_funct_1,
inference(cnfConj,[status(thm)],[2542]) ).
thf(255,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(2599,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(641,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(4781,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)],[641]) ).
thf(967,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(6330,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)],[967]) ).
thf(29741,plain,
! [A: $i] :
( ( A != sk157 )
| ( k1_xboole_0 @ v6_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,2744]) ).
thf(29742,plain,
( ( k1_xboole_0 @ v6_lattices )
| ( sk157 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29741:[bind(A,$thf( sk157 ))]]) ).
thf(461,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(3853,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)],[461]) ).
thf(61,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(1336,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)],[61]) ).
thf(729,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(5275,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)],[729]) ).
thf(5276,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)],[5275]) ).
thf(5277,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk370 ) @ r2_hidden ) )
| ( ( E @ ( F @ sk369 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk370 ) )
= E )
| ( ( E @ ( F @ sk369 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk370 ) @ r2_hidden ) )
| ( F @ ( E @ ( F @ sk369 ) @ r2_hidden ) ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk370 ) )
= E )
| ( F @ ( E @ ( F @ sk369 ) @ 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)],[5276]) ).
thf(5281,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[5277]) ).
thf(5286,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[5281]) ).
thf(5287,plain,
! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[5286]) ).
thf(39613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5287,1243]) ).
thf(39614,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ k1_tarski @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[39613]) ).
thf(39631,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[39614]) ).
thf(39646,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[39631]) ).
thf(268,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(2675,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(804,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 ) )
=> ( ! [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 @ m2_lattice4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_2) ).
thf(5628,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 @ ( 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 @ m2_lattice4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(32064,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,1023]) ).
thf(32065,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk1 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[32064:[bind(A,$thf( sk1 ))]]) ).
thf(122,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(1797,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)],[122]) ).
thf(281,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(2728,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)],[281]) ).
thf(403,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(3520,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)],[403]) ).
thf(584,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(4516,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)],[584]) ).
thf(536,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(4257,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)],[536]) ).
thf(40566,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( A @ ( C @ sk13 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1119,40565]) ).
thf(40567,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk13 ) )
= A ),
inference(pattern_uni,[status(thm)],[40566:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(144,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(1934,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)],[144]) ).
thf(2948,plain,
sk187 @ v6_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(431,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(3697,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)],[431]) ).
thf(240,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(2500,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)],[240]) ).
thf(94,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(1543,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)],[94]) ).
thf(330,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(3107,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)],[330]) ).
thf(717,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 @ k6_lattices @ r2_hidden ) )
& ( A @ v14_lattices ) )
=> ( ( ( B @ ( A @ k19_filter_2 ) )
= ( A @ u1_struct_0 ) )
& ( A @ k17_filter_2 @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_2) ).
thf(5223,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 @ k6_lattices @ r2_hidden ) )
& ( A @ v14_lattices ) )
=> ( ( ( B @ ( A @ k19_filter_2 ) )
= ( A @ u1_struct_0 ) )
& ( A @ k17_filter_2 @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(154,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(1981,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)],[154]) ).
thf(1014,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(6526,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)],[1014]) ).
thf(188,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(2145,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)],[188]) ).
thf(1972,plain,
sk71 @ v2_funct_1,
inference(cnfConj,[status(thm)],[1969]) ).
thf(508,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m2_filter_2 ) )
<=> ! [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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_2) ).
thf(4106,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( 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 @ k3_lattices ) ) @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) )
=> ( A @ ( B @ m2_filter_2 ) ) )
& ( ( A @ ( B @ m2_filter_2 ) )
=> ! [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 ) ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(762,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(5453,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)],[762]) ).
thf(846,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(5809,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)],[846]) ).
thf(4143,plain,
sk279 @ l1_struct_0,
inference(cnfConj,[status(thm)],[4142]) ).
thf(497,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 ) )
=> ! [D: $i] :
( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( ( E @ ( A @ k8_filter_2 ) @ ( D @ ( A @ k8_filter_2 ) @ ( A @ k20_filter_2 ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k5_filter_0 ) ) ) )
& ( ( E @ ( D @ ( A @ k1_lattice2 @ k20_filter_2 ) ) )
= ( E @ ( A @ k8_filter_2 ) @ ( D @ ( A @ k8_filter_2 ) @ ( A @ k5_filter_0 ) ) ) )
& ( ( C @ ( A @ k7_filter_2 ) @ ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k20_filter_2 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k20_filter_2 ) ) )
= ( C @ ( A @ k7_filter_2 ) @ ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k5_filter_0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_2) ).
thf(4046,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 ) )
=> ! [D: $i] :
( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( ( E @ ( A @ k8_filter_2 ) @ ( D @ ( A @ k8_filter_2 ) @ ( A @ k20_filter_2 ) ) )
= ( E @ ( D @ ( A @ k1_lattice2 @ k5_filter_0 ) ) ) )
& ( ( E @ ( D @ ( A @ k1_lattice2 @ k20_filter_2 ) ) )
= ( E @ ( A @ k8_filter_2 ) @ ( D @ ( A @ k8_filter_2 ) @ ( A @ k5_filter_0 ) ) ) )
& ( ( C @ ( A @ k7_filter_2 ) @ ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k20_filter_2 ) ) )
= ( C @ ( B @ ( A @ k5_filter_0 ) ) ) )
& ( ( C @ ( B @ ( A @ k20_filter_2 ) ) )
= ( C @ ( A @ k7_filter_2 ) @ ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k5_filter_0 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(666,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(4932,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)],[666]) ).
thf(29862,plain,
! [A: $i] :
( ( A != sk94 )
| ( k1_xboole_0 @ v3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,2210]) ).
thf(29863,plain,
( ( k1_xboole_0 @ v3_lattices )
| ( sk94 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29862:[bind(A,$thf( sk94 ))]]) ).
thf(570,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(4431,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)],[570]) ).
thf(913,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(6086,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)],[913]) ).
thf(1140,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)],[1137]) ).
thf(290,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(2860,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)],[290]) ).
thf(744,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(5364,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)],[744]) ).
thf(2949,plain,
sk187 @ v9_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(29751,plain,
! [A: $i] :
( ( A != sk456 )
| ( k1_xboole_0 @ v3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,6374]) ).
thf(29752,plain,
( ( k1_xboole_0 @ v3_lattices )
| ( sk456 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[29751:[bind(A,$thf( sk456 ))]]) ).
thf(976,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(6358,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)],[976]) ).
thf(692,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(5100,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)],[692]) ).
thf(643,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(4795,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)],[643]) ).
thf(959,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(6301,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)],[959]) ).
thf(943,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(6220,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)],[943]) ).
thf(529,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(4217,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)],[529]) ).
thf(98,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(1617,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)],[98]) ).
thf(543,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(4289,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)],[543]) ).
thf(600,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(4587,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)],[600]) ).
thf(990,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(6408,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)],[990]) ).
thf(1949,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(cnf,[status(esa)],[1948]) ).
thf(131,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(1844,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)],[131]) ).
thf(8806,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3323,2438]) ).
thf(8807,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8806]) ).
thf(8812,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk216 ),
inference(simp,[status(thm)],[8807]) ).
thf(26518,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk71 ) ),
inference(paramod_ordered,[status(thm)],[2046,8040]) ).
thf(26519,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk71 ),
inference(pattern_uni,[status(thm)],[26518:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(26561,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk71 ),
inference(simp,[status(thm)],[26519]) ).
thf(837,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(5771,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)],[837]) ).
thf(336,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(3139,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)],[336]) ).
thf(141,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(1918,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)],[141]) ).
thf(2479,plain,
k13_nat_lat @ v7_lattices,
inference(cnfConj,[status(thm)],[2470]) ).
thf(992,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 ) ) )
=> ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( C @ r2_hidden ) )
& ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( B @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_2) ).
thf(6425,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 ) ) )
=> ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( C @ r2_hidden ) )
& ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( B @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(652,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(4851,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)],[652]) ).
thf(4727,plain,
sk317 @ v9_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(872,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(5917,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)],[872]) ).
thf(3067,plain,
sk196 @ v14_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(1180,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)],[1179]) ).
