%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT336+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 : n017.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 07:47:21 AM UTC 2026
% Result : Theorem 164.99s 46.39s
% Output : Refutation 171.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1107
% Syntax : Number of formulae : 3560 ( 644 unt; 0 typ; 67 def)
% Number of atoms : 20071 (3290 equ; 0 cnn)
% Maximal formula atoms : 58 ( 5 avg)
% Number of connectives : 67432 (5237 ~;2842 |;7193 &;46603 @)
% ( 244 <=>;5313 =>; 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 : 8210 ( 53 ^;7735 !; 355 ?;8210 :)
% ( 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(v15_lattices_decl,type,
v15_lattices: $i > $o ).
thf(v16_lattices_decl,type,
v16_lattices: $i > $o ).
thf(v12_lattices_decl,type,
v12_lattices: $i > $o ).
thf(k23_filter_2_decl,type,
k23_filter_2: $i > $i > $i ).
thf(k18_filter_2_decl,type,
k18_filter_2: $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(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(m2_lattice4_decl,type,
m2_lattice4: $i > $i > $o ).
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(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(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(r1_filter_2_decl,type,
r1_filter_2: $i > $i > $i > $o ).
thf(k19_filter_2_decl,type,
k19_filter_2: $i > $i > $i ).
thf(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(k5_lattices_decl,type,
k5_lattices: $i > $i ).
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(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(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(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k24_filter_2_decl,type,
k24_filter_2: $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(r2_lattices_decl,type,
r2_lattices: $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(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(v1_lattice4_decl,type,
v1_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(k8_domain_1_decl,type,
k8_domain_1: $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(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(k22_filter_2_decl,type,
k22_filter_2: $i > $i > $i > $i ).
thf(r1_filter_0_decl,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(a_2_0_filter_0_decl,type,
a_2_0_filter_0: $i > $i > $i ).
thf(r4_lattice4_decl,type,
r4_lattice4: $i > $i > $i > $o ).
thf(v1_setwiseo_decl,type,
v1_setwiseo: $i > $i > $o ).
thf(a_3_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(v3_lattice4_decl,type,
v3_lattice4: $i > $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(r1_lattice4_decl,type,
r1_lattice4: $i > $i > $i > $o ).
thf(k1_struct_0_decl,type,
k1_struct_0: $i > $i > $i ).
thf(k1_filter_2_decl,type,
k1_filter_2: $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(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(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(sk254_decl,type,
sk254: $i > $i ).
thf(sk282_decl,type,
sk282: $i ).
thf(sk300_decl,type,
sk300: $i ).
thf(sk304_decl,type,
sk304: $i ).
thf(sk319_decl,type,
sk319: $i ).
thf(sk321_decl,type,
sk321: $i ).
thf(sk336_decl,type,
sk336: $o ).
thf(sk337_decl,type,
sk337: $i ).
thf(sk338_decl,type,
sk338: $i ).
thf(sk344_decl,type,
sk344: $o ).
thf(sk345_decl,type,
sk345: $i ).
thf(sk346_decl,type,
sk346: $i ).
thf(sk348_decl,type,
sk348: $i ).
thf(sk351_decl,type,
sk351: $i ).
thf(sk352_decl,type,
sk352: $o ).
thf(sk353_decl,type,
sk353: $i ).
thf(sk354_decl,type,
sk354: $i ).
thf(sk356_decl,type,
sk356: $i > $i ).
thf(sk364_decl,type,
sk364: $i ).
thf(sk365_decl,type,
sk365: $i ).
thf(sk368_decl,type,
sk368: $i ).
thf(sk373_decl,type,
sk373: $i > $i > $i ).
thf(sk374_decl,type,
sk374: $i > $i > $i ).
thf(sk379_decl,type,
sk379: $o ).
thf(sk380_decl,type,
sk380: $i ).
thf(sk381_decl,type,
sk381: $i ).
thf(sk395_decl,type,
sk395: $i > $i ).
thf(sk413_decl,type,
sk413: $i ).
thf(sk426_decl,type,
sk426: $i ).
thf(sk451_decl,type,
sk451: $o ).
thf(sk452_decl,type,
sk452: $i ).
thf(sk453_decl,type,
sk453: $i ).
thf(sk461_decl,type,
sk461: $i ).
thf(sk474_decl,type,
sk474: $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 ) )
=> ( ( ( A @ v12_lattices )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ l3_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v16_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v15_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v10_lattices )
& ~ ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v3_struct_0 ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( ( sk1 @ v12_lattices )
& ( sk1 @ l3_lattices )
& ( sk1 @ v16_lattices )
& ( sk1 @ v15_lattices )
& ( sk1 @ v10_lattices )
& ~ ( sk1 @ v3_struct_0 ) )
=> ( ( A @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ l3_lattices )
& ( A @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
& ( A @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v15_lattices )
& ( A @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
& ~ ( A @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ) ) ) ) ) ).
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(sk254_def,definition,
( sk254
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk282_def,definition,
( sk282
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk300_def,definition,
( sk300
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk304_def,definition,
( sk304
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk319_def,definition,
( sk319
= ( @+[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(sk321_def,definition,
( sk321
= ( @+[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(sk337_def,definition,
( sk337
= ( @+[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(sk338_def,definition,
( sk338
= ( @+[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(sk345_def,definition,
( sk345
= ( @+[A: $i] :
~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).
thf(sk346_def,definition,
( sk346
= ( @+[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(sk348_def,definition,
( sk348
= ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).
thf(sk351_def,definition,
( sk351
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk353_def,definition,
( sk353
= ( @+[A: $i] :
~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).
thf(sk354_def,definition,
( sk354
= ( @+[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(sk356_def,definition,
( sk356
= ( ^ [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(sk364_def,definition,
( sk364
= ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).
thf(sk365_def,definition,
( sk365
= ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).
thf(sk368_def,definition,
( sk368
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk373_def,definition,
( sk373
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
=> ( C = B ) ) ) ) ).
thf(sk374_def,definition,
( sk374
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk380_def,definition,
( sk380
= ( @+[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(sk381_def,definition,
( sk381
= ( @+[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(sk395_def,definition,
( sk395
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk413_def,definition,
( sk413
= ( @+[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(sk426_def,definition,
( sk426
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk452_def,definition,
( sk452
= ( @+[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(sk453_def,definition,
( sk453
= ( @+[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(sk461_def,definition,
( sk461
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk474_def,definition,
( sk474
= ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).
thf(185,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(2157,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)],[185]) ).
thf(2158,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)],[2157]) ).
thf(2159,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)],[2158]) ).
thf(2163,plain,
! [A: $i] : ( A @ sk80 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2159]) ).
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(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 ) )
=> ( ( 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(471,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(3962,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
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(5116,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(498,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(4094,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)],[498]) ).
thf(205,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(2306,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(2307,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(cnf,[status(esa)],[2306]) ).
thf(370,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(3358,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(3359,plain,
( ( sk216 @ v1_funct_1 )
& ( sk216 @ v1_xboole_0 )
& ( sk216 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3358]) ).
thf(3362,plain,
sk216 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3359]) ).
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(1076,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(1077,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)],[1076]) ).
thf(1078,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)],[1077]) ).
thf(1079,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)],[1078]) ).
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 ) )
=> ( ( ( A @ v12_lattices )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ l3_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v16_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v15_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v10_lattices )
& ~ ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v3_struct_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_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 ) )
=> ( ( ( A @ v12_lattices )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ l3_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v16_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v15_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v10_lattices )
& ~ ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v3_struct_0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1042,plain,
~ ! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ v12_lattices )
& ( A @ l3_lattices )
& ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ l3_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v16_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v15_lattices )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v10_lattices )
& ~ ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v3_struct_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1043,plain,
( ( ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ l3_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v15_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) )
& ( sk1 @ v12_lattices )
& ( sk1 @ l3_lattices )
& ( sk1 @ v16_lattices )
& ( sk1 @ v15_lattices )
& ( sk1 @ v10_lattices )
& ~ ( sk1 @ v3_struct_0 )
& ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
& ( sk1 @ l3_lattices )
& ( sk1 @ v10_lattices )
& ~ ( sk1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1042]) ).
thf(1045,plain,
sk1 @ v12_lattices,
inference(cnfConj,[status(thm)],[1043]) ).
thf(7195,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v12_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)],[1079,1045]) ).
thf(7196,plain,
! [A: $i] :
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[7195:[bind(A,$thf( sk1 ))]]) ).
thf(7231,plain,
! [A: $i] :
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[7196]) ).
thf(9667,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3362,7231]) ).
thf(9668,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9667]) ).
thf(9669,plain,
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9668:[bind(A,$thf( sk216 ))]]) ).
thf(16996,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,9669]) ).
thf(16997,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16996]) ).
thf(17041,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[16997]) ).
thf(17072,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[17041]) ).
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(4899,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(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(1995,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(1996,plain,
( ( sk71 @ v1_xboole_0 )
& ( sk71 @ v2_funct_1 )
& ( sk71 @ v1_funct_1 )
& ( sk71 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1995]) ).
thf(2000,plain,
sk71 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[1996]) ).
thf(879,axiom,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(6029,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(6030,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[6029]) ).
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(1241,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(1242,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)],[1241]) ).
thf(1244,plain,
! [A: $i] :
( ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk14 @ ( A @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1242]) ).
thf(42605,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)],[6030,1244]) ).
thf(42606,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42605]) ).
thf(42607,plain,
~ ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[42606:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ k8_subset_1 ))]]) ).
thf(42779,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,42607]) ).
thf(42780,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42779]) ).
thf(42828,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk71 ),
inference(simp,[status(thm)],[42780]) ).
thf(335,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(3167,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)],[335]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(2463,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
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(1313,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(1314,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)],[1313]) ).
thf(1315,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1314]) ).
thf(1322,plain,
! [A: $i] :
( ( A @ sk18 @ v1_relat_1 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1315]) ).
thf(332,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(3153,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)],[332]) ).
thf(3154,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)],[3153]) ).
thf(3155,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)],[3154]) ).
thf(3157,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3155]) ).
thf(3159,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3157]) ).
thf(3160,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[3159]) ).
thf(232,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(2474,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(2475,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[2474]) ).
thf(2476,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[2475]) ).
thf(8824,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,2476]) ).
thf(8825,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8824]) ).
thf(8849,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8825]) ).
thf(32223,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k4_tarski ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,8849]) ).
thf(32224,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k4_tarski ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[32223]) ).
thf(32225,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[32224:[bind(A,$thf( E @ ( D @ k4_tarski ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(35548,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[32225]) ).
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(1080,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(1081,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)],[1080]) ).
thf(1082,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)],[1081]) ).
thf(1083,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)],[1082]) ).
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(1107,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(1108,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)],[1107]) ).
thf(1110,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)],[1108]) ).
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(5385,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(193,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(2198,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(2199,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[2198]) ).
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(1665,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(255,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(2630,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)],[255]) ).
thf(455,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(3873,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)],[455]) ).
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(1393,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(1394,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)],[1393]) ).
thf(1395,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)],[1394]) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1395]) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1400]) ).
thf(1411,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_funct_1 ),
inference(simp,[status(thm)],[1410]) ).
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(5365,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(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(5088,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(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(1369,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(1031,axiom,
? [A: $i] : ( A @ l3_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(6668,plain,
? [A: $i] : ( A @ l3_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(6669,plain,
sk474 @ l3_lattices,
inference(cnf,[status(esa)],[6668]) ).
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(1168,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(317,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(3053,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)],[317]) ).
thf(568,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(4464,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)],[568]) ).
thf(372,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(3370,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(3371,plain,
( ( sk218 @ v1_relat_1 )
& ~ ( sk218 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3370]) ).
thf(3372,plain,
~ ( sk218 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3371]) ).
thf(8836,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,3372]) ).
thf(8837,plain,
( ( sk218 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8836]) ).
thf(8850,plain,
sk218 != k1_xboole_0,
inference(simp,[status(thm)],[8837]) ).
thf(34372,plain,
! [A: $i] :
( ( A != sk218 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,8850]) ).
thf(34373,plain,
! [A: $i] :
( ( A != sk218 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[34372]) ).
thf(34374,plain,
sk218 @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[34373:[bind(A,$thf( sk218 ))]]) ).