thf(127,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(1817,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)],[127]) ).
thf(343,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(3171,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)],[343]) ).
thf(2960,plain,
sk188 @ v8_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(408,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(3548,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)],[408]) ).
thf(2215,plain,
sk94 @ v8_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(877,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(5934,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)],[877]) ).
thf(119,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(1781,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)],[119]) ).
thf(2209,plain,
sk94 @ v4_lattices,
inference(cnfConj,[status(thm)],[2206]) ).
thf(2743,plain,
sk157 @ v8_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(311,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(2997,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)],[311]) ).
thf(488,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(4006,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)],[488]) ).
thf(516,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(4170,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)],[516]) ).
thf(3056,plain,
sk196 @ v5_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(769,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 @ ( A @ k19_filter_2 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
& ( C @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_2) ).
thf(5485,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 @ ( A @ k19_filter_2 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
& ( C @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(4730,plain,
sk317 @ v16_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(510,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(4121,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)],[510]) ).
thf(964,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(6322,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)],[964]) ).
thf(645,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(4806,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)],[645]) ).
thf(395,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(3484,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)],[395]) ).
thf(4683,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[4681]) ).
thf(13048,plain,
! [B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,4064]) ).
thf(13049,plain,
! [B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13048]) ).
thf(13068,plain,
! [B: $i,A: $i] :
( ( A @ sk251 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[13049]) ).
thf(18165,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( B @ k1_zfmisc_1 ) )
| ( ( A @ sk251 )
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1951,13068]) ).
thf(18166,plain,
! [A: $i] :
( ( A @ sk251 )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[18165:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(372,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(3336,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)],[372]) ).
thf(306,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(2971,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)],[306]) ).
thf(399,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(3501,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)],[399]) ).
thf(335,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(3136,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)],[335]) ).
thf(2416,plain,
sk118 @ v10_lattices,
inference(cnfConj,[status(thm)],[2414]) ).
thf(301,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(2934,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)],[301]) ).
thf(276,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(2707,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)],[276]) ).
thf(728,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(5272,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)],[728]) ).
thf(608,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(4615,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)],[608]) ).
thf(244,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(2532,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)],[244]) ).
thf(1101,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[1100]) ).
thf(484,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(3991,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)],[484]) ).
thf(440,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(3748,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)],[440]) ).
thf(718,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(5228,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)],[718]) ).
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 ) )
=> ( ( 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(2026,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)],[164]) ).
thf(402,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(3516,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)],[402]) ).
thf(578,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(4495,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)],[578]) ).
thf(688,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(5087,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(185,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(2130,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)],[185]) ).
thf(7668,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1063,7113]) ).
thf(7669,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7668]) ).
thf(7686,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7669]) ).
thf(7701,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk71 @ v1_relat_1 )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[7686]) ).
thf(8082,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ l3_lattices ) ),
inference(rewrite,[status(thm)],[7701,1970]) ).
thf(8083,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[8082]) ).
thf(775,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(5505,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)],[775]) ).
thf(537,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(4261,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)],[537]) ).
thf(874,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 @ m2_filter_2 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( D @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_2) ).
thf(5922,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 @ m2_filter_2 ) )
=> ( ( D @ ( B @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
& ( D @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(224,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(2394,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)],[224]) ).
thf(325,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(3085,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)],[325]) ).
thf(544,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(4293,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)],[544]) ).
thf(987,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_filter_2) ).
thf(6397,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(755,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(5409,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)],[755]) ).
thf(1017,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 ) @ m2_filter_2 ) )
=> ( A @ v13_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_2) ).
thf(6536,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 ) @ m2_filter_2 ) )
=> ( A @ v13_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(714,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(5211,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)],[714]) ).
thf(799,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(5590,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)],[799]) ).
thf(16235,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,7113]) ).
thf(16236,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16235]) ).
thf(16278,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16236]) ).
thf(16303,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16278]) ).
thf(234,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(2447,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)],[234]) ).
thf(2944,plain,
sk187 @ v14_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(161,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(2009,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)],[161]) ).
thf(850,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(5828,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)],[850]) ).
thf(1027,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)],[1026]) ).
thf(1029,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)],[1027]) ).
thf(1030,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)],[1029]) ).
thf(883,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(5963,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)],[883]) ).
thf(3181,plain,
k6_nat_lat @ v9_lattices,
inference(cnfConj,[status(thm)],[3175]) ).
thf(2475,plain,
k13_nat_lat @ v9_lattices,
inference(cnfConj,[status(thm)],[2470]) ).
thf(961,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(6305,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)],[961]) ).
thf(782,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(5532,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)],[782]) ).
thf(297,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(2912,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)],[297]) ).
thf(549,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(4321,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)],[549]) ).
thf(955,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(6290,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)],[955]) ).
thf(8835,plain,
! [A: $i] :
( ( ( sk216 @ 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)],[3324,7014]) ).
thf(8836,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8835]) ).
thf(8837,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8836:[bind(A,$thf( sk216 ))]]) ).
thf(515,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
<=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v16_lattices )
& ( A @ k1_lattice2 @ v15_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_2) ).
thf(4153,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v16_lattices )
& ( A @ k1_lattice2 @ v15_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) )
=> ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) ) )
& ( ( ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v16_lattices )
& ( A @ k1_lattice2 @ v15_lattices )
& ( A @ k1_lattice2 @ v10_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(693,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(5109,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(682,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(5040,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)],[682]) ).
thf(12976,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2073,9882]) ).
thf(12977,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12976]) ).
thf(13023,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk71 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12977]) ).
thf(13040,plain,
( ( ( sk71 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13023]) ).
thf(404,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(3529,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)],[404]) ).
thf(5695,plain,
( ( sk407 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5691]) ).
thf(5699,plain,
( ( sk407 @ v1_funct_1 )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5695]) ).
thf(193,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(2162,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)],[193]) ).
thf(791,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(5568,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)],[791]) ).
thf(858,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(5869,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)],[858]) ).
thf(12365,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,7218]) ).
thf(12366,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12365]) ).
thf(12427,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk138 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12366]) ).
thf(136,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(1893,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)],[136]) ).
thf(60,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(1309,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)],[60]) ).
thf(2739,plain,
sk157 @ v4_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(708,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(5196,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)],[708]) ).
thf(821,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(5704,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)],[821]) ).
thf(12381,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,9106]) ).
thf(12382,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk315 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12381]) ).
thf(12438,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk315 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12382]) ).
thf(12480,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk315 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12438]) ).
thf(493,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( ( C = D )
& ( ( 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 @ ( A @ k19_filter_2 ) )
= ( D @ ( B @ k19_filter_2 ) ) )
& ( ( C @ ( A @ k3_filter_2 ) )
= ( D @ ( B @ k3_filter_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l48_filter_2) ).
thf(4025,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 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( ( C = D )
& ( ( 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 @ ( A @ k19_filter_2 ) )
= ( D @ ( B @ k19_filter_2 ) ) )
& ( ( C @ ( A @ k3_filter_2 ) )
= ( D @ ( B @ k3_filter_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(162,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(2019,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)],[162]) ).
thf(1159,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)],[1158]) ).
thf(1161,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)],[1159]) ).
thf(2421,plain,
sk118 @ v8_lattices,
inference(cnfConj,[status(thm)],[2414]) ).
thf(209,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(2287,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)],[209]) ).
thf(105,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(1642,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)],[105]) ).
thf(87,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(1512,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)],[87]) ).
thf(56,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(1280,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)],[56]) ).
thf(7863,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,2438]) ).
thf(7864,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7863]) ).
thf(7868,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk71 ),
inference(simp,[status(thm)],[7864]) ).
thf(678,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(5004,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)],[678]) ).
thf(46,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(1229,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)],[46]) ).
thf(787,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(5554,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)],[787]) ).
thf(783,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_0) ).
thf(5537,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)],[783]) ).
thf(4719,plain,
sk317 @ v7_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(2736,plain,
sk157 @ v9_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(679,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(5014,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)],[679]) ).
thf(187,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(2142,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(378,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(3379,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)],[378]) ).
thf(1112,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)],[1109]) ).
thf(1116,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)],[1112]) ).
thf(138,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(1908,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)],[138]) ).
thf(149,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(1957,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)],[149]) ).
thf(564,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(4399,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)],[564]) ).
thf(622,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(4687,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)],[622]) ).
thf(628,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4706,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(108,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(1678,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)],[108]) ).
thf(646,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(4809,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)],[646]) ).
thf(463,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(3865,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)],[463]) ).
thf(977,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 @ ( A @ k7_filter_2 ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).
thf(6361,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 @ ( A @ k7_filter_2 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(71,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(1395,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)],[71]) ).
thf(27802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k2_tarski ) )
!= ( D @ ( C @ k2_tarski ) ) )
| ( ( A @ k1_tarski )
!= ( B @ sk251 ) ) ),
inference(paramod_ordered,[status(thm)],[4614,13063]) ).
thf(27803,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski )
!= ( B @ sk251 ) ),
inference(pattern_uni,[status(thm)],[27802:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(100,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(1625,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)],[100]) ).
thf(458,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(3837,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)],[458]) ).
thf(1370,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1368]) ).
thf(1379,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1370]) ).
thf(1380,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1379]) ).
thf(257,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(2604,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)],[257]) ).
thf(2951,plain,
sk187 @ v3_lattices,
inference(cnfConj,[status(thm)],[2941]) ).
thf(5764,plain,
k6_nat_lat @ l3_lattices,
inference(cnfConj,[status(thm)],[5760]) ).
thf(766,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(5477,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)],[766]) ).
thf(747,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(5371,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)],[747]) ).
thf(1003,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(6490,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)],[1003]) ).
thf(618,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(4663,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)],[618]) ).
thf(554,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(4357,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)],[554]) ).
thf(603,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(4597,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)],[603]) ).
thf(30343,plain,
! [A: $i] :
( ( A != sk216 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,16312]) ).
thf(30344,plain,
! [A: $i] :
( ( A != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(simp,[status(thm)],[30343]) ).
thf(30345,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ( sk216 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[30344:[bind(A,$thf( sk216 ))]]) ).
thf(723,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(5247,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)],[723]) ).
thf(751,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(5398,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)],[751]) ).
thf(556,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(4367,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(349,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(3203,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)],[349]) ).
thf(875,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(5926,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)],[875]) ).
thf(3062,plain,
sk196 @ v3_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(337,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(3145,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)],[337]) ).
thf(2746,plain,
sk157 @ v13_lattices,
inference(cnfConj,[status(thm)],[2733]) ).
thf(4442,plain,
sk300 @ l1_struct_0,
inference(cnf,[status(esa)],[4441]) ).
thf(12408,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,7424]) ).
thf(12409,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12408]) ).
thf(12444,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12409]) ).
thf(3275,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[3274]) ).
thf(18776,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
inference(rewrite,[status(thm)],[3275,2548]) ).
thf(316,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(3015,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)],[316]) ).
thf(731,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(5300,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)],[731]) ).
thf(68,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(1363,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)],[68]) ).
thf(634,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(4755,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)],[634]) ).
thf(410,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(3560,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)],[410]) ).
thf(823,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(5709,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)],[823]) ).
thf(374,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(3347,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)],[374]) ).
thf(3177,plain,
k6_nat_lat @ v4_lattices,
inference(cnfConj,[status(thm)],[3175]) ).
thf(448,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(3804,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)],[448]) ).
thf(12980,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2073,8443]) ).
thf(12981,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12980]) ).
thf(13012,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12981]) ).
thf(13028,plain,
( ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13012]) ).
thf(681,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(5019,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)],[681]) ).
thf(853,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k17_filter_2 )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_2) ).
thf(5835,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k17_filter_2 )
= ( A @ u1_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(171,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(2070,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)],[171]) ).
thf(40172,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,34848]) ).
thf(40173,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[40172]) ).
thf(40297,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( ( k1_xboole_0 @ k1_tarski @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[40173]) ).
thf(40317,plain,
( ( ( k1_xboole_0 @ k1_tarski @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[40297]) ).
thf(460,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(3850,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)],[460]) ).
thf(275,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(2704,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)],[275]) ).
thf(1169,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ k2_funct_1 ) )
| ( B @ k1_relat_1 @ ( A @ ( B @ sk11 ) @ 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)],[1163]) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( B @ k1_relat_1 @ ( A @ ( B @ sk11 ) @ 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)],[1169]) ).
thf(72,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(1410,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)],[72]) ).
thf(829,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(5741,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)],[829]) ).
thf(2417,plain,
sk118 @ v4_lattices,
inference(cnfConj,[status(thm)],[2414]) ).
thf(1056,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ 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)],[1055]) ).
thf(759,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(5441,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)],[759]) ).
thf(120,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(1789,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)],[120]) ).
thf(14266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk315 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14217,1093]) ).
thf(14267,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk315 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14266]) ).
thf(14268,plain,
! [A: $i] : ( sk315 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14267:[bind(A,$thf( sk315 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14293,plain,
! [A: $i] : ( sk315 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14268]) ).
thf(38093,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,34382]) ).
thf(38094,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[38093]) ).
thf(38189,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( ( sk364 @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[38094]) ).
thf(38205,plain,
( ( ( sk364 @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[38189]) ).
thf(26511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk216 ) ),
inference(paramod_ordered,[status(thm)],[2046,8815]) ).
thf(26512,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk216 ),
inference(pattern_uni,[status(thm)],[26511:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(26558,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk216 ),
inference(simp,[status(thm)],[26512]) ).
thf(2961,plain,
sk188 @ v6_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(225,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(2404,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)],[225]) ).
thf(797,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(5586,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)],[797]) ).
thf(200,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(2223,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)],[200]) ).
thf(715,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(5215,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)],[715]) ).
thf(703,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(5176,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)],[703]) ).
thf(9078,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,2438]) ).
thf(9079,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9078]) ).
thf(9083,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk296 ),
inference(simp,[status(thm)],[9079]) ).
thf(427,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(3673,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)],[427]) ).
thf(64,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(1346,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)],[64]) ).
thf(1007,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(6503,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)],[1007]) ).
thf(249,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(2549,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)],[249]) ).
thf(805,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(5637,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)],[805]) ).
thf(509,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(4118,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)],[509]) ).
thf(719,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(5236,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)],[719]) ).
thf(848,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(5821,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)],[848]) ).
thf(76,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(1431,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)],[76]) ).
thf(3076,plain,
sk197 @ v7_lattices,
inference(cnfConj,[status(thm)],[3071]) ).
thf(808,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 ) ) )
=> ( ( C @ ( B @ ( A @ k22_filter_2 ) ) )
= ( C @ ( B @ ( A @ a_3_2_filter_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_filter_2) ).
thf(5645,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 ) ) )
=> ( ( C @ ( B @ ( A @ k22_filter_2 ) ) )
= ( C @ ( B @ ( A @ a_3_2_filter_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(30575,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,1021]) ).
thf(30576,plain,
( ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
| ( sk2 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[30575:[bind(A,$thf( sk2 ))]]) ).
thf(241,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(2502,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)],[241]) ).
thf(651,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(4848,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)],[651]) ).
thf(927,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(6136,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)],[927]) ).
thf(66,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(1352,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)],[66]) ).
thf(711,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(5204,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)],[711]) ).
thf(152,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(1977,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)],[152]) ).
thf(2966,plain,
sk188 @ v3_lattices,
inference(cnfConj,[status(thm)],[2956]) ).
thf(54,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(1268,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)],[54]) ).
thf(432,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(3701,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)],[432]) ).
thf(39113,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,34613]) ).
thf(39114,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[39113]) ).
thf(39214,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( ( sk218 @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[39114]) ).
thf(39226,plain,
( ( ( sk218 @ sk19 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk218 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[39214]) ).
thf(3057,plain,
sk196 @ v9_lattices,
inference(cnfConj,[status(thm)],[3055]) ).
thf(534,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(4242,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)],[534]) ).
thf(412,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(3570,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)],[412]) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1368]) ).
thf(1383,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1374]) ).
thf(1384,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_funct_1 ),
inference(simp,[status(thm)],[1383]) ).