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(1160,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(1161,plain,
! [A: $i] :
( ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1160]) ).
thf(1162,plain,
! [A: $i] :
( ~ ( A @ v1_relat_1 )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1161]) ).
thf(36190,plain,
! [A: $i] :
( ( ( sk218 @ sk18 @ 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)],[34374,1162]) ).
thf(36191,plain,
! [A: $i] :
( ( ( sk218 @ sk18 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[36190]) ).
thf(36192,plain,
( ( sk218 @ sk18 @ k1_relat_1 @ ( sk218 @ sk18 @ k9_relat_1 ) )
= ( sk218 @ sk18 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[36191:[bind(A,$thf( sk218 @ sk18 ))]]) ).
thf(1003,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(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 @ 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)],[1003]) ).
thf(283,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(2770,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)],[283]) ).
thf(2771,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)],[2770]) ).
thf(2778,plain,
sk157 @ v13_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(723,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5291,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(5292,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5291]) ).
thf(5293,plain,
~ ( sk368 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5292]) ).
thf(8842,plain,
( ( ( sk368 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,5293]) ).
thf(8843,plain,
( ( sk368 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8842]) ).
thf(8844,plain,
sk368 != k1_xboole_0,
inference(simp,[status(thm)],[8843]) ).
thf(34450,plain,
! [A: $i] :
( ( A != sk368 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,8844]) ).
thf(34451,plain,
! [A: $i] :
( ( A != sk368 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[34450]) ).
thf(34452,plain,
sk368 @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[34451:[bind(A,$thf( sk368 ))]]) ).
thf(716,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(5260,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)],[716]) ).
thf(1007,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(6544,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)],[1007]) ).
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(1233,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(1234,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)],[1233]) ).
thf(1235,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)],[1234]) ).
thf(1237,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)],[1235]) ).
thf(945,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(6283,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)],[945]) ).
thf(515,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(4183,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)],[515]) ).
thf(428,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(3698,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)],[428]) ).
thf(978,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(6448,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)],[978]) ).
thf(822,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(5778,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)],[822]) ).
thf(1010,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(6555,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)],[1010]) ).
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(1179,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(211,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(2331,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)],[211]) ).
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(1818,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(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(1295,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(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(1686,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(198,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(2243,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)],[198]) ).
thf(2244,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)],[2243]) ).
thf(2250,plain,
sk94 @ l3_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
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(1750,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(1013,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(6576,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)],[1013]) ).
thf(495,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(4075,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)],[495]) ).
thf(325,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(3108,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)],[325]) ).
thf(800,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(5669,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)],[800]) ).
thf(598,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(4614,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)],[598]) ).
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(1305,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(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(1437,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(570,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(4479,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)],[570]) ).
thf(173,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2110,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(2111,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(cnf,[status(esa)],[2110]) ).
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(1089,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(1090,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)],[1089]) ).
thf(351,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(3244,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(3245,plain,
( ( sk207 @ v1_funct_1 )
& ( sk207 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3244]) ).
thf(3247,plain,
sk207 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3245]) ).
thf(1048,plain,
~ ( sk1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[1043]) ).
thf(7147,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)],[1079,1048]) ).
thf(7148,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[7147:[bind(A,$thf( sk1 ))]]) ).
thf(7329,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)],[7148]) ).
thf(9477,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)],[3247,7329]) ).
thf(9478,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9477]) ).
thf(9479,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9478:[bind(A,$thf( sk207 ))]]) ).
thf(9770,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( 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 @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1090,9479]) ).
thf(9771,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( 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 @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[9770]) ).
thf(9775,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk207 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[9771]) ).
thf(9779,plain,
( ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk207 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk207 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[9775]) ).
thf(3246,plain,
sk207 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3245]) ).
thf(40280,plain,
( ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk207 @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(rewrite,[status(thm)],[9779,3246]) ).
thf(40281,plain,
( ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk207 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[40280]) ).
thf(40385,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk207 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2111,40281]) ).
thf(40386,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk207 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[40385]) ).
thf(40438,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk207 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[40386]) ).
thf(40493,plain,
( ( ( sk207 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk207 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[40438]) ).
thf(425,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(3680,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)],[425]) ).
thf(485,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(4043,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)],[485]) ).
thf(484,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(4037,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)],[484]) ).
thf(239,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(2507,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)],[239]) ).
thf(2508,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)],[2507]) ).
thf(2512,plain,
k13_nat_lat @ v4_lattices,
inference(cnfConj,[status(thm)],[2508]) ).
thf(176,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(2117,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)],[176]) ).
thf(1049,plain,
sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[1043]) ).
thf(42594,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)],[1049,1244]) ).
thf(42595,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)],[42594]) ).
thf(42633,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ( sk2 != A )
| ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42595]) ).
thf(42659,plain,
( ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42633]) ).
thf(43770,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,42659]) ).
thf(43771,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[43770]) ).
thf(43818,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk71 )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[43771]) ).
thf(705,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(5225,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)],[705]) ).
thf(263,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(2695,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(2696,plain,
( ( sk152 @ v1_relat_1 )
& ( sk152 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2695]) ).
thf(2697,plain,
sk152 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[2696]) ).
thf(6939,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,3372]) ).
thf(6940,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6939]) ).
thf(6944,plain,
sk218 != sk152,
inference(simp,[status(thm)],[6940]) ).
thf(992,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(6495,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)],[992]) ).
thf(1998,plain,
sk71 @ v1_funct_1,
inference(cnfConj,[status(thm)],[1996]) ).
thf(7375,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1998,7231]) ).
thf(7376,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7375]) ).
thf(7377,plain,
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7376:[bind(A,$thf( sk71 ))]]) ).
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(1060,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(1061,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)],[1060]) ).
thf(1066,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)],[1061]) ).
thf(1067,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)],[1066]) ).
thf(1068,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)],[1067]) ).
thf(451,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( 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(3858,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)],[451]) ).
thf(540,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(4311,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)],[540]) ).
thf(901,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [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(6106,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)],[901]) ).
thf(436,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(3762,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)],[436]) ).
thf(3361,plain,
sk216 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[3359]) ).
thf(9585,plain,
( ( ( sk368 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,5293]) ).
thf(9586,plain,
( ( sk368 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9585]) ).
thf(9590,plain,
sk368 != sk216,
inference(simp,[status(thm)],[9586]) ).
thf(347,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(3230,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)],[347]) ).
thf(2776,plain,
~ ( sk157 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2771]) ).
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(1808,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(379,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(3417,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)],[379]) ).
thf(299,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(2953,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(725,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(5297,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)],[725]) ).
thf(385,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(3450,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)],[385]) ).
thf(3451,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)],[3450]) ).
thf(3452,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)],[3451]) ).
thf(3454,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( C @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[3452]) ).
thf(3459,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( C @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[3454]) ).
thf(3460,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[3459]) ).
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(1422,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(297,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(2947,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)],[297]) ).
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(1939,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(2248,plain,
sk94 @ v10_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
thf(845,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(5878,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)],[845]) ).
thf(324,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(3092,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)],[324]) ).
thf(3093,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)],[3092]) ).
thf(3098,plain,
sk196 @ v8_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
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(1071,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(1072,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)],[1071]) ).
thf(1073,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)],[1072]) ).
thf(464,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(3910,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)],[464]) ).
thf(823,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(5780,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)],[823]) ).
thf(5781,plain,
! [A: $i] :
( ( ( ( A @ ( sk413 @ ( 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 @ ( sk413 @ ( 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 @ ( sk413 @ ( 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 @ ( sk413 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( sk413 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ) ),
inference(cnf,[status(esa)],[5780]) ).
thf(5785,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5781]) ).
thf(5793,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ v1_funct_2 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5785]) ).
thf(954,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(6338,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)],[954]) ).
thf(340,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(3194,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)],[340]) ).
thf(3195,plain,
( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(miniscope,[status(thm)],[3194]) ).
thf(3196,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[3195]) ).
thf(3197,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3196]) ).
thf(8908,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3197,7231]) ).
thf(8909,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8908]) ).
thf(8910,plain,
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8909:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(16861,plain,
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8910,2307]) ).
thf(16862,plain,
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16861]) ).
thf(868,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(5982,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)],[868]) ).
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(1205,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(175,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(2114,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)],[175]) ).
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(1135,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(1136,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)],[1135]) ).
thf(1138,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)],[1136]) ).
thf(1142,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)],[1138]) ).
thf(1047,plain,
sk1 @ l3_lattices,
inference(cnfConj,[status(thm)],[1043]) ).
thf(7089,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)],[1079,1047]) ).
thf(7090,plain,
! [A: $i] :
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[7089:[bind(A,$thf( sk1 ))]]) ).
thf(7300,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)],[7090]) ).
thf(7848,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)],[1998,7300]) ).
thf(7849,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7848]) ).
thf(7850,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7849:[bind(A,$thf( sk71 ))]]) ).
thf(624,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(4735,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)],[624]) ).
thf(4736,plain,
! [A: $i] :
( ( ( ( A @ ( sk319 @ ( 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 @ ( sk319 @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ v1_funct_2 ) ) )
& ( sk319 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[4735]) ).
thf(4737,plain,
sk319 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4736]) ).
thf(10123,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4737,7231]) ).
thf(10124,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10123]) ).
thf(10125,plain,
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10124:[bind(A,$thf( sk319 ))]]) ).
thf(880,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(6031,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)],[880]) ).
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(4973,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(345,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(3212,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)],[345]) ).
thf(3213,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)],[3212]) ).
thf(3217,plain,
k6_nat_lat @ v10_lattices,
inference(cnfConj,[status(thm)],[3213]) ).
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(1655,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(5784,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5781]) ).
thf(5792,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ m2_relset_1 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5784]) ).
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(1153,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(1154,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)],[1153]) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[1154]) ).
thf(15630,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ 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)],[5792,1156]) ).
thf(15631,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[15630]) ).
thf(15632,plain,
( ( f2_s11_funct_2 @ ( sk413 @ k2_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[15631:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk413 ))]]) ).
thf(691,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(5146,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(585,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(4564,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)],[585]) ).
thf(529,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(4247,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)],[529]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( B @ ( A @ k2_filter_2 ) @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_2) ).
thf(6336,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)],[953]) ).
thf(1063,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)],[1061]) ).
thf(31834,plain,
! [A: $i] :
( ( A != sk474 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,6669]) ).
thf(31835,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk474 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31834:[bind(A,$thf( sk474 ))]]) ).
thf(182,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(2146,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)],[182]) ).
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(1458,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(365,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(3334,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(3335,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(cnf,[status(esa)],[3334]) ).
thf(3336,plain,
! [A: $i] :
( ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) )
= ( A @ k2_subset_1 ) ),
inference(lifteq,[status(thm)],[3335]) ).
thf(249,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(2584,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(2585,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(cnf,[status(esa)],[2584]) ).
thf(2586,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(lifteq,[status(thm)],[2585]) ).
thf(328,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(3129,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(3130,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3129]) ).
thf(3131,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3130]) ).
thf(40692,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_subset_1 ) )
= A ),
inference(rewrite,[status(thm)],[3336,2586,3131]) ).
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(1705,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(1000,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(6522,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)],[1000]) ).
thf(864,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(5967,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)],[864]) ).
thf(965,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(6391,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)],[965]) ).