thf(6693,plain,
( ( ( sk364 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,5246]) ).
thf(6694,plain,
( ( sk364 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6693]) ).
thf(6697,plain,
sk364 != sk152,
inference(simp,[status(thm)],[6694]) ).
thf(237,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(2467,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)],[237]) ).
thf(6373,plain,
~ ( sk456 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[6371]) ).
thf(983,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(6383,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)],[983]) ).
thf(658,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(4876,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)],[658]) ).
thf(16252,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2269,8837]) ).
thf(16253,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16252]) ).
thf(16283,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16253]) ).
thf(16309,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16283]) ).
thf(836,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(5768,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)],[836]) ).
thf(972,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(6348,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)],[972]) ).
thf(39587,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27277,1243]) ).
thf(39588,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[39587]) ).
thf(39629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( k1_xboole_0 != C ) ),
inference(simp,[status(thm)],[39588]) ).
thf(39644,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( k1_xboole_0 @ k1_tarski @ ( B @ k4_xboole_0 ) ) ),
inference(simp,[status(thm)],[39629]) ).
thf(5046,plain,
sk347 @ v3_lattices,
inference(cnfConj,[status(thm)],[5044]) ).
thf(838,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(5774,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)],[838]) ).
thf(630,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(4713,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)],[630]) ).
thf(135,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(1885,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)],[135]) ).
thf(944,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(6222,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)],[944]) ).
thf(398,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(3494,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)],[398]) ).
thf(471,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(3918,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(205,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(2270,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)],[205]) ).
thf(765,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(5473,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)],[765]) ).
thf(221,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(2372,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)],[221]) ).
thf(599,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(4584,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)],[599]) ).
thf(25781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25760,1079]) ).
thf(25782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[25781]) ).
thf(25783,plain,
! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[25782:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk218 @ k9_relat_1 ) )),bind(C,$thf( sk218 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(25867,plain,
! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[25783]) ).
thf(822,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(5707,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)],[822]) ).
thf(930,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(6145,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)],[930]) ).
thf(170,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(2059,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)],[170]) ).
thf(386,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(3432,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)],[386]) ).
thf(1066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ~ ( 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 @ ( B @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1065]) ).
thf(1069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r1_binop_1 ) ) )
| ~ ( 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 @ ( B @ m1_subset_1 ) )
| ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) ),
inference(lifteq,[status(thm)],[1066]) ).
thf(466,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(3901,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)],[466]) ).
thf(315,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(3013,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)],[315]) ).
thf(388,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(3437,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)],[388]) ).
thf(698,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(5155,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)],[698]) ).
thf(391,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(3461,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)],[391]) ).
thf(861,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(5877,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)],[861]) ).
thf(627,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(4702,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)],[627]) ).
thf(30577,plain,
! [A: $i] :
( ( A
!= ( sk1 @ u1_struct_0 ) )
| ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
| ( A @ sk19 @ v1_funct_1 ) ),
inference(paramod_ordered,[status(thm)],[1296,1021]) ).
thf(30578,plain,
( ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ sk19 @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[30577:[bind(A,$thf( sk1 @ u1_struct_0 ))]]) ).
thf(365,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(3299,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)],[365]) ).
thf(4723,plain,
sk317 @ l3_lattices,
inference(cnfConj,[status(thm)],[4716]) ).
thf(594,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( 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(4555,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)],[594]) ).
thf(329,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(3096,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)],[329]) ).
thf(44100,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3122,43893]) ).
thf(44101,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[44100]) ).
thf(44147,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[44101]) ).
thf(173,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(2074,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)],[173]) ).
thf(38133,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,34382]) ).
thf(38134,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[38133]) ).
thf(38190,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( ( sk364 @ sk19 )
!= sk315 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk364 @ sk19 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[38134]) ).
thf(842,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(5788,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)],[842]) ).
thf(726,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(5261,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)],[726]) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
| ~ ( B @ ( A @ ( C @ sk3 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1034]) ).
thf(235,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(2453,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)],[235]) ).
thf(498,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(4056,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)],[498]) ).
thf(921,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(6119,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)],[921]) ).
thf(217,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(2351,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)],[217]) ).
thf(520,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(4189,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)],[520]) ).
thf(1086,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( 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 ) ) ) )
| ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( 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 @ ( 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)],[1081]) ).
thf(1088,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ m1_subset_1 ) )
| ~ ( A @ ( E @ m1_subset_1 ) )
| ~ ( A @ ( D @ m1_subset_1 ) )
| ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
| ~ ( 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 @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
| ~ ( B @ v1_funct_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(lifteq,[status(thm)],[1086]) ).
thf(902,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(6035,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)],[902]) ).
thf(9062,plain,
( ( ( sk364 @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4387,5246]) ).
thf(9063,plain,
( ( sk364 @ v1_xboole_0 )
!= ( sk296 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9062]) ).
thf(9087,plain,
sk364 != sk296,
inference(simp,[status(thm)],[9063]) ).
thf(125,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(1812,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)],[125]) ).
thf(655,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(4858,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)],[655]) ).
thf(12395,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4684,8837]) ).
thf(12396,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk315 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12395]) ).
thf(12456,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk315 != sk216 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12396]) ).
thf(914,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(6094,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)],[914]) ).
thf(139,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(1912,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)],[139]) ).
thf(869,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(5911,plain,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(414,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(3575,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)],[414]) ).
thf(487,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(4002,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(48936,plain,
$false,
inference(e,[status(thm)],[1501,1024,4729,3167,6285,3927,4728,6387,8186,6405,2744,6355,2889,2295,4101,5593,2031,6530,5896,2072,4062,43863,3930,6431,2787,6317,6512,8843,1083,2427,2480,2559,4015,6074,2544,5999,2331,4682,1950,6374,5069,5242,4960,4603,2114,1200,6142,12458,6057,3185,6022,1211,3072,2210,2117,6177,2940,3317,5168,3905,3762,3813,3230,1443,2659,6199,13062,3153,8811,2953,2947,2248,16156,1073,5625,26562,42382,4326,4215,1971,4614,1692,4623,6031,21570,1041,3382,1173,6295,14741,6278,6127,4528,1999,34848,2712,4856,29740,1988,1342,5782,2042,5192,6640,4543,5967,8182,4633,3429,5565,2035,3332,6246,5755,8568,4011,2740,2918,5701,4279,5713,2476,5163,3562,32700,6117,1063,6370,13029,3276,2216,2046,16304,13516,1046,14488,1366,6102,4665,3597,2869,4941,3370,3335,1196,2348,3350,5977,15863,3994,1243,3915,6268,2548,4266,6381,5745,5195,4803,4124,5723,5938,5056,11731,3898,4760,1529,4511,44068,4386,2957,1628,5429,6039,2667,1871,3061,3821,6066,3653,2274,9552,6519,13067,39648,4238,3442,5765,3263,4439,2328,4524,3938,4348,2735,2814,25760,2698,4956,39212,3046,3689,4415,5759,13030,9084,2269,4654,3617,4334,6350,2217,3125,1826,4130,6315,3410,7867,1455,6113,5182,2897,5989,6332,4766,4428,1059,29744,1132,2745,33138,6010,6049,3998,1704,2158,5727,4383,2989,1100,6071,2420,5355,3463,2857,5605,1087,1514,16300,5199,4194,36923,29869,4492,5323,6272,15509,3084,1115,3470,4551,1931,5942,4141,4952,3180,4390,5091,4471,4793,3602,5493,6364,19578,4411,1302,9882,2090,3724,5804,5914,1151,5360,2073,3771,33023,2007,2950,4696,5957,36909,5264,6002,3322,1946,4396,1465,4443,2105,3075,4297,2469,4733,16448,1418,3453,3473,7775,6189,1682,1136,5680,4815,4724,5650,1020,2540,5985,3923,3093,1581,6438,4718,6451,12430,3036,4924,4825,5489,1201,12966,5824,6474,5045,7413,5572,2964,6591,3986,3068,5448,4033,2281,5643,2190,3421,30653,5375,3712,16312,5648,1119,1622,2424,5296,6498,5343,5246,3676,5846,2137,4536,3955,3243,6327,2965,8443,4628,4211,5970,2205,6210,1696,44148,3184,2982,4082,15958,3510,4065,3435,2954,5174,23581,5406,5875,39650,12457,5545,6250,12474,1915,2737,1636,1074,2922,35105,3011,1206,4962,5530,2473,8046,1306,5017,34382,4531,1199,2364,2164,6139,18852,12446,2047,5117,3767,2232,3054,7078,5540,1067,1736,2660,4059,2382,13644,7110,3795,1047,1057,2589,1091,5670,1021,2541,40735,4920,1255,1824,6509,4661,16307,2441,5206,2673,1900,1723,3261,6343,2601,6122,1123,4878,5579,6528,4989,5349,1217,32583,2147,4521,3989,34613,3069,5470,2937,4499,29861,5507,3814,5396,4044,3286,2958,5655,3314,1951,3600,32904,1210,32946,4080,3033,1106,3271,4295,6303,8810,26563,5702,2873,1032,3980,5492,14804,14217,4192,2670,3810,5465,4608,9512,8026,2477,3403,4725,1968,3065,3556,5690,1178,1296,6292,12461,8181,2179,1836,5113,44149,1079,2213,27277,1195,2211,6267,29981,1128,3727,2741,9080,1634,4732,5936,4680,5515,13063,19484,5066,5854,3784,4957,7421,8562,2692,40565,5583,3632,3078,7874,1089,3909,1234,6339,3831,1143,3122,2946,27282,1259,1534,6153,6375,6195,6477,2973,2577,17142,1064,2709,1970,1227,1878,2726,1138,4227,29750,3237,2268,8815,5497,3001,3060,3176,3087,3018,4817,35111,2460,5941,6175,3179,4983,1182,2419,1424,1214,1160,3952,2877,1082,2023,5075,7559,5818,30580,1659,3407,3210,3094,4721,5253,5337,5786,13066,1584,5588,1791,4861,3428,9085,6395,6501,40042,2108,21572,5905,4457,6275,2472,2649,23874,1155,4736,6033,1266,5639,4717,1984,1246,3920,2968,2504,5317,3656,6134,3486,1099,1478,5481,6097,2536,3126,2681,4508,1382,7014,12429,3059,7221,1974,6433,6207,6129,5973,1192,7738,1060,40160,5776,5683,1874,3115,5305,1429,5217,3064,5603,5369,1979,3074,4069,3083,3201,4223,2370,3215,3834,9081,1814,2208,13026,5833,1071,5909,1185,5872,1732,2909,6514,3755,3903,5557,5747,5711,2546,5402,4625,3587,3183,3856,44599,14708,3306,7414,2076,2748,1170,2963,1286,2915,2440,2408,2793,5209,2221,4036,15344,5513,2423,44066,6524,1278,1135,4708,2391,3042,5451,16311,4393,5928,6422,5400,5043,3343,3707,5666,1510,5483,2413,5996,6053,5524,3491,8040,3079,2570,11737,4657,5960,3738,2734,5882,5095,6228,3274,4269,3686,30143,4017,5715,4489,1389,1125,16302,5121,1388,5831,8027,5239,2959,3536,4943,5698,4144,6234,12441,4998,3070,6468,6493,32888,2525,2657,5844,8814,3736,3081,5940,3283,4677,8809,4605,11729,4590,3404,3868,4612,4769,4758,32713,5503,4946,2695,1256,2161,4558,4186,3077,5908,3208,1107,1997,5190,2425,6248,6549,6372,3532,4526,1139,7218,3751,2220,1707,2293,4099,2738,4764,3123,3832,1090,3579,4854,3641,3091,2474,1638,4245,1224,2358,1356,23751,3170,6061,2119,7594,2151,29867,21667,2802,4773,1194,12445,2079,2361,2478,3251,4369,2084,2214,5244,2415,2987,3038,2422,4305,1117,1806,16306,13064,6147,3957,14193,1048,6197,4699,1349,8831,2955,6321,11735,12413,5491,5901,5880,11733,9118,5054,1144,2943,3710,2945,3197,5346,1043,1122,5381,3182,3066,4388,1175,44073,5202,4882,4569,4277,2410,6429,3583,27834,1177,5987,6969,1667,5563,2824,4694,4203,4635,5367,5511,6004,1080,2632,4541,2742,5920,3027,7113,4833,5994,3073,5175,4064,4731,5335,3572,1162,3165,4208,4181,3192,14910,5656,1149,5318,1022,4726,2664,4993,2278,4684,13069,5838,1061,1952,2418,6377,2212,1213,1044,2620,2086,4502,6288,3806,1176,5575,2101,5089,6029,5340,1198,6345,4720,2439,1926,2962,2365,1474,16310,4085,3159,2369,2592,9106,26564,1435,4918,15529,3363,3325,6100,1726,7558,2967,4196,6325,3512,3178,1102,4497,7916,2207,5326,44070,6212,6698,19409,1973,4441,3206,2471,3161,5757,1018,4581,6115,1551,6641,1049,1076,5661,8180,3009,4426,1948,5688,2239,13065,4405,4690,1809,2952,1873,4013,1203,9086,15276,34151,4886,6191,4319,4177,2629,1990,5165,6517,15539,1340,5652,15524,5763,5807,4722,1181,13027,6069,27595,6472,4922,3659,3129,3228,4593,8039,6012,2942,44146,5570,5452,5047,1516,12502,4360,1025,4864,6399,1070,5250,23769,3842,2661,5125,3082,40577,2732,4200,32131,2678,4287,3209,12968,3058,4971,2720,1531,4630,8813,2160,5790,5018,6389,3818,3063,6513,3774,1220,3080,2747,1053,1499,4561,4346,5420,1716,3940,31726,5418,1452,3273,3334,6037,1188,1186,1038,15519,5912,13032,44065,8808,4222,4145,3823,6298,2337,9082,6125,2219,6352,3544,40026,5543,2322,1538,2701,6436,2545,2599,3623,3412,4781,3174,2044,1130,6330,29742,1218,3853,1336,39646,2675,5628,1023,32065,2543,1797,2728,3520,4516,4257,40567,1934,2948,3697,42172,2500,1543,3107,5223,1141,1981,1221,6526,23659,2145,1972,1052,4106,5453,5809,4143,4046,4932,8185,29863,4431,6086,1094,1140,2860,5364,2949,29752,6358,3156,5100,4795,6301,6220,4217,1617,4289,4587,6408,1949,1157,1844,8812,26561,5771,3139,14732,1918,4698,2479,6425,4851,4727,5917,3067,1180,1817,3171,2960,8183,3548,2215,5934,1781,1216,2209,1126,5907,2743,2997,1189,4006,3320,4170,3056,5485,1108,4730,43991,5315,4121,6322,4806,3484,4683,18166,3336,2971,3501,3136,2416,2934,1253,2707,5272,4615,1062,2532,15436,1101,4715,3991,3748,5228,2026,3516,4495,5087,2130,8083,5505,4261,5922,2394,3085,4293,6397,5409,1212,6536,5211,5590,16303,2447,2944,2009,5828,1030,5963,3181,2475,3324,6305,5532,2912,4321,6290,8837,4153,5109,5040,4387,13040,3529,5699,1077,14289,2162,5568,5869,12427,1893,1309,2739,5196,5194,5704,12480,4025,2019,1161,2421,5287,14806,2287,1642,1512,1280,7868,5004,1229,5554,5537,4719,2736,5014,2142,3379,1116,1908,2123,1133,1957,4399,4687,4706,1678,4809,3865,6361,1395,27803,1625,3837,1380,2604,2951,5764,5477,5371,6490,8574,4663,4357,4597,30345,5247,5398,4367,3203,5926,3062,3145,2746,4442,12444,18776,3015,5700,5300,1363,4755,3560,5709,3347,3177,3804,13028,13068,5019,5835,2070,40317,3850,2704,1172,1410,5741,2417,21468,1056,5441,1789,14293,2366,38205,26558,1033,43893,2961,2404,5586,3323,2223,5215,5176,9083,3673,1346,6503,2549,5637,4118,9124,5236,5821,2539,1431,3076,5645,1120,30576,1093,5275,1236,2502,4848,6136,1352,5204,3128,1977,1129,2966,1268,3701,39226,1152,3057,4242,3570,33271,1384,3605,6697,2467,6373,6383,4876,16309,5768,6348,39644,5046,5774,4713,1885,6222,9842,3812,3494,3918,2270,4221,5473,2372,8184,4584,25867,5707,6145,2059,3432,1069,3296,3901,3013,3437,5155,3461,5877,4702,30578,3299,4723,4555,3096,44147,2074,38190,5788,5261,8179,2436,2438,1037,2453,4056,6119,2351,4189,1088,6035,9087,1812,4858,7424,12456,6094,1912,5911,3575,15516,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT328+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
% 0.13/0.39 % Computer : n026.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 20:58:14 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.15/1.69 % [INFO] Parsing done (711ms).