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(1608,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(3109,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)],[3108]) ).
thf(3120,plain,
sk197 @ v1_lattice2,
inference(cnfConj,[status(thm)],[3109]) ).
thf(996,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(6505,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)],[996]) ).
thf(315,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(3049,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)],[315]) ).
thf(4739,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[4736]) ).
thf(779,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(5589,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)],[779]) ).
thf(1044,plain,
sk1 @ v16_lattices,
inference(cnfConj,[status(thm)],[1043]) ).
thf(6987,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v16_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)],[1079,1044]) ).
thf(6988,plain,
! [A: $i] :
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6987:[bind(A,$thf( sk1 ))]]) ).
thf(7249,plain,
! [A: $i] :
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[6988]) ).
thf(9625,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3362,7249]) ).
thf(9626,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9625]) ).
thf(9627,plain,
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9626:[bind(A,$thf( sk216 ))]]) ).
thf(13237,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,9627]) ).
thf(13238,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13237]) ).
thf(13317,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[13238]) ).
thf(305,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(2993,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)],[305]) ).
thf(2994,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)],[2993]) ).
thf(3004,plain,
sk188 @ v3_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
thf(452,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(3862,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)],[452]) ).
thf(3863,plain,
! [A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk254 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[3862]) ).
thf(3865,plain,
! [A: $i] : ( A @ sk254 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3863]) ).
thf(13718,plain,
! [A: $i] :
( ( ( A @ sk254 @ v1_xboole_0 )
!= ( sk368 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3865,5293]) ).
thf(13719,plain,
! [A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
!= ( sk368 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13718]) ).
thf(13722,plain,
! [A: $i] :
( ( A @ sk254 )
!= sk368 ),
inference(simp,[status(thm)],[13719]) ).
thf(934,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(6246,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)],[934]) ).
thf(1155,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[1154]) ).
thf(15598,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ 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)],[5792,1155]) ).
thf(15599,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk413 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[15598]) ).
thf(15600,plain,
( ( f1_s11_funct_2 @ ( sk413 @ k1_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[15599:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk413 ))]]) ).
thf(31944,plain,
! [A: $i] :
( ( A != sk196 )
| ( k1_xboole_0 @ v8_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,3098]) ).
thf(31945,plain,
( ( k1_xboole_0 @ v8_lattices )
| ( sk196 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31944:[bind(A,$thf( sk196 ))]]) ).
thf(1999,plain,
sk71 @ v2_funct_1,
inference(cnfConj,[status(thm)],[1996]) ).
thf(208,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(2316,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)],[208]) ).
thf(9469,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)],[3247,7300]) ).
thf(9470,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9469]) ).
thf(9471,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9470:[bind(A,$thf( sk207 ))]]) ).
thf(16947,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)],[2307,9471]) ).
thf(16948,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)],[16947]) ).
thf(17047,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)],[16948]) ).
thf(17079,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[17047]) ).
thf(228,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(2448,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)],[228]) ).
thf(1046,plain,
sk1 @ v10_lattices,
inference(cnfConj,[status(thm)],[1043]) ).
thf(7017,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)],[1079,1046]) ).
thf(7018,plain,
! [A: $i] :
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[7017:[bind(A,$thf( sk1 ))]]) ).
thf(7264,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)],[7018]) ).
thf(10111,plain,
! [A: $i] :
( ( ( sk319 @ 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)],[4737,7264]) ).
thf(10112,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10111]) ).
thf(10113,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10112:[bind(A,$thf( sk319 ))]]) ).
thf(16898,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,10113]) ).
thf(16899,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16898]) ).
thf(17037,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[16899]) ).
thf(17068,plain,
( ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[17037]) ).
thf(896,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(6089,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)],[896]) ).
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(4856,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(561,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4439,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(4440,plain,
sk300 @ v1_xboole_0,
inference(cnf,[status(esa)],[4439]) ).
thf(605,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(4650,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)],[605]) ).
thf(254,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(2627,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)],[254]) ).
thf(186,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(2168,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)],[186]) ).
thf(353,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(3253,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)],[353]) ).
thf(447,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(3826,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)],[447]) ).
thf(229,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(2451,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)],[229]) ).
thf(2452,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)],[2451]) ).
thf(2459,plain,
sk118 @ v6_lattices,
inference(cnfConj,[status(thm)],[2452]) ).
thf(3121,plain,
sk197 @ v8_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(1034,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(6680,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)],[1034]) ).
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(1216,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(1217,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)],[1216]) ).
thf(1220,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)],[1217]) ).
thf(1222,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)],[1220]) ).
thf(213,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(2360,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)],[213]) ).
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 @ 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(6046,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)],[887]) ).
thf(1050,plain,
sk1 @ v15_lattices,
inference(cnfConj,[status(thm)],[1043]) ).
thf(7129,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v15_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)],[1079,1050]) ).
thf(7130,plain,
! [A: $i] :
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[7129:[bind(A,$thf( sk1 ))]]) ).
thf(7320,plain,
! [A: $i] :
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[7130]) ).
thf(9670,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3362,7320]) ).
thf(9671,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9670]) ).
thf(9672,plain,
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9671:[bind(A,$thf( sk216 ))]]) ).
thf(448,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(3836,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)],[448]) ).
thf(248,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(2579,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(2580,plain,
( ( sk138 @ v2_funct_1 )
& ( sk138 @ v1_funct_1 )
& ( sk138 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2579]) ).
thf(2582,plain,
sk138 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2580]) ).
thf(7845,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)],[2582,7300]) ).
thf(7846,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7845]) ).
thf(7847,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7846:[bind(A,$thf( sk138 ))]]) ).
thf(16973,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[2307,7847]) ).
thf(16974,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[16973]) ).
thf(17049,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16974]) ).
thf(17081,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[17049]) ).
thf(814,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(5745,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)],[814]) ).
thf(855,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(5921,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)],[855]) ).
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(1935,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(357,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(3281,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)],[357]) ).
thf(816,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(5750,plain,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(634,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(4770,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)],[634]) ).
thf(4771,plain,
( ( sk321 @ v17_lattices )
& ( sk321 @ v16_lattices )
& ( sk321 @ v15_lattices )
& ( sk321 @ v14_lattices )
& ( sk321 @ v13_lattices )
& ( sk321 @ v11_lattices )
& ( sk321 @ v10_lattices )
& ( sk321 @ v9_lattices )
& ( sk321 @ v8_lattices )
& ( sk321 @ v7_lattices )
& ( sk321 @ v6_lattices )
& ( sk321 @ v5_lattices )
& ( sk321 @ v4_lattices )
& ( sk321 @ v3_lattices )
& ~ ( sk321 @ v3_struct_0 )
& ( sk321 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4770]) ).
thf(4775,plain,
sk321 @ v11_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(3103,plain,
sk196 @ v9_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(628,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(4751,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(4752,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4751]) ).
thf(4753,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[4752]) ).
thf(8828,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,4753]) ).
thf(8829,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8828]) ).
thf(8851,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8829]) ).
thf(983,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(6466,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)],[983]) ).
thf(812,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(5740,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)],[812]) ).
thf(31976,plain,
! [A: $i] :
( ( A != sk197 )
| ( k1_xboole_0 @ v1_lattice2 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,3120]) ).
thf(31977,plain,
( ( k1_xboole_0 @ v1_lattice2 )
| ( sk197 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31976:[bind(A,$thf( sk197 ))]]) ).
thf(502,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(4112,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(4113,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4112]) ).
thf(4114,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[4113]) ).
thf(8840,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,4114]) ).
thf(8841,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8840]) ).
thf(8848,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8841]) ).
thf(302,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(2972,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)],[302]) ).
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(2046,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(936,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [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(6251,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)],[936]) ).
thf(225,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(2432,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)],[225]) ).
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(5388,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(5389,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk381 @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) )
| ~ ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk379 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk381 @ m2_relset_1 ) ) )
| ~ sk379 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk381 @ v1_funct_2 ) ) )
| ~ sk379 )
& ( ( sk381 @ v1_funct_1 )
| ~ sk379 )
& ( sk379
| ~ ( A @ ( sk380 @ p1_s3_funct_2 ) )
| ~ ( f2_s3_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk379
| ( f1_s3_funct_2 @ ( sk380 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[5388]) ).
thf(5393,plain,
( sk379
| ( f1_s3_funct_2 @ ( sk380 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[5389]) ).
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(1127,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(942,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(6268,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)],[942]) ).
thf(236,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(2491,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)],[236]) ).
thf(1243,plain,
~ ( sk14 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1242]) ).
thf(304,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(2978,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)],[304]) ).
thf(2979,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)],[2978]) ).
thf(2985,plain,
~ ( sk187 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2979]) ).
thf(575,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(4496,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)],[575]) ).
thf(808,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(5723,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)],[808]) ).
thf(820,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(5770,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)],[820]) ).
thf(517,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(4198,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)],[517]) ).
thf(169,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(2082,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)],[169]) ).
thf(31881,plain,
! [A: $i] :
( ( A != sk94 )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,2248]) ).
thf(31882,plain,
( ( k1_xboole_0 @ v10_lattices )
| ( sk94 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31881:[bind(A,$thf( sk94 ))]]) ).
thf(14907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,1156]) ).
thf(14908,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14907]) ).
thf(14909,plain,
f2_s4_funct_2 @ ( sk319 @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[14908:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk319 ))]]) ).
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(1118,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(1119,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)],[1118]) ).
thf(1120,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)],[1119]) ).
thf(14952,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk319 @ 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)],[14909,1120]) ).
thf(14953,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk319 @ 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)],[14952]) ).
thf(14954,plain,
! [A: $i] : ( sk319 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14953:[bind(A,$thf( sk319 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14969,plain,
! [A: $i] : ( sk319 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14954]) ).
thf(900,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(6102,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)],[900]) ).
thf(2516,plain,
k13_nat_lat @ v8_lattices,
inference(cnfConj,[status(thm)],[2508]) ).
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(4963,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(285,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(2825,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)],[285]) ).
thf(9655,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)],[3362,7264]) ).
thf(9656,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9655]) ).
thf(9657,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9656:[bind(A,$thf( sk216 ))]]) ).
thf(989,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(6483,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)],[989]) ).
thf(609,axiom,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(4665,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(510,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(4156,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)],[510]) ).
thf(457,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(3880,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)],[457]) ).
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(1228,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(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(1482,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(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(1254,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(3360,plain,
sk216 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3359]) ).
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(1074,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(1075,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)],[1074]) ).
thf(9554,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)],[3360,1075]) ).
thf(9555,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)],[9554]) ).
thf(9556,plain,
! [A: $i] : ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[9555:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).
thf(15884,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)],[3360,1162]) ).
thf(15885,plain,
! [A: $i] :
( ( ( sk216 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15884]) ).
thf(15886,plain,
( ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) )
= ( sk216 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15885:[bind(A,$thf( sk216 ))]]) ).
thf(26708,plain,
! [A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[9556,15886]) ).
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(1104,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(1105,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(miniscope,[status(thm)],[1104]) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[1105]) ).
thf(26717,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)],[26708,1106]) ).
thf(26718,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)],[26717]) ).
thf(26719,plain,
! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[26718:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk216 @ k9_relat_1 ) )),bind(C,$thf( sk216 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(26802,plain,
! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[26719]) ).
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(5024,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(733,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(5352,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)],[733]) ).
thf(825,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(5797,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)],[825]) ).
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(1709,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(547,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(4348,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)],[547]) ).
thf(559,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(4422,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)],[559]) ).
thf(267,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(2708,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)],[267]) ).
thf(893,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(6066,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)],[893]) ).
thf(196,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(2217,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)],[196]) ).
thf(415,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(3612,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)],[415]) ).
thf(443,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(3803,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)],[443]) ).
thf(277,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(2745,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)],[277]) ).
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(1977,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1978,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[1977]) ).
thf(12253,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1978,8848]) ).
thf(12254,plain,
( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12253:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(460,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(3891,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)],[460]) ).
thf(601,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(4637,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)],[601]) ).
thf(352,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(3248,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)],[352]) ).
thf(31863,plain,
! [A: $i] :
( ( A != sk94 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,2250]) ).
thf(31864,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk94 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31863:[bind(A,$thf( sk94 ))]]) ).
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 ) )
=> ! [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(5953,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)],[859]) ).
thf(382,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(3442,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)],[382]) ).
thf(10081,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4737,7249]) ).
thf(10082,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10081]) ).
thf(10083,plain,
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10082:[bind(A,$thf( sk319 ))]]) ).
thf(16951,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,10083]) ).
thf(16952,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16951]) ).
thf(17044,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[16952]) ).
thf(17075,plain,
( ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[17044]) ).
thf(8113,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1998,7320]) ).
thf(8114,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8113]) ).
thf(8115,plain,
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8114:[bind(A,$thf( sk71 ))]]) ).
thf(13282,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,8115]) ).
thf(13283,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13282]) ).
thf(13313,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[13283]) ).
thf(3221,plain,
k6_nat_lat @ v9_lattices,
inference(cnfConj,[status(thm)],[3213]) ).
thf(778,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(5585,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)],[778]) ).
thf(577,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(4524,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)],[577]) ).