% 3.57/1.71 % [INFO] Running in sequential loop mode.
% 4.68/2.06 % [INFO] eprover registered as external prover.
% 4.68/2.06 % [INFO] Scanning for conjecture ...
% 5.38/2.25 % [INFO] Found a conjecture (or negated_conjecture) and 3000 axioms. Running axiom selection ...
% 8.28/3.06 % [INFO] Axiom selection finished. Selected 1015 axioms (removed 1985 axioms).
% 11.27/3.90 % [INFO] Problem is first-order (TPTP FOF).
% 11.27/3.97 % [INFO] Type checking passed.
% 11.27/3.98 % [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 ...
% 171.62/49.03 % External prover 'e' found a proof!
% 171.62/49.03 % [INFO] Killing All external provers ...
% 171.62/49.04 % Time passed: 48497ms (effective reasoning time: 47317ms)
% 171.62/49.04 % 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)>
% 172.45/49.04 % Axioms used in derivation (1015): t31_lattice2, d14_filter_2, t7_filter_0, dt_k4_filter_2, t1_filter_2, t45_lattice4, t2_filter_0, t21_zfmisc_1, t11_filter_2, t13_relset_1, dt_k7_filter_0, rc1_lattice2, d1_lattices, t119_funct_2, t158_relat_1, t17_lattice4, dt_k9_filter_2, t50_lattice4, redefinition_m2_relset_1, fraenkel_a_1_0_domain_1, t51_partfun1, t24_filter_0, t10_lattice2, d13_filter_0, t38_filter_2, fraenkel_a_3_2_domain_1, cc5_lattice2, t31_filter_0, t37_lattice2, t78_filter_0, t43_lattice2, dt_m1_lattice4, fc1_zfmisc_1, t35_subset_1, t135_zfmisc_1, t25_relset_1, t30_relat_1, d4_funct_1, t20_lattice4, t39_lattices, t76_lattice2, d10_lattices, t20_zfmisc_1, d1_tarski, dt_k2_lattice2, d20_binop_1, t66_funct_2, t62_filter_0, t66_partfun1, dt_k1_filter_2, t80_filter_0, t53_subset_1, t44_filter_2, d6_filter_0, d5_relat_1, t109_xboole_1, redefinition_k16_filter_2, t25_lattice2, d10_binop_1, t10_filter_2, t36_lattice4, t19_filter_2, t34_filter_2, t29_filter_0, fc2_filter_0, t81_filter_0, t24_lattice4, d13_lattices, cc3_lattice2, d14_binop_1, dt_k9_domain_1, d6_lattice2, t7_subset_1, t30_lattice2, t32_funct_2, d11_binop_1, t2_realset1, t3_xboole_1, d4_lattice4, t3_realset1, d3_subset_1, fc1_xboole_0, rc12_lattices, dt_k7_domain_1, t34_xboole_1, t29_lattice2, t59_filter_2, d1_lattice2, t56_partfun1, t63_filter_2, t59_partfun1, s12_funct_2, t43_lattices, s3_funct_2, t28_filter_2, t42_filter_0, cc6_lattices, t57_lattice2, t33_lattice2, t16_funct_2, d16_lattices, t113_zfmisc_1, t67_lattice2, t7_lattice2, t48_domain_1, t111_zfmisc_1, dt_k2_subset_1, t8_subset_1, t80_lattice2, t9_filter_2, existence_l1_lattices, t32_lattice4, d5_tarski, t15_funct_1, dt_k11_domain_1, t26_lattices, fc4_relat_1, t19_lattices, t4_ordinal1, t1_subset, dt_k1_lattice4, t147_relat_1, t10_partfun1, t47_lattice2, d5_xboole_0, t4_lattice4, t9_lattice2, fc4_subset_1, t12_filter_2, t168_funct_2, t10_relset_1, dt_k15_filter_2, fc3_relat_1, d8_funct_1, t69_filter_0, t57_filter_2, t144_relat_1, t57_domain_1, existence_l3_lattices, dt_k6_nat_lat, t39_filter_2, t53_lattices, dt_k3_funct_2, dt_k5_lattices, t7_funct_2, t87_filter_0, fc4_lattice2, t42_zfmisc_1, t21_lattice2, t14_binop_1, dt_k1_subset_1, t19_relat_1, dt_k16_filter_2, t28_binop_1, dt_k13_domain_1, fc1_lattice2, dt_g2_struct_0, t72_lattice2, t117_zfmisc_1, t32_relat_1, dt_k4_subset_1, t83_filter_0, t35_lattice4, t55_filter_2, t23_filter_0, redefinition_k12_filter_2, t16_lattice4, abstractness_v2_struct_0, t46_lattice4, dt_m2_nat_lat, d7_binop_1, existence_m3_lattice4, existence_m1_struct_0, dt_k3_lattice4, t35_zfmisc_1, t18_filter_0, rc2_struct_0, dt_k1_lattice2, t65_partfun1, t44_funct_2, fraenkel_a_2_0_lattice4, t117_funct_1, d10_filter_0, cc4_lattice2, dt_k1_struct_0, t26_lattice4, cc2_lattice2, t85_filter_0, dt_m1_realset1, t110_zfmisc_1, t103_zfmisc_1, dt_k19_filter_2, dt_u2_struct_0, t63_partfun1, t15_relset_1, t14_filter_0, fraenkel_a_2_0_filter_0, rc2_partfun1, t18_relat_1, fc1_filter_0, t48_filter_0, d9_lattice4, t49_funct_2, t41_lattice2, t64_filter_2, t50_funct_2, t70_zfmisc_1, t69_zfmisc_1, cc4_lattices, redefinition_k11_filter_0, fc2_filter_2, rc3_funct_1, fraenkel_a_3_3_domain_1, l70_filter_2, dt_k5_filter_0, dt_k3_filter_0, d1_struct_0, t27_zfmisc_1, t37_xboole_1, t41_zfmisc_1, fc2_lattice2, dt_m2_relset_1, cc1_relat_1, dt_k7_funct_2, dt_k5_filter_2, t59_lattice2, t70_partfun1, fc3_lattice2, t26_filter_0, t56_relat_1, t83_lattice2, t17_funct_1, t21_filter_2, t43_filter_2, redefinition_k2_funct_2, t2_funct_1, t36_subset_1, t29_partfun1, t33_lattice4, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, t32_filter_0, commutativity_k7_domain_1, t46_lattice2, fraenkel_a_2_0_domain_1, d2_tarski, dt_k2_binop_1, involutiveness_k3_subset_1, rc1_funct_1, t53_filter_0, d5_lattices, t17_binop_1, t25_funct_2, t31_relat_1, t15_binop_1, dt_m2_realset1, redefinition_k13_filter_2, redefinition_k6_filter_0, dt_k1_filter_0, dt_k6_filter_2, t115_zfmisc_1, t66_lattice2, t62_funct_1, t65_funct_2, t19_funct_1, dt_m2_lattice4, t41_filter_2, d11_filter_0, t26_filter_2, t31_lattices, s13_funct_2, fraenkel_a_2_2_domain_1, t129_zfmisc_1, d4_subset_1, t2_binop_1, d6_binop_1, dt_m1_filter_2, t27_lattices, t64_funct_2, reflexivity_r3_lattices, t20_filter_2, d1_xboole_0, d9_lattices, t56_filter_0, fraenkel_a_3_0_filter_0, t130_zfmisc_1, t3_filter_2, t175_partfun1, t15_relat_1, t48_funct_2, fraenkel_a_3_7_domain_1, d16_lattice4, t70_filter_0, t72_filter_0, t48_filter_2, t46_filter_0, t40_lattice2, t64_relat_1, t138_zfmisc_1, t25_subset_1, t37_filter_0, rc11_lattices, rc3_lattices, t52_filter_0, t108_zfmisc_1, t165_