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(4866,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(1009,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(6552,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)],[1009]) ).
thf(932,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(6242,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)],[932]) ).
thf(423,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(3644,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)],[423]) ).
thf(356,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(3275,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)],[356]) ).
thf(882,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(6034,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)],[882]) ).
thf(2698,plain,
sk152 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2696]) ).
thf(3116,plain,
sk197 @ v7_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(260,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(2667,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(509,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(4151,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)],[509]) ).
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(1871,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(407,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(3574,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)],[407]) ).
thf(631,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4761,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(970,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(6423,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)],[970]) ).
thf(4778,plain,
sk321 @ v14_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(3373,plain,
sk218 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3371]) ).
thf(15879,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)],[3373,1162]) ).
thf(15880,plain,
! [A: $i] :
( ( ( sk218 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15879]) ).
thf(15881,plain,
( ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) )
= ( sk218 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15880:[bind(A,$thf( sk218 ))]]) ).
thf(438,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(3776,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(327,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(3125,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)],[327]) ).
thf(692,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(5150,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)],[692]) ).
thf(505,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(4130,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)],[505]) ).
thf(774,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5571,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(5572,plain,
! [A: $i] : ( A @ ( A @ sk395 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[5571]) ).
thf(42551,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk395 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5572,1244]) ).
thf(42552,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk395 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42551]) ).
thf(42553,plain,
~ ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[42552:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ sk395 ))]]) ).
thf(42701,plain,
( ( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,42553]) ).
thf(42702,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42701]) ).
thf(42748,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk216 ),
inference(simp,[status(thm)],[42702]) ).
thf(190,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(2185,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)],[190]) ).
thf(695,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(5160,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)],[695]) ).
thf(432,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(3744,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)],[432]) ).
thf(952,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(6332,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)],[952]) ).
thf(999,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(6517,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(6518,plain,
( ( sk461 @ v3_lattices )
& ~ ( sk461 @ v3_struct_0 )
& ( sk461 @ l3_lattices ) ),
inference(cnf,[status(esa)],[6517]) ).
thf(6519,plain,
sk461 @ l3_lattices,
inference(cnfConj,[status(thm)],[6518]) ).
thf(722,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(5289,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)],[722]) ).
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(4984,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(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(1462,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(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(1052,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(1053,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)],[1052]) ).
thf(1055,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)],[1053]) ).
thf(1058,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)],[1055]) ).
thf(1059,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)],[1058]) ).
thf(931,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(6240,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)],[931]) ).
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(1147,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(1022,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 @ 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(6626,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)],[1022]) ).
thf(3216,plain,
k6_nat_lat @ v7_lattices,
inference(cnfConj,[status(thm)],[3213]) ).
thf(272,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(2730,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)],[272]) ).
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(2024,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(21,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(1144,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1145,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[1144]) ).
thf(1146,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[1145]) ).
thf(1229,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1228]) ).
thf(1230,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1229]) ).
thf(1231,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1230]) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
= A ),
inference(cnf,[status(esa)],[1231]) ).
thf(40010,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
= A ),
inference(lifteq,[status(thm)],[1232]) ).
thf(40021,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)],[1146,40010]) ).
thf(40022,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk13 ) )
= A ),
inference(pattern_uni,[status(thm)],[40021:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(2989,plain,
sk187 @ v14_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(5089,plain,
! [A: $i] :
( ( ( ( A @ ( sk354 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s13_funct_2 ) )
| ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk352 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk354 @ m2_relset_1 ) ) )
| ~ sk352 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk354 @ v1_funct_2 ) ) )
| ~ sk352 )
& ( ( sk354 @ v1_funct_1 )
| ~ sk352 )
& ( sk352
| ~ ( f2_s13_funct_2 @ ( sk353 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
& ( sk352
| ( f1_s13_funct_2 @ ( sk353 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[5088]) ).
thf(5091,plain,
( sk352
| ( f1_s13_funct_2 @ ( sk353 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[5089]) ).
thf(453,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(3866,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)],[453]) ).
thf(706,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(5231,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)],[706]) ).
thf(223,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(2420,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)],[223]) ).
thf(3099,plain,
sk196 @ v4_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(937,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(6253,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)],[937]) ).
thf(269,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(2713,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(504,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(4119,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)],[504]) ).
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(1379,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(373,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(3374,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)],[373]) ).
thf(375,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(3385,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)],[375]) ).
thf(841,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(5863,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)],[841]) ).
thf(5864,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)],[5863]) ).
thf(5868,plain,
k6_nat_lat @ l3_lattices,
inference(cnfConj,[status(thm)],[5864]) ).
thf(6467,plain,
( ( k13_nat_lat @ l3_lattices )
& ( k13_nat_lat @ v10_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[6466]) ).
thf(6470,plain,
k13_nat_lat @ l3_lattices,
inference(cnfConj,[status(thm)],[6467]) ).
thf(701,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(5213,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(5214,plain,
sk364 @ l2_struct_0,
inference(cnf,[status(esa)],[5213]) ).
thf(782,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(5605,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)],[782]) ).
thf(635,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(4788,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)],[635]) ).
thf(220,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(2399,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)],[220]) ).
thf(2400,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)],[2399]) ).
thf(2403,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2400]) ).
thf(421,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(3638,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)],[421]) ).
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(1087,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(516,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(4194,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
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(1245,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(1246,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)],[1245]) ).
thf(1247,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)],[1246]) ).
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 @ 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(4358,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)],[549]) ).
thf(995,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(6502,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)],[995]) ).
thf(361,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(3312,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(3313,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[3312]) ).
thf(19414,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
inference(rewrite,[status(thm)],[3313,2586]) ).
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(1479,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(573,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(4492,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)],[573]) ).
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(5397,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(599,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(4622,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)],[599]) ).
thf(8290,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)],[2582,7329]) ).
thf(8291,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8290]) ).
thf(8292,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8291:[bind(A,$thf( sk138 ))]]) ).
thf(16992,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[2307,8292]) ).
thf(16993,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[16992]) ).
thf(17052,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16993]) ).
thf(17085,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[17052]) ).
thf(323,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(3084,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)],[323]) ).
thf(1109,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)],[1108]) ).
thf(1115,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)],[1109]) ).
thf(387,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(3470,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)],[387]) ).
thf(837,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 @ k23_filter_2 ) @ k6_lattices )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_filter_2) ).
thf(5851,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 @ k23_filter_2 ) @ k6_lattices )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(734,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(5362,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(5363,plain,
~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5362]) ).
thf(5364,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5363]) ).
thf(8838,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,5364]) ).
thf(8839,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8838]) ).
thf(8847,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8839]) ).
thf(32870,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_tarski ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,8847]) ).
thf(32871,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_tarski ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[32870]) ).
thf(32872,plain,
! [A: $i] : ( A @ k1_tarski @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[32871:[bind(A,$thf( C @ k1_tarski )),bind(B,$thf( C ))]]) ).
thf(35186,plain,
! [A: $i] : ( A @ k1_tarski @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[32872]) ).
thf(34024,plain,
! [A: $i] :
( ( A
!= ( sk1 @ u1_struct_0 ) )
| ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1049]) ).
thf(34025,plain,
( ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[34024:[bind(A,$thf( sk1 @ u1_struct_0 ))]]) ).
thf(10070,plain,
! [A: $i] :
( ( ( sk319 @ 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)],[4737,7300]) ).
thf(10071,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10070]) ).
thf(10072,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10071:[bind(A,$thf( sk319 ))]]) ).
thf(13270,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,10072]) ).
thf(13271,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13270]) ).
thf(13355,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk319 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[13271]) ).
thf(13393,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[13355]) ).
thf(7959,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,5364]) ).
thf(7960,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7959]) ).
thf(7965,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk71 ),
inference(simp,[status(thm)],[7960]) ).
thf(877,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ v12_lattices )
=> ( B @ ( A @ k23_filter_2 ) @ v12_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_2) ).
thf(6025,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ v12_lattices )
=> ( B @ ( A @ k23_filter_2 ) @ v12_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(6732,plain,
( ( ( sk71 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,1243]) ).
thf(6733,plain,
( ( sk71 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6732]) ).
thf(6734,plain,
sk71 != sk14,
inference(simp,[status(thm)],[6733]) ).
thf(288,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(2852,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)],[288]) ).
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(1098,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(1099,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)],[1098]) ).
thf(1100,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)],[1099]) ).
thf(785,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(5617,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)],[785]) ).
thf(531,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(4253,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)],[531]) ).
thf(355,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(3268,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)],[355]) ).
thf(440,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(3788,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)],[440]) ).
thf(2456,plain,
sk118 @ v10_lattices,
inference(cnfConj,[status(thm)],[2452]) ).
thf(9581,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,5364]) ).
thf(9582,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9581]) ).
thf(9593,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk216 ),
inference(simp,[status(thm)],[9582]) ).
thf(849,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(5892,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)],[849]) ).
thf(472,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(3966,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)],[472]) ).
thf(2782,plain,
sk157 @ v4_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(200,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(2259,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)],[200]) ).
thf(177,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(2122,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)],[177]) ).
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 ) )
=> ! [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(6176,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)],[918]) ).
thf(694,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(5156,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)],[694]) ).
thf(503,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(4115,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
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(2017,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(803,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ 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(5682,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)],[803]) ).
thf(894,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v13_lattices )
=> ( ( ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ k5_lattices )
= ( A @ k5_lattices ) )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v13_lattices ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_filter_2) ).
thf(6081,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v13_lattices )
=> ( ( ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ k5_lattices )
= ( A @ k5_lattices ) )
& ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v13_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(15876,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)],[3246,1162]) ).
thf(15877,plain,
! [A: $i] :
( ( ( sk207 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15876]) ).
thf(15878,plain,
( ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) )
= ( sk207 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15877:[bind(A,$thf( sk207 ))]]) ).
thf(298,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(2950,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)],[298]) ).
thf(860,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(5957,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)],[860]) ).
thf(717,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(5264,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)],[717]) ).
thf(874,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(6002,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)],[874]) ).
thf(397,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(3524,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)],[397]) ).
thf(14926,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk319 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14909,1106]) ).
thf(14927,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk319 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14926]) ).
thf(14928,plain,
! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk319 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14927:[bind(A,$thf( sk319 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14970,plain,
! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk319 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14928]) ).
thf(15447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( A @ ( sk319 @ 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)],[14970,1106]) ).
thf(15448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( A @ ( sk319 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[15447]) ).
thf(15449,plain,
! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk319 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[15448:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk319 @ k2_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f2_s4_funct_2 )),bind(D,$thf( D ))]]) ).
thf(15500,plain,
! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk319 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[15449]) ).
thf(341,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(3199,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)],[341]) ).
thf(929,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(6227,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)],[929]) ).
thf(2083,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(cnf,[status(esa)],[2082]) ).
thf(2084,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
= ( A @ k1_tarski @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[2083]) ).
thf(3645,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)],[3644]) ).
thf(3646,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)],[3645]) ).
thf(3651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != B )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(cnfConj,[status(thm)],[3646]) ).
thf(3663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != B )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(lifteq,[status(thm)],[3651]) ).
thf(3664,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ r2_hidden ) ),
inference(simp,[status(thm)],[3663]) ).
thf(28525,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)],[2084,3664]) ).
thf(28526,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[28525:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(28563,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[28526]) ).
thf(563,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(4443,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)],[563]) ).
thf(683,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(5084,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1032,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] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( ( D @ ( C @ ( A @ k4_lattices ) ) )
= ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ k4_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ k3_lattices ) ) )
= ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_filter_2) ).
thf(6670,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 ) )
=> ! [E: $i] :
( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( ( D @ ( C @ ( A @ k4_lattices ) ) )
= ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ k4_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ k3_lattices ) ) )
= ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(840,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(5861,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)],[840]) ).
thf(532,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(4257,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(4258,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(cnf,[status(esa)],[4257]) ).
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(1373,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(2996,plain,
sk188 @ v3_filter_0,
inference(cnfConj,[status(thm)],[2994]) ).
thf(13239,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,10083]) ).
thf(13240,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13239]) ).
thf(13339,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk319 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[13240]) ).
thf(13382,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[13339]) ).
thf(13716,plain,
! [B: $i,A: $i] :
( ( ( A @ sk254 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3865,4114]) ).
thf(13717,plain,
! [B: $i,A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13716]) ).
thf(13726,plain,
! [B: $i,A: $i] :
( ( A @ sk254 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[13717]) ).
thf(16017,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( B @ k1_zfmisc_1 ) )
| ( ( A @ sk254 )
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1978,13726]) ).
thf(16018,plain,
! [A: $i] :
( ( A @ sk254 )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[16017:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(8110,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2582,7320]) ).
thf(8111,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8110]) ).
thf(8112,plain,
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8111:[bind(A,$thf( sk138 ))]]) ).
thf(13233,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,8112]) ).
thf(13234,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13233]) ).
thf(13312,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[13234]) ).
thf(8293,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)],[1998,7329]) ).
thf(8294,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8293]) ).
thf(8295,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8294:[bind(A,$thf( sk71 ))]]) ).
thf(8421,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)],[1090,8295]) ).
thf(8422,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)],[8421]) ).
thf(8425,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)],[8422]) ).
thf(8427,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)],[8425]) ).
thf(1997,plain,
sk71 @ v1_relat_1,
inference(cnfConj,[status(thm)],[1996]) ).
thf(26922,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)],[8427,1997]) ).
thf(26923,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)],[26922]) ).
thf(26988,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)],[2111,26923]) ).
thf(26989,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)],[26988]) ).
thf(27047,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)],[26989]) ).
thf(27070,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)],[27047]) ).
thf(333,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(3161,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(3162,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3161]) ).
thf(3163,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3162]) ).
thf(839,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(5856,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)],[839]) ).
thf(14421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,1155]) ).
thf(14422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14421]) ).
thf(14423,plain,
f1_s4_funct_2 @ ( sk319 @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[14422:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk319 ))]]) ).
thf(966,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(6393,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)],[966]) ).
thf(6394,plain,
( ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk453 @ r2_hidden ) )
| ~ ( sk453 @ p1_s4_subset_1 )
| sk451 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk453 @ p1_s4_subset_1 )
| ~ ( sk453 @ p1_s4_subset_1 )
| sk451 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk453 @ r2_hidden ) )
| ( f3_s4_subset_1 @ ( sk453 @ r2_hidden ) )
| sk451 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk453 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk453 @ r2_hidden ) )
| sk451 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk453 @ m1_subset_1 ) )
| sk451 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk451
| ~ ( f2_s4_subset_1 @ ( sk452 @ r2_hidden ) )
| ~ ( sk452 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk451
| ( sk452 @ p1_s4_subset_1 )
| ~ ( sk452 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk451
| ~ ( f2_s4_subset_1 @ ( sk452 @ r2_hidden ) )
| ( f2_s4_subset_1 @ ( sk452 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk451
| ( sk452 @ p1_s4_subset_1 )
| ( f2_s4_subset_1 @ ( sk452 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk451
| ( f1_s4_subset_1 @ ( sk452 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[6393]) ).
thf(6403,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk453 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk453 @ r2_hidden ) )
| sk451 ),
inference(cnfConj,[status(thm)],[6394]) ).
thf(6410,plain,
( ( sk453 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk453 @ r2_hidden ) )
| sk451
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[6403]) ).
thf(388,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(3473,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)],[388]) ).
thf(1004,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(6534,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)],[1004]) ).
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(4847,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(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(1383,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(2254,plain,
sk94 @ v4_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
thf(242,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(2540,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)],[242]) ).
thf(829,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(5805,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)],[829]) ).
thf(728,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(5311,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)],[728]) ).
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(2034,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(2777,plain,
sk157 @ v11_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(4783,plain,
sk321 @ v9_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
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(1283,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(167,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(2073,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)],[167]) ).
thf(1051,plain,
( ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ l3_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v15_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(cnfConj,[status(thm)],[1043]) ).
thf(42716,plain,
( ( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,42553]) ).
thf(42717,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42716]) ).
thf(42754,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk152 ),
inference(simp,[status(thm)],[42717]) ).
thf(637,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(4810,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)],[637]) ).
thf(821,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(5773,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)],[821]) ).
thf(429,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(3712,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)],[429]) ).
thf(2772,plain,
sk157 @ v10_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(789,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(5629,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)],[789]) ).
thf(8878,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3197,7249]) ).
thf(8879,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8878]) ).
thf(8880,plain,
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8879:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(16857,plain,
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8880,2307]) ).
thf(16858,plain,
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16857]) ).
thf(985,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_nat_lat ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_filter_2) ).
thf(6474,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_nat_lat ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
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(5045,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(680,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(5058,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(5059,plain,
sk348 @ l1_lattices,
inference(cnf,[status(esa)],[5058]) ).
thf(621,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(4718,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)],[621]) ).
thf(811,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(5738,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)],[811]) ).
thf(33880,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v16_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1044]) ).
thf(33881,plain,
( ( k1_xboole_0 @ v16_lattices )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[33880:[bind(A,$thf( sk1 ))]]) ).
thf(1024,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(6631,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)],[1024]) ).
thf(9300,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)],[3246,1075]) ).
thf(9301,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)],[9300]) ).
thf(9302,plain,
! [A: $i] : ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[9301:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).
thf(24541,plain,
! [A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[9302,15878]) ).
thf(489,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(4055,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(524,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(4230,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(9614,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)],[3362,7300]) ).
thf(9615,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9614]) ).
thf(9616,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9615:[bind(A,$thf( sk216 ))]]) ).
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(5379,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(13235,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[4739,9471]) ).
thf(13236,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[13235]) ).
thf(13305,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[13236]) ).
thf(1036,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_2 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( 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_2) ).
thf(6685,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] :
( ( C @ ( D @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_filter_2 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_filter_2 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ r3_lattices ) ) )
& ( A = D )
& ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
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(1213,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(1214,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)],[1213]) ).
thf(1215,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)],[1214]) ).
thf(927,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(6221,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)],[927]) ).
thf(17020,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)],[2307,9479]) ).
thf(17021,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)],[17020]) ).
thf(17028,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)],[17021]) ).
thf(17058,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[17028]) ).
thf(731,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(5343,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)],[731]) ).
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(1526,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(468,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(3955,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)],[468]) ).
thf(876,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(6021,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)],[876]) ).
thf(204,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(2286,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)],[204]) ).
thf(257,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(2639,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)],[257]) ).
thf(279,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(2750,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)],[279]) ).
thf(1401,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1395]) ).
thf(1404,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1401]) ).
thf(1405,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1404]) ).
thf(603,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(4643,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)],[603]) ).
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(1189,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(1190,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)],[1189]) ).
thf(1194,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)],[1190]) ).
thf(1201,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)],[1194]) ).
thf(690,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(5137,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)],[690]) ).
thf(916,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(6156,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)],[916]) ).
thf(454,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(3870,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)],[454]) ).
thf(410,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(3588,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)],[410]) ).
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(4892,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(552,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(4379,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)],[552]) ).
thf(13704,plain,
! [A: $i] :
( ( ( A @ sk254 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3865,1243]) ).
thf(13705,plain,
! [A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13704]) ).
thf(13725,plain,
! [A: $i] :
( ( A @ sk254 )
!= sk14 ),
inference(simp,[status(thm)],[13705]) ).
thf(9583,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,4114]) ).
thf(9584,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9583]) ).
thf(9589,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk216 ),
inference(simp,[status(thm)],[9584]) ).
thf(6858,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,3372]) ).
thf(6859,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6858]) ).
thf(6860,plain,
sk218 != sk71,
inference(simp,[status(thm)],[6859]) ).
thf(2982,plain,
sk187 @ v13_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
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(1975,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(10024,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,4114]) ).
thf(10025,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10024]) ).
thf(10029,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk300 ),
inference(simp,[status(thm)],[10025]) ).
thf(493,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(4065,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)],[493]) ).
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(1863,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(408,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(3582,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)],[408]) ).
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(5406,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(32086,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1046]) ).
thf(32087,plain,
( ( k1_xboole_0 @ v10_lattices )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[32086:[bind(A,$thf( sk1 ))]]) ).
thf(405,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(3567,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)],[405]) ).
thf(17600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( sk413 @ 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)],[15632,1106]) ).
thf(17601,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( sk413 @ 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)],[17600]) ).
thf(17602,plain,
! [A: $i] :
( ( f2_s11_funct_2 @ ( A @ ( sk413 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[17601:[bind(A,$thf( sk413 @ k2_relat_1 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( C ))]]) ).
thf(17655,plain,
! [A: $i] :
( ( f2_s11_funct_2 @ ( A @ ( sk413 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[17602]) ).
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(1470,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(897,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(6092,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)],[897]) ).
thf(462,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(3899,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)],[462]) ).
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(2011,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(3097,plain,
~ ( sk196 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3093]) ).
thf(308,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(3011,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)],[308]) ).
thf(595,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(4604,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)],[595]) ).
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(5012,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(844,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(5875,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)],[844]) ).
thf(360,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(3301,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)],[360]) ).
thf(763,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(5530,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(592,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(4589,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)],[592]) ).
thf(817,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(5751,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)],[817]) ).
thf(246,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(2574,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)],[246]) ).
thf(8227,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,2476]) ).
thf(8228,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8227]) ).
thf(8233,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk71 ),
inference(simp,[status(thm)],[8228]) ).
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(5411,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(9705,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)],[3373,1075]) ).
thf(9706,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)],[9705]) ).
thf(9707,plain,
! [A: $i] : ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[9706:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).
thf(26815,plain,
! [A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[9707,15881]) ).
thf(477,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(3984,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)],[477]) ).
thf(910,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(6139,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)],[910]) ).
thf(892,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(6062,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(6063,plain,
( ~ ( sk426 @ v3_struct_0 )
& ( sk426 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[6062]) ).
thf(6064,plain,
sk426 @ l2_struct_0,
inference(cnfConj,[status(thm)],[6063]) ).
thf(890,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(6058,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)],[890]) ).
thf(1017,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(6588,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)],[1017]) ).
thf(9579,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,3372]) ).
thf(9580,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9579]) ).
thf(9588,plain,
sk218 != sk216,
inference(simp,[status(thm)],[9580]) ).
thf(479,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(3995,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(770,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(5562,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)],[770]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(4059,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(976,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(6442,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)],[976]) ).
thf(164,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(2061,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)],[164]) ).
thf(402,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(3550,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)],[402]) ).
thf(2773,plain,
sk157 @ v7_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(982,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(6464,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)],[982]) ).
thf(1054,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)],[1053]) ).
thf(1056,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)],[1054]) ).
thf(1057,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)],[1056]) ).
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(1163,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(1028,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(6652,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)],[1028]) ).
thf(266,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(2705,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)],[266]) ).
thf(203,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(2277,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)],[203]) ).
thf(824,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(5794,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)],[824]) ).
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(1570,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(3650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != A )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(cnfConj,[status(thm)],[3646]) ).
thf(3659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != A )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(lifteq,[status(thm)],[3650]) ).
thf(3660,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[3659]) ).
thf(319,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(3065,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)],[319]) ).
thf(3066,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)],[3065]) ).
thf(3067,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)],[3066]) ).
thf(3068,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3067]) ).
thf(3070,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3068]) ).
thf(3071,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[3070]) ).
thf(28390,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)],[3660,3071]) ).
thf(28391,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[28390]) ).
thf(28408,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) )
!= k1_xboole_0 )
| ( A != C ) ),
inference(simp,[status(thm)],[28391]) ).
thf(28420,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k2_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[28408]) ).
thf(35143,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ k2_tarski ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,28420]) ).
thf(35144,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ k2_tarski ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[35143]) ).
thf(35145,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[35144:[bind(A,$thf( E @ ( D @ k2_tarski ) )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).
thf(35499,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[35145]) ).
thf(4666,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(cnf,[status(esa)],[4665]) ).
thf(4667,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(lifteq,[status(thm)],[4666]) ).
thf(13706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk254 @ v1_xboole_0 )
!= ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3865,4753]) ).
thf(13707,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
!= ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13706]) ).
thf(13720,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk254 )
!= ( C @ ( B @ k2_tarski ) ) ),
inference(simp,[status(thm)],[13707]) ).
thf(28962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k2_tarski ) )
!= ( D @ ( C @ k2_tarski ) ) )
| ( ( A @ k1_tarski )
!= ( B @ sk254 ) ) ),
inference(paramod_ordered,[status(thm)],[4667,13720]) ).
thf(28963,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski )
!= ( B @ sk254 ) ),
inference(pattern_uni,[status(thm)],[28962:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(414,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(3610,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)],[414]) ).