funct_2, t57_filter_0, dt_l1_lattices, dt_k12_filter_2, dt_k4_lattice4, t45_filter_2, t60_partfun1, existence_m1_realset1, dt_k11_filter_2, t31_partfun1, dt_k7_lattices, t3_funct_2, rc2_subset_1, existence_l2_lattices, l59_filter_2, t27_relset_1, t52_domain_1, t118_zfmisc_1, t55_partfun1, s4_subset_1, t8_funct_2, t118_funct_2, t29_lattice4, t76_nat_lat, t14_relset_1, t39_lattice4, t16_relset_1, t38_lattice4, d13_relat_1, t28_lattice2, t164_funct_2, d15_lattice4, fc2_funct_2, t6_boole, t12_funct_1, dt_k6_subset_1, t10_relat_1, d1_relat_1, t59_filter_0, t1_xboole_1, t26_relset_1, t64_partfun1, t47_lattice4, d5_filter_2, existence_l2_struct_0, t32_lattices, t19_filter_0, t44_lattice4, t49_filter_0, t5_subset, t17_filter_2, redefinition_k12_filter_0, t29_relat_1, d14_lattice4, cc6_lattice2, t50_filter_2, t77_funct_2, t59_domain_1, t34_filter_0, d4_filter_2, t5_lattice4, t54_filter_2, t22_lattices, t32_partfun1, d6_tarski, t4_relat_1, t26_binop_1, t28_subset_1, d12_lattices, d17_lattice4, fc3_subset_1, t128_zfmisc_1, t39_partfun1, t75_zfmisc_1, redefinition_k4_filter_2, t8_lattice4, rc1_filter_0, d2_realset1, t51_filter_2, fc2_subset_1, t45_funct_2, d9_filter_2, t25_zfmisc_1, d4_relat_1, d7_lattices, t6_lattice2, t23_binop_1, t150_relat_1, existence_m1_relset_1, t1_zfmisc_1, dt_m2_filter_2, t47_filter_2, t50_lattices, fc4_filter_2, s8_domain_1, dt_l3_lattices, t48_lattice2, t30_filter_2, d16_nat_lat, t79_zfmisc_1, t12_lattice2, t5_funct_2, dt_k8_funct_2, d12_lattice4, t16_filter_2, t167_funct_2, dt_m1_struct_0, t17_lattices, t11_funct_2, t40_funct_2, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t24_binop_1, t27_lattice4, t75_lattice2, t4_filter_0, t89_filter_0, dt_l2_lattices, redefinition_k7_domain_1, t40_filter_0, d3_filter_2, d12_filter_2, t72_partfun1, t8_funct_1, t2_tarski, t16_funct_1, t28_zfmisc_1, t72_zfmisc_1, t82_funct_2, dt_k4_filter_0, t33_xboole_1, s9_domain_1, t84_lattice2, t47_lattices, d7_filter_2, d20_lattices, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t38_filter_0, d3_lattices, t23_zfmisc_1, t34_lattice4, cc5_lattices, t4_subset, t38_subset_1, d18_lattices, t169_funct_2, t44_lattices, dt_k2_funct_1, cc1_funct_2, t39_subset_1, d8_filter_0, t56_lattice2, t52_subset_1, t60_filter_0, t5_ordinal1, rc13_lattices, t4_boole, t71_lattice2, d2_funct_2, t22_lattice2, t8_filter_2, t70_lattice2, dt_k8_domain_1, dt_k17_filter_2, fc3_filter_2, t15_lattice4, t74_zfmisc_1, t32_xboole_1, t61_filter_2, dt_k8_filter_0, t14_funct_1, t5_filter_2, t9_zfmisc_1, d7_filter_0, existence_m2_realset1, existence_m3_realset1, t56_subset_1, dt_k1_domain_1, t17_funct_2, t85_lattice2, redefinition_k14_filter_2, t75_filter_0, t13_lattice2, fc1_realset1, t25_filter_2, t132_funct_2, t45_lattices, t49_lattice4, t51_funct_2, d12_binop_1, t21_lattices, t12_zfmisc_1, d2_lattice4, t38_lattice2, t139_zfmisc_1, t16_lattice2, cc1_funct_1, t4_funct_2, redefinition_k1_filter_2, d10_lattice4, s11_funct_2, d3_relat_2, s2_domain_1, rc3_struct_0, t3_ordinal1, t9_domain_1, d6_filter_2, t25_lattices, t7_boole, dt_k14_filter_2, dt_k5_lattice4, t11_binop_1, t55_filter_0, t143_relat_1, d2_subset_1, t27_lattice2, commutativity_k4_lattices, redefinition_k9_filter_2, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, rc2_lattice2, commutativity_k2_struct_0, t7_filter_2, t23_filter_2, dt_k6_domain_1, t157_funct_1, t31_lattice4, fc5_lattice2, d17_lattices, dt_k2_partfun1, rc2_funct_1, t158_funct_2, dt_k9_filter_0, t90_filter_0, redefinition_k15_filter_2, t4_subset_1, redefinition_k1_domain_1, rc1_funct_2, l48_filter_2, t26_zfmisc_1, t6_filter_2, t69_partfun1, t7_ordinal1, dt_k10_filter_2, t9_funct_2, t31_funct_2, rc1_subset_1, t48_lattice4, t68_filter_0, fc6_lattice2, t8_lattice2, t18_lattices, cc1_lattices, t5_filter_0, t64_zfmisc_1, fc5_relat_1, dt_k3_lattice2, t30_filter_0, t40_lattice4, t13_filter_2, redefinition_r3_lattices, t40_lattices, t4_filter_2, t113_funct_2, t71_partfun1, d21_lattices, t41_lattices, t159_funct_2, t116_zfmisc_1, d4_lattices, existence_m1_filter_0, t2_lattice2, redefinition_m1_filter_2, dt_k2_struct_0, t49_lattices, t14_funct_2, t27_binop_1, t48_lattices, dt_k2_lattice4, t9_filter_0, t65_funct_1, t40_filter_2, fc1_nat_lat, fraenkel_a_3_1_domain_1, t60_funct_2, t7_lattice4, t36_filter_2, cc2_funct_1, t5_realset1, s4_funct_2, t41_lattice4, rc9_lattices, dt_k7_filter_2, d2_zfmisc_1, cc1_filter_0, t169_partfun1, fraenkel_a_2_1_lattice4, t26_lattice2, dt_k24_filter_2, t17_lattice2, t18_funct_1, d3_lattice2, t4_relset_1, t10_filter_0, t31_subset_1, t3_subset, cc1_relset_1, fc1_filter_2, t25_binop_1, d2_binop_1, d6_lattice4, t30_lattice4, s1_domain_1, t12_filter_0, t124_funct_1, t50_lattice2, t55_subset_1, t79_funct_2, dt_u1_lattices, fraenkel_a_2_1_domain_1, d13_filter_2, existence_m1_subset_1, t22_lattice4, existence_m1_filter_2, commutativity_k2_tarski, t3_relat_1, t22_filter_0, t24_relat_1, t8_relset_1, t106_zfmisc_1, t125_zfmisc_1, t73_filter_0, t11_relset_1, t155_relat_1, t27_filter_2, t15_subset_1, t44_filter_0, t118_funct_1, d9_binop_1, t19_lattice2, t146_relat_1, t35_xboole_1, t49_domain_1, d17_binop_1, dt_k2_filter_0, dt_k2_funct_2, d2_filter_0, rc1_nat_lat, t5_lattice2, free_g2_struct_0, dt_k20_filter_2, t17_relset_1, cc3_lattices, d5_subset_1, t99_partfun1, t107_zfmisc_1, t9_realset1, t121_funct_2, t114_zfmisc_1, dt_k23_filter_2, t58_partfun1, d1_zfmisc_1, t27_filter_0, t15_filter_2, t11_lattice4, rc2_relat_1, t36_lattice2, existence_m2_relset_1, d4_binop_1, t64_filter_0, t38_zfmisc_1, t75_nat_lat, t9_lattice4, t69_enumset1, t82_lattice2, t22_zfmisc_1, t14_filter_2, d1_filter_0, redefinition_k7_filter_0, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, t62_lattice2, t39_filter_0, t74_lattice2, t11_filter_0, t29_filter_2, existence_m2_lattice4, t23_lattice4, d4_lattice2, t116_funct_2, fraenkel_a_3_6_domain_1, t168_partfun1, s14_funct_2, t51_filter_0, t14_lattice4, t37_lattice4, redefinition_k2_binop_1, t74_filter_0, t60_nat_lat, t61_lattice2, t6_funct_2, redefinition_k24_filter_2, t32_filter_2, t58_filter_2, t44_lattice2, t41_subset_1, fc3_nat_lat, d3_lattice4, t157_relat_1, cc3_finsub_1, t56_filter_2, t65_lattice2, t42_filter_2, t51_subset_1, t21_subset_1, existence_m1_lattice4, d5_filter_0, d10_filter_2, t36_zfmisc_1, d4_filter_0, reflexivity_r1_filter_2, t45_lattice2, t8_realset1, dt_m3_lattice4, d3_tarski, cc6_funct_2, redefinition_k1_struct_0, t25_lattice4, d8_realset1, rc1_relat_1, t54_funct_1, t24_filter_2, t40_subset_1, t17_subset_1, t6_relset_1, d1_relset_1, redefinition_k11_filter_2, fc1_struct_0, t52_lattice2, t18_binop_1, redefinition_k3_lattices, t78_lattice2, t37_filter_2, fraenkel_a_3_1_filter_0, t39_zfmisc_1, d1_realset1, d15_lattices, t131_funct_2, dt_k22_filter_2, t119_zfmisc_1, dt_k4_lattices, t60_relat_1, rc1_lattice4, t77_lattice2, fraenkel_a_3_4_domain_1, t24_lattice2, t19_lattice4, reflexivity_r1_tarski, t9_funct_1, t6_zfmisc_1, t18_funct_2, dt_l2_struct_0, t52_lattices, t1_realset1, t2_xboole_1, t35_lattice2, t57_partfun1, t9_mcart_1, t34_funct_2, t67_filter_0, t52_filter_2, symmetry_r1_filter_2, t27_finsub_1, redefinition_m1_struct_0, t18_filter_2, t10_subset_1, t41_filter_0, existence_m2_nat_lat, d12_funct_1, d2_lattices, t9_relset_1, dt_g3_lattices, fc6_relat_1, d15_binop_1, rc6_lattices, free_g3_lattices, t77_filter_0, cc7_lattices, d14_lattices, dt_k10_filter_0, t54_lattice2, t21_lattice4, t36_xboole_1, dt_k8_subset_1, dt_k3_filter_2, t58_filter_0, redefinition_k2_filter_2, d4_xboole_0, t47_filter_0, t39_lattice2, d7_lattice4, d8_filter_2, t20_relat_1, dt_k1_lattices, t73_zfmisc_1, t69_lattice2, dt_k12_domain_1, t53_filter_2, t18_lattice4, d5_binop_1, t54_subset_1, t123_funct_1, t29_lattices, t88_filter_0, d1_relat_2, t82_filter_0, t33_filter_2, redefinition_k2_struct_0, t54_filter_0, t15_filter_0, dt_k2_filter_2, t68_zfmisc_1, t12_funct_2, d16_binop_1, t20_filter_0, t28_finsub_1, t32_lattice2, d8_binop_1, abstractness_v3_lattices, t26_finsub_1, t51_lattice2, t136_zfmisc_1, t8_boole, rc1_xboole_0, t24_partfun1, redefinition_k8_funct_2, t35_filter_2, t34_zfmisc_1, t80_zfmisc_1, t5_relat_1, t24_zfmisc_1, t55_lattice2, t120_funct_2, t59_funct_2, fc7_relat_1, t60_funct_1, t46_filter_2, t23_finsub_1, t30_finsub_1, dt_k21_filter_2, t134_zfmisc_1, fc8_relat_1, t10_realset1, dt_k3_binop_1, rc5_struct_0, t23_relat_1, t10_zfmisc_1, t2_subset, redefinition_k21_filter_2, d9_filter_0, t38_funct_2, t33_partfun1, t34_finsub_1, d3_relat_1, t85_funct_2, t37_zfmisc_1, t49_filter_2, t65_relat_1, t21_relat_1, dt_k6_filter_0, t156_relat_1, t109_zfmisc_1, fraenkel_a_2_3_domain_1, t60_domain_1, t152_relat_1, dt_k6_lattices, t25_partfun1, dt_m1_filter_0, d18_binop_1, redefinition_k10_filter_2, t115_funct_2, d6_lattices, t9_tarski, t51_lattices, commutativity_k3_lattices, t149_relat_1, fc2_realset1, d13_lattice4, t32_finsub_1, t48_subset_1, d1_lattice4, d8_lattices, t28_relat_1, d1_funct_1, d1_filter_2, t81_lattice2, t34_lattices, d12_filter_0, t42_lattice4, t50_subset_1, t65_filter_0, d10_xboole_0, d2_lattice2, d11_filter_2, t34_lattice2, dt_k2_lattices, d19_lattices, t67_partfun1, t3_boole, fc1_lattice4, dt_u2_lattices, d8_relat_2, t25_relat_1, dt_k8_filter_2, t13_binop_1, t53_lattice2, existence_l1_struct_0, t45_filter_0, t49_subset_1, t7_tarski, rc1_partfun1, t71_filter_0, redefinition_r1_filter_2, t28_lattice4, t79_lattice2, d5_funct_1, t6_ordinal1, dt_k18_filter_2, redefinition_k6_subset_1, rc10_lattices, t12_relset_1, cc1_lattice2, cc5_funct_2, t60_lattice2, t50_filter_0, t43_lattice4, t58_lattice2, t22_filter_2, d3_filter_0, d1_binop_1, rc2_xboole_0, fraenkel_a_3_5_domain_1, s7_domain_1, t62_filter_2, dt_m3_realset1, dt_k13_nat_lat, t30_zfmisc_1, rc4_struct_0, dt_k10_domain_1, t49_lattice2, fraenkel_a_0_1_domain_1, t66_filter_0, t16_binop_1, t31_filter_2, t6_filter_0, redefinition_k3_filter_2, d13_binop_1, idempotence_k4_subset_1, t40_zfmisc_1, d11_lattices, t63_filter_0, t63_lattice2, t174_partfun1, t55_funct_2, t18_lattice2, t112_zfmisc_1, t73_lattice2, existence_m2_filter_2, d3_binop_1, t60_filter_2, t6_lattice4, t14_lattice2, dt_k13_filter_2, t13_filter_0, d2_relat_1, dt_k3_lattices, t68_lattice2, d19_binop_1, cc2_lattices, redefinition_k4_lattices, t61_funct_2, fc3_lattices, dt_k3_subset_1, fraenkel_a_0_2_domain_1, fc1_funct_2, cc1_binop_1, t6_relat_1, t172_partfun1, t33_subset_1, t30_partfun1, t65_zfmisc_1, t63_subset_1, t112_partfun1, t38_xboole_1, fraenkel_a_4_1_domain_1, t23_lattices, t3_filter_0, t10_lattice4, antisymmetry_r2_hidden, d5_lattice4, d8_lattice4, t64_lattice2, t22_subset_1, redefinition_k6_domain_1
% 172.45/49.04 % No. of inferences in proof: 3364
% 172.45/49.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 48497 ms resp. 47317 ms w/o parsing
% 178.33/50.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 178.33/50.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------