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(5107,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(5108,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)],[5107]) ).
thf(5109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk356 @ ( E @ r2_hidden ) )
| ( A @ sk356 @ ( E @ r2_tarski ) )
| ~ ( A @ sk356 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk356 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk356 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk356 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk356 @ ( B @ r2_hidden ) ) )
& ( A @ sk356 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[5108]) ).
thf(5110,plain,
! [A: $i] : ( A @ sk356 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[5109]) ).
thf(18116,plain,
! [B: $i,A: $i] :
( ( ( A @ sk356 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5110,3071]) ).
thf(18117,plain,
! [B: $i,A: $i] :
( ( A @ sk356 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[18116]) ).
thf(18129,plain,
! [B: $i,A: $i] :
( ( ( A @ sk356 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[18117]) ).
thf(18132,plain,
! [A: $i] :
( ( A @ sk356 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[18129]) ).
thf(33058,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk356 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,18132]) ).
thf(33059,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk356 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[33058]) ).
thf(33060,plain,
! [A: $i] : ( A @ sk356 @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[33059:[bind(A,$thf( C @ sk356 )),bind(B,$thf( C ))]]) ).
thf(35220,plain,
! [A: $i] : ( A @ sk356 @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[33060]) ).
thf(4785,plain,
sk321 @ v4_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
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(1824,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(219,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(2396,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1020,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(6620,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)],[1020]) ).
thf(16896,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)],[2307,9616]) ).
thf(16897,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)],[16896]) ).
thf(17031,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)],[16897]) ).
thf(17061,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[17031]) ).
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(1898,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1899,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1898]) ).
thf(1900,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1899]) ).
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(1723,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(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(1223,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(619,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(4712,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)],[619]) ).
thf(6933,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)],[1997,1075]) ).
thf(6934,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)],[6933]) ).
thf(6935,plain,
! [A: $i] : ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6934:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).
thf(15873,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)],[1997,1162]) ).
thf(15874,plain,
! [A: $i] :
( ( ( sk71 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15873]) ).
thf(15875,plain,
( ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) )
= ( sk71 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15874:[bind(A,$thf( sk71 ))]]) ).
thf(22169,plain,
! [A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6935,15875]) ).
thf(783,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(5611,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)],[783]) ).
thf(810,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(5734,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)],[810]) ).
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(1091,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(42703,plain,
( ( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,42553]) ).
thf(42704,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42703]) ).
thf(42751,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk71 ),
inference(simp,[status(thm)],[42704]) ).
thf(273,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(2733,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)],[273]) ).
thf(473,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(3972,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)],[473]) ).
thf(2249,plain,
sk94 @ v9_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
thf(873,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(6000,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)],[873]) ).
thf(962,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(6371,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)],[962]) ).
thf(1002,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(6528,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)],[1002]) ).
thf(32145,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,12254]) ).
thf(32146,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[32145]) ).
thf(32147,plain,
k1_xboole_0 @ k1_tarski @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[32146:[bind(A,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(36404,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ sk18 @ 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)],[32147,1162]) ).
thf(36405,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ sk18 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[36404]) ).
thf(36406,plain,
( ( k1_xboole_0 @ k1_tarski @ sk18 @ k1_relat_1 @ ( k1_xboole_0 @ k1_tarski @ sk18 @ k9_relat_1 ) )
= ( k1_xboole_0 @ k1_tarski @ sk18 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[36405:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ sk18 ))]]) ).
thf(349,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(3239,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)],[349]) ).
thf(565,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(4449,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)],[565]) ).
thf(330,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(3134,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)],[330]) ).
thf(444,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(3807,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)],[444]) ).
thf(3808,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)],[3807]) ).
thf(3809,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)],[3808]) ).
thf(3810,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[3809]) ).
thf(3813,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[3810]) ).
thf(3814,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[3813]) ).
thf(2986,plain,
sk187 @ l3_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(14468,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk319 @ 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)],[14423,1120]) ).
thf(14469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk319 @ 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)],[14468]) ).
thf(14470,plain,
! [A: $i] : ( sk319 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14469:[bind(A,$thf( sk319 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14484,plain,
! [A: $i] : ( sk319 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14470]) ).
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(4836,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(608,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(4661,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)],[608]) ).
thf(14441,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk319 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14423,1106]) ).
thf(14442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk319 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14441]) ).
thf(14443,plain,
! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk319 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14442:[bind(A,$thf( sk319 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14485,plain,
! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk319 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14443]) ).
thf(15383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( A @ ( sk319 @ 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)],[14485,1106]) ).
thf(15384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( A @ ( sk319 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[15383]) ).
thf(15385,plain,
! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk319 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[15384:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk319 @ k1_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f1_s4_funct_2 )),bind(D,$thf( D ))]]) ).
thf(15439,plain,
! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk319 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[15385]) ).
thf(1236,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)],[1234]) ).
thf(1238,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)],[1236]) ).
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(2015,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(459,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(3889,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)],[459]) ).
thf(261,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(2670,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)],[261]) ).
thf(233,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(2477,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
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(1171,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(1172,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)],[1171]) ).
thf(1174,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)],[1172]) ).
thf(1177,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)],[1174]) ).
thf(1178,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)],[1177]) ).
thf(461,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(3894,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)],[461]) ).
thf(194,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(2200,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)],[194]) ).
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(1157,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(1158,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)],[1157]) ).
thf(1159,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)],[1158]) ).
thf(10012,plain,
( ( ( sk300 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,1243]) ).
thf(10013,plain,
( ( sk300 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10012]) ).
thf(10035,plain,
sk300 != sk14,
inference(simp,[status(thm)],[10013]) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1395]) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1398]) ).
thf(1407,plain,
! [A: $i] : ( A @ ( A @ ( k1_xboole_0 @ sk25 ) @ k2_relat_1 @ r1_tarski ) ),
inference(simp,[status(thm)],[1406]) ).
thf(1128,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[1127]) ).
thf(613,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(4680,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)],[613]) ).
thf(383,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(3445,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(334,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(3164,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(3165,plain,
~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[3164]) ).
thf(3166,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[3165]) ).
thf(469,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(3958,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)],[469]) ).
thf(7661,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)],[2582,7264]) ).
thf(7662,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7661]) ).
thf(7663,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7662:[bind(A,$thf( sk138 ))]]) ).
thf(339,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(3191,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)],[339]) ).
thf(6924,plain,
( ( ( sk368 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,5293]) ).
thf(6925,plain,
( ( sk368 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6924]) ).
thf(6926,plain,
sk368 != sk71,
inference(simp,[status(thm)],[6925]) ).
thf(280,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(2758,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)],[280]) ).
thf(476,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(3980,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)],[476]) ).
thf(3456,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[3452]) ).
thf(3461,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[3456]) ).
thf(3462,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[3461]) ).
thf(41136,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)],[2084,3462]) ).
thf(41137,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[41136:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(41205,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[41137]) ).
thf(41223,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)],[41205,1106]) ).
thf(41224,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)],[41223]) ).
thf(41225,plain,
! [B: $i,A: $i] : ( B @ k1_tarski @ k1_zfmisc_1 @ ( A @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[41224:[bind(A,$thf( G )),bind(B,$thf( k1_xboole_0 @ k1_tarski )),bind(C,$thf( G @ k1_tarski @ k1_zfmisc_1 )),bind(D,$thf( D ))]]) ).
thf(41301,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)],[41225]) ).
thf(596,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(4608,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)],[596]) ).
thf(9510,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)],[3247,7264]) ).
thf(9511,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9510]) ).
thf(9512,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9511:[bind(A,$thf( sk207 ))]]) ).
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(1920,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(362,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(3314,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)],[362]) ).
thf(977,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(6445,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)],[977]) ).
thf(630,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(4757,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)],[630]) ).
thf(392,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(3499,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)],[392]) ).
thf(4776,plain,
sk321 @ v13_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(412,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(3600,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)],[412]) ).
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(1836,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(32070,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,8848]) ).
thf(32071,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[32070]) ).
thf(32072,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[32071:[bind(A,$thf( C @ k1_zfmisc_1 )),bind(B,$thf( C ))]]) ).
thf(35528,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[32072]) ).
thf(898,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(6096,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)],[898]) ).
thf(772,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_2 ) )
=> ( ( B @ ( A @ k8_filter_0 ) )
= ( B @ ( A @ k23_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_2) ).
thf(5566,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_filter_2 ) )
=> ( ( B @ ( A @ k8_filter_0 ) )
= ( B @ ( A @ k23_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(891,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(6060,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)],[891]) ).
thf(623,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(4732,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)],[623]) ).
thf(858,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(5936,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)],[858]) ).
thf(197,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(2228,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)],[197]) ).
thf(174,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(2112,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)],[174]) ).
thf(870,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(5993,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)],[870]) ).
thf(378,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(3408,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)],[378]) ).
thf(42795,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)],[3160,42607]) ).
thf(42796,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42795]) ).
thf(42827,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[42796]) ).
thf(492,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(4063,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)],[492]) ).
thf(1041,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(6709,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)],[1041]) ).
thf(2515,plain,
k13_nat_lat @ v9_lattices,
inference(cnfConj,[status(thm)],[2508]) ).
thf(784,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(5615,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)],[784]) ).
thf(3119,plain,
sk197 @ v4_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(17004,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,8115]) ).
thf(17005,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[17004]) ).
thf(17035,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 @ v15_lattices ) ),
inference(simp,[status(thm)],[17005]) ).
thf(17065,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[17035]) ).
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(5081,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(343,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(3205,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(2245,plain,
~ ( sk94 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2244]) ).
thf(838,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(5854,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)],[838]) ).
thf(3105,plain,
sk196 @ l3_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(386,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(3467,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)],[386]) ).
thf(42719,plain,
( ( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,42553]) ).
thf(42720,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42719]) ).
thf(42747,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[42720]) ).
thf(416,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(3615,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)],[416]) ).
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(1541,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(237,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(2498,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)],[237]) ).
thf(44203,plain,
! [A: $i] :
( ( A
!= ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,42827]) ).
thf(44204,plain,
! [A: $i] :
( ( A
!= ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[44203]) ).
thf(44205,plain,
sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[44204:[bind(A,$thf( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ))]]) ).
thf(806,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(5714,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)],[806]) ).
thf(287,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(2840,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)],[287]) ).
thf(1139,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)],[1136]) ).
thf(1143,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)],[1139]) ).
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(1263,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(1264,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)],[1263]) ).
thf(1265,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)],[1264]) ).
thf(1267,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[1265]) ).
thf(1269,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
| ( A != C ) ),
inference(lifteq,[status(thm)],[1267]) ).
thf(1270,plain,
! [B: $i,A: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ r2_hidden ) ),
inference(simp,[status(thm)],[1269]) ).
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(1851,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(3122,plain,
sk197 @ v13_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(2990,plain,
sk187 @ v7_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(718,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(5270,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)],[718]) ).
thf(610,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(4668,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)],[610]) ).
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(1953,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(730,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(5322,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)],[730]) ).
thf(5323,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)],[5322]) ).
thf(5324,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk374 ) @ r2_hidden ) )
| ( ( E @ ( F @ sk373 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk374 ) )
= E )
| ( ( E @ ( F @ sk373 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk374 ) @ r2_hidden ) )
| ( F @ ( E @ ( F @ sk373 ) @ r2_hidden ) ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk374 ) )
= E )
| ( F @ ( E @ ( F @ sk373 ) @ 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)],[5323]) ).
thf(5330,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[5324]) ).
thf(5335,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[5330]) ).
thf(5336,plain,
! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[5335]) ).
thf(40154,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)],[5336,1270]) ).
thf(40155,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)],[40154]) ).
thf(40172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[40155]) ).
thf(40194,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[40172]) ).
thf(749,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(5423,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)],[749]) ).
thf(6959,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)],[2698,1075]) ).
thf(6960,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)],[6959]) ).
thf(6961,plain,
! [A: $i] : ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6960:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).
thf(15843,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)],[2698,1162]) ).
thf(15844,plain,
! [A: $i] :
( ( ( sk152 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15843]) ).
thf(15845,plain,
( ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) )
= ( sk152 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15844:[bind(A,$thf( sk152 ))]]) ).
thf(22264,plain,
! [A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6961,15845]) ).
thf(2668,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(cnf,[status(esa)],[2667]) ).
thf(2669,plain,
! [A: $i] :
( ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) )
= ( A @ k1_subset_1 ) ),
inference(lifteq,[status(thm)],[2668]) ).
thf(40676,plain,
! [A: $i] :
( ( A @ ( A @ k3_subset_1 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[2669,2586,3131]) ).
thf(290,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(2895,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)],[290]) ).
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(1121,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(1019,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(6603,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)],[1019]) ).
thf(247,axiom,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(2577,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(374,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(3381,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)],[374]) ).
thf(909,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(6133,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)],[909]) ).
thf(1064,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)],[1061]) ).
thf(1111,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)],[1108]) ).
thf(776,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(5577,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)],[776]) ).
thf(1224,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)],[1223]) ).
thf(1227,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)],[1224]) ).
thf(3218,plain,
k6_nat_lat @ v4_lattices,
inference(cnfConj,[status(thm)],[3213]) ).
thf(487,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(4048,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)],[487]) ).
thf(1092,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)],[1091]) ).
thf(1093,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)],[1092]) ).
thf(1096,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)],[1093]) ).
thf(2509,plain,
k13_nat_lat @ v10_lattices,
inference(cnfConj,[status(thm)],[2508]) ).
thf(3102,plain,
sk196 @ v10_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(750,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(5428,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)],[750]) ).
thf(9622,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)],[3362,7329]) ).
thf(9623,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9622]) ).
thf(9624,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9623:[bind(A,$thf( sk216 ))]]) ).
thf(777,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(5583,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)],[777]) ).
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(1719,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(867,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(5978,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)],[867]) ).
thf(1021,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(6624,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)],[1021]) ).
thf(836,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(5847,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)],[836]) ).
thf(482,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(4012,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)],[482]) ).
thf(907,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(6128,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)],[907]) ).
thf(501,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(4109,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)],[501]) ).
thf(912,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(6148,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)],[912]) ).
thf(758,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(5497,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)],[758]) ).
thf(3001,plain,
sk188 @ v5_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
thf(639,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(4817,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)],[639]) ).
thf(534,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(4263,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)],[534]) ).
thf(611,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(4676,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)],[611]) ).
thf(2460,plain,
sk118 @ v7_lattices,
inference(cnfConj,[status(thm)],[2452]) ).
thf(16826,plain,
! [B: $i,A: $i] :
( ( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2163,3071]) ).
thf(16827,plain,
! [B: $i,A: $i] :
( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[16826]) ).
thf(16840,plain,
! [B: $i,A: $i] :
( ( ( A @ sk80 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[16827]) ).
thf(16847,plain,
! [A: $i] :
( ( A @ sk80 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16840]) ).
thf(854,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k1_filter_2 @ ( A @ k23_filter_2 ) )
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) )
& ( ( A @ k17_filter_2 @ ( A @ k23_filter_2 ) )
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_filter_2) ).
thf(5915,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( A @ k1_filter_2 @ ( A @ k23_filter_2 ) )
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) )
& ( ( A @ k17_filter_2 @ ( A @ k23_filter_2 ) )
= ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(3094,plain,
sk196 @ v15_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(411,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(3596,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)],[411]) ).
thf(938,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(6256,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)],[938]) ).
thf(172,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(2108,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)],[172]) ).
thf(13198,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[4739,9512]) ).
thf(13199,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[13198]) ).
thf(13309,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13199]) ).
thf(3206,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3205]) ).
thf(3208,plain,
k1_xboole_0 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3206]) ).
thf(9089,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)],[3208,1075]) ).
thf(9090,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)],[9089]) ).
thf(9091,plain,
! [A: $i] : ( k1_xboole_0 @ k1_relat_1 @ ( k1_xboole_0 @ k9_relat_1 ) @ ( A @ ( k1_xboole_0 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[9090:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(24470,plain,
k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ),
inference(rewrite,[status(thm)],[9091,3163]) ).
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(1329,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(3302,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)],[3301]) ).
thf(3303,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)],[3302]) ).
thf(3306,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3303]) ).
thf(3310,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3306]) ).
thf(3311,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3310]) ).
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(1942,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(466,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(3922,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)],[466]) ).
thf(805,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(5694,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)],[805]) ).
thf(3000,plain,
sk188 @ v10_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
thf(9525,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3247,7320]) ).
thf(9526,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9525]) ).
thf(9527,plain,
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9526:[bind(A,$thf( sk207 ))]]) ).
thf(13265,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,9527]) ).
thf(13266,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13265]) ).
thf(13308,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[13266]) ).
thf(794,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(5651,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)],[794]) ).
thf(4772,plain,
sk321 @ l3_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(903,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(6116,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)],[903]) ).
thf(1180,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)],[1179]) ).
thf(1182,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)],[1180]) ).
thf(5786,plain,
( ( ( f4_s11_funct_2 @ ( sk413 @ ( 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)],[5781]) ).
thf(5791,plain,
( ( ( f4_s11_funct_2 @ ( sk413 @ ( 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)],[5786]) ).
thf(1030,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 ) ) @ ( A @ k23_filter_2 ) @ k5_lattices )
= B )
& ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ k6_lattices )
= C )
& ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ v15_lattices ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_filter_2) ).
thf(6661,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 ) ) @ ( A @ k23_filter_2 ) @ k5_lattices )
= B )
& ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ k6_lattices )
= C )
& ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ v15_lattices ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(960,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(6363,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)],[960]) ).
thf(813,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(5743,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)],[813]) ).
thf(7483,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1998,7249]) ).
thf(7484,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7483]) ).
thf(7485,plain,
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7484:[bind(A,$thf( sk71 ))]]) ).
thf(16937,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,7485]) ).
thf(16938,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16937]) ).
thf(17043,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[16938]) ).
thf(17074,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[17043]) ).
thf(381,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(3441,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(207,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(2312,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)],[207]) ).
thf(2455,plain,
~ ( sk118 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2452]) ).
thf(579,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(4545,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)],[579]) ).
thf(168,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(2080,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)],[168]) ).
thf(713,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(5253,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)],[713]) ).
thf(1402,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1395]) ).
thf(1413,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk25 ) @ k1_relat_1 )
= B )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1402]) ).
thf(1414,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk25 ) @ k1_relat_1 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1413]) ).
thf(192,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(2196,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)],[192]) ).
thf(1088,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)],[1087]) ).
thf(9772,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)],[1088,9479]) ).
thf(9773,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)],[9772]) ).
thf(9774,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)],[9773]) ).
thf(9778,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)],[9774]) ).
thf(37418,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)],[9778,3246]) ).
thf(37419,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)],[37418]) ).
thf(37508,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)],[24470,37419]) ).
thf(37509,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)],[37508]) ).
thf(37586,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)],[37509]) ).
thf(37619,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)],[37586]) ).
thf(1206,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)],[1205]) ).
thf(1207,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)],[1206]) ).
thf(424,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(3671,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)],[424]) ).
thf(170,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(2085,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)],[170]) ).
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(1644,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(944,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(6275,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)],[944]) ).
thf(943,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(6271,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)],[943]) ).
thf(2781,plain,
sk157 @ v6_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(6065,plain,
~ ( sk426 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[6063]) ).
thf(1114,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)],[1108]) ).
thf(7963,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,5364]) ).
thf(7964,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7963]) ).
thf(7966,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk152 ),
inference(simp,[status(thm)],[7964]) ).
thf(533,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(4259,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)],[533]) ).
thf(13220,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[4739,9624]) ).
thf(13221,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[13220]) ).
thf(13340,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk216 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13221]) ).
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(1150,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(755,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(5481,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)],[755]) ).
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(1451,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(881,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(6033,plain,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
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(1539,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(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(1456,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(972,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(6433,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)],[972]) ).
thf(865,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(5973,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)],[865]) ).
thf(528,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(4244,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)],[528]) ).
thf(2581,plain,
sk138 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2580]) ).
thf(231,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(2465,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)],[231]) ).
thf(238,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(2505,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)],[238]) ).
thf(445,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(3819,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)],[445]) ).
thf(3222,plain,
k6_nat_lat @ v6_lattices,
inference(cnfConj,[status(thm)],[3213]) ).
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(2006,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(6930,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)],[2581,1075]) ).
thf(6931,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)],[6930]) ).
thf(6932,plain,
! [A: $i] : ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6931:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).
thf(15867,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)],[2581,1162]) ).
thf(15868,plain,
! [A: $i] :
( ( ( sk138 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15867]) ).
thf(15869,plain,
( ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) )
= ( sk138 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15868:[bind(A,$thf( sk138 ))]]) ).
thf(20028,plain,
! [A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6932,15869]) ).
thf(16926,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)],[2307,9624]) ).
thf(16927,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)],[16926]) ).
thf(17034,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)],[16927]) ).
thf(17064,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[17034]) ).
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(1984,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(979,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(6450,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)],[979]) ).
thf(3115,plain,
sk197 @ v3_filter_0,
inference(cnfConj,[status(thm)],[3109]) ).
thf(289,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(2862,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)],[289]) ).
thf(507,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(4135,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)],[507]) ).
thf(282,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(2766,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)],[282]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(3692,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
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(4902,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(968,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v13_lattices )
=> ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v15_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_filter_2) ).
thf(6418,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v13_lattices )
=> ( B @ ( A @ k18_filter_2 ) @ ( A @ k23_filter_2 ) @ v15_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(7480,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2582,7249]) ).
thf(7481,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7480]) ).
thf(7482,plain,
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7481:[bind(A,$thf( sk138 ))]]) ).
thf(16953,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,7482]) ).
thf(16954,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16953]) ).
thf(17038,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[16954]) ).
thf(17069,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[17038]) ).
thf(827,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(5801,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)],[827]) ).
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(1979,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(914,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(6152,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)],[914]) ).
thf(320,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(3074,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)],[320]) ).
thf(3005,plain,
sk188 @ l3_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
thf(497,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(4086,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)],[497]) ).
thf(928,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(6224,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)],[928]) ).
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(1759,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(3215,plain,
k6_nat_lat @ v5_lattices,
inference(cnfConj,[status(thm)],[3213]) ).
thf(8911,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3197,7320]) ).
thf(8912,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8911]) ).
thf(8913,plain,
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8912:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(16853,plain,
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8913,2307]) ).
thf(16854,plain,
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16853]) ).
thf(710,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(5245,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)],[710]) ).
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(1333,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(434,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(3755,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)],[434]) ).
thf(765,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(5544,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)],[765]) ).
thf(1193,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)],[1190]) ).
thf(1202,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)],[1193]) ).
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(5402,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(4782,plain,
sk321 @ v6_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(450,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(3856,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)],[450]) ).
thf(1169,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)],[1168]) ).
thf(1170,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)],[1169]) ).
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(5417,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(7799,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,4114]) ).
thf(7800,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7799]) ).
thf(7802,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk152 ),
inference(simp,[status(thm)],[7800]) ).
thf(32674,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1047]) ).
thf(32675,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[32674:[bind(A,$thf( sk1 ))]]) ).
thf(8834,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,3166]) ).
thf(8835,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8834]) ).
thf(8846,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8835]) ).
thf(815,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(5747,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)],[815]) ).
thf(1085,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)],[1082]) ).
thf(1086,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)],[1085]) ).
thf(33583,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1048]) ).
thf(33584,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[33583:[bind(A,$thf( sk1 ))]]) ).
thf(265,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(2702,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)],[265]) ).
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(4889,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(338,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(3183,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)],[338]) ).
thf(833,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(5833,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)],[833]) ).
thf(20036,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)],[20028,1106]) ).
thf(20037,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)],[20036]) ).
thf(20038,plain,
! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[20037:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk138 @ k9_relat_1 ) )),bind(C,$thf( sk138 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(20096,plain,
! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[20038]) ).
thf(863,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(5964,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)],[863]) ).
thf(940,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(6260,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)],[940]) ).
thf(1026,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(6647,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)],[1026]) ).
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(1286,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(363,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(3321,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)],[363]) ).
thf(753,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(5447,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)],[753]) ).
thf(2402,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2400]) ).
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(1184,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(1185,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)],[1184]) ).
thf(1187,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)],[1185]) ).
thf(294,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(2915,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)],[294]) ).
thf(221,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(2404,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)],[221]) ).
thf(2405,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)],[2404]) ).
thf(2408,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2405]) ).
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(1663,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(856,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(5930,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)],[856]) ).
thf(394,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(3508,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)],[394]) ).
thf(1164,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)],[1163]) ).
thf(1167,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)],[1164]) ).
thf(191,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(2189,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)],[191]) ).
thf(884,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(6038,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)],[884]) ).
thf(2995,plain,
sk188 @ v7_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
thf(843,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(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 @ 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)],[843]) ).
thf(539,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(4308,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)],[539]) ).
thf(993,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(6497,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)],[993]) ).
thf(8231,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,2476]) ).
thf(8232,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8231]) ).
thf(8234,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk152 ),
inference(simp,[status(thm)],[8232]) ).
thf(581,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(4550,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)],[581]) ).
thf(1001,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(6524,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)],[1001]) ).
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(1273,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(245,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(2570,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)],[245]) ).
thf(861,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(5960,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)],[861]) ).
thf(9573,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,4753]) ).
thf(9574,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9573]) ).
thf(9594,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk216 ),
inference(simp,[status(thm)],[9574]) ).
thf(588,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(4577,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)],[588]) ).
thf(792,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(5647,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)],[792]) ).
thf(27531,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)],[2084,8851]) ).
thf(27532,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[27531:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(27582,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[27532]) ).
thf(802,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(5679,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)],[802]) ).
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(2001,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(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(1248,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(1249,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)],[1248]) ).
thf(1250,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)],[1249]) ).
thf(1251,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)],[1250]) ).
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(4919,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(974,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 @ k23_filter_2 ) @ v13_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_filter_2) ).
thf(6437,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 @ k23_filter_2 ) @ v13_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(615,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(4685,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)],[615]) ).
thf(40015,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)],[1900,40010]) ).
thf(40016,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk13 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[40015:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
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(1101,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(1102,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)],[1101]) ).
thf(1103,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)],[1102]) ).
thf(2253,plain,
sk94 @ v3_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
thf(31873,plain,
! [A: $i] :
( ( A != k13_nat_lat )
| ( k1_xboole_0 @ v4_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,2512]) ).
thf(31874,plain,
( ( k1_xboole_0 @ v4_lattices )
| ( k13_nat_lat @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31873:[bind(A,$thf( k13_nat_lat ))]]) ).
thf(593,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(4594,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)],[593]) ).
thf(1219,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)],[1217]) ).
thf(1038,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(6699,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)],[1038]) ).
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(4874,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(760,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(5508,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)],[760]) ).
thf(10020,plain,
( ( ( sk300 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,3372]) ).
thf(10021,plain,
( ( sk300 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10020]) ).
thf(10030,plain,
sk300 != sk218,
inference(simp,[status(thm)],[10021]) ).
thf(391,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(3491,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)],[391]) ).
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(1927,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(1014,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(6578,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)],[1014]) ).
thf(10078,plain,
! [A: $i] :
( ( ( sk319 @ 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)],[4737,7329]) ).
thf(10079,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10078]) ).
thf(10080,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10079:[bind(A,$thf( sk319 ))]]) ).
thf(13253,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,10080]) ).
thf(13254,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13253]) ).
thf(13327,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk319 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13254]) ).
thf(13372,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13327]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( 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(3289,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)],[358]) ).
thf(544,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(4340,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(458,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(3888,plain,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(981,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(6454,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)],[981]) ).
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 ) )
=> ! [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(6546,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)],[1008]) ).
thf(3111,plain,
sk197 @ v6_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(991,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(6492,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)],[991]) ).
thf(889,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(6052,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)],[889]) ).
thf(708,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(5241,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)],[708]) ).
thf(4786,plain,
sk321 @ v16_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
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(4998,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(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(1833,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(857,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(5933,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)],[857]) ).
thf(9480,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3247,7249]) ).
thf(9481,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9480]) ).
thf(9482,plain,
( ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9481:[bind(A,$thf( sk207 ))]]) ).
thf(16994,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,9482]) ).
thf(16995,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16994]) ).
thf(17050,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[16995]) ).
thf(17083,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[17050]) ).
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(1652,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(2991,plain,
sk187 @ v3_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
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(5097,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(270,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(2716,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)],[270]) ).
thf(707,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(5239,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)],[707]) ).
thf(826,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(5799,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)],[826]) ).
thf(420,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(3636,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)],[420]) ).
thf(467,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(3925,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)],[467]) ).
thf(757,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(5488,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)],[757]) ).
thf(574,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4494,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(7732,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 @ v16_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)],[1088,7482]) ).
thf(7733,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 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7732]) ).
thf(7747,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[7733]) ).
thf(7756,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[7747]) ).
thf(8579,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 @ v16_lattices ) ),
inference(rewrite,[status(thm)],[7756,2581]) ).
thf(8580,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[8579]) ).
thf(2981,plain,
sk187 @ v10_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(788,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(5627,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)],[788]) ).
thf(354,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(3266,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)],[354]) ).
thf(2514,plain,
k13_nat_lat @ v5_lattices,
inference(cnfConj,[status(thm)],[2508]) ).
thf(862,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(5962,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)],[862]) ).
thf(832,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 @ k23_filter_2 ) @ v14_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_filter_2) ).
thf(5831,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 @ k23_filter_2 ) @ v14_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(930,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(6229,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)],[930]) ).
thf(618,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(4709,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)],[618]) ).
thf(1226,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)],[1224]) ).
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(1256,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(28380,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)],[2084,3660]) ).
thf(28381,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[28380:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(28421,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[28381]) ).
thf(316,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(3051,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)],[316]) ).
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 )
& ~ ( 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(2308,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)],[206]) ).
thf(851,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(5908,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)],[851]) ).
thf(427,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(3695,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)],[427]) ).
thf(326,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(3123,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)],[326]) ).
thf(754,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] :
( ( A @ ( C @ m2_nat_lat ) )
=> ( ( C
= ( B @ ( A @ k23_filter_2 ) ) )
<=> ? [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',d16_filter_2) ).
thf(5449,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 @ ( C @ m2_nat_lat ) )
=> ( ( ? [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 @ k23_filter_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k23_filter_2 ) ) )
=> ? [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)],[754]) ).
thf(872,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(5997,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)],[872]) ).
thf(369,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(3355,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)],[369]) ).
thf(209,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(2319,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)],[209]) ).
thf(875,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(6016,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)],[875]) ).
thf(768,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(5556,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)],[768]) ).
thf(346,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(3223,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)],[346]) ).
thf(530,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(4251,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)],[530]) ).
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(5039,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(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(1669,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(9571,plain,
( ( ( sk216 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,1243]) ).
thf(9572,plain,
( ( sk216 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9571]) ).
thf(9587,plain,
sk216 != sk14,
inference(simp,[status(thm)],[9572]) ).
thf(3118,plain,
~ ( sk197 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3109]) ).
thf(10022,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,5364]) ).
thf(10023,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10022]) ).
thf(10034,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk300 ),
inference(simp,[status(thm)],[10023]) ).
thf(499,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(4096,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)],[499]) ).
thf(508,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(4149,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)],[508]) ).
thf(512,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(4171,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)],[512]) ).
thf(526,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(4236,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)],[526]) ).
thf(16990,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,10072]) ).
thf(16991,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16990]) ).
thf(17046,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[16991]) ).
thf(17077,plain,
( ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[17046]) ).
thf(296,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(2935,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)],[296]) ).
thf(3002,plain,
~ ( sk188 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2994]) ).
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(4822,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(42775,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,42607]) ).
thf(42776,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42775]) ).
thf(42826,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk300 ),
inference(simp,[status(thm)],[42776]) ).
thf(557,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(4413,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)],[557]) ).
thf(5085,plain,
( ( sk351 @ v3_lattices )
& ( sk351 @ l3_lattices ) ),
inference(cnf,[status(esa)],[5084]) ).
thf(5086,plain,
sk351 @ l3_lattices,
inference(cnfConj,[status(thm)],[5085]) ).
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(1239,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(226,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(2442,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)],[226]) ).
thf(700,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(5207,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)],[700]) ).
thf(417,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(3619,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)],[417]) ).
thf(2457,plain,
sk118 @ v9_lattices,
inference(cnfConj,[status(thm)],[2452]) ).
thf(602,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(4640,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)],[602]) ).
thf(422,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(3641,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)],[422]) ).
thf(905,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(6123,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)],[905]) ).
thf(399,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(3532,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)],[399]) ).
thf(620,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(4716,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)],[620]) ).
thf(987,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(6478,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)],[987]) ).
thf(3101,plain,
sk196 @ v6_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(1012,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(6572,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)],[1012]) ).
thf(2774,plain,
sk157 @ v3_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(199,axiom,
? [A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_struct_0) ).
thf(2255,plain,
? [A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(2256,plain,
( ( sk95 @ v2_struct_0 )
& ( sk95 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[2255]) ).
thf(2257,plain,
sk95 @ l2_struct_0,
inference(cnfConj,[status(thm)],[2256]) ).
thf(955,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(6340,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)],[955]) ).
thf(32053,plain,
! [A: $i] :
( ( A != sk188 )
| ( k1_xboole_0 @ v3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,3004]) ).
thf(32054,plain,
( ( k1_xboole_0 @ v3_lattices )
| ( sk188 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[32053:[bind(A,$thf( sk188 ))]]) ).
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(1376,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(2510,plain,
k13_nat_lat @ v3_lattices,
inference(cnfConj,[status(thm)],[2508]) ).
thf(1016,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(6585,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)],[1016]) ).
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(1209,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(368,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(3352,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)],[368]) ).
thf(523,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(4228,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)],[523]) ).
thf(241,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(2538,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)],[241]) ).
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(1853,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(801,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] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( D @ ( C @ ( A @ r3_lattices ) ) )
<=> ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_filter_2) ).
thf(5671,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 ) )
=> ! [E: $i] :
( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
=> ( ( ( D = F )
& ( C = E ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ r3_lattices ) ) )
=> ( D @ ( C @ ( A @ r3_lattices ) ) ) )
& ( ( D @ ( C @ ( A @ r3_lattices ) ) )
=> ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(2478,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(cnf,[status(esa)],[2477]) ).
thf(258,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(2642,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)],[258]) ).
thf(9569,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,2476]) ).
thf(9570,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9569]) ).
thf(9592,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk216 ),
inference(simp,[status(thm)],[9570]) ).
thf(709,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(5243,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(5244,plain,
sk365 @ l2_lattices,
inference(cnf,[status(esa)],[5243]) ).
thf(437,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(3764,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)],[437]) ).
thf(8571,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,4753]) ).
thf(8572,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8571]) ).
thf(8573,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk152 ),
inference(simp,[status(thm)],[8572]) ).
thf(27562,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)],[2084,8573]) ).
thf(27563,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk152 ),
inference(pattern_uni,[status(thm)],[27562:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(27594,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk152 ),
inference(simp,[status(thm)],[27563]) ).
thf(2987,plain,
sk187 @ v6_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(761,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(5520,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)],[761]) ).
thf(256,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(2637,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1113,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)],[1108]) ).
thf(1117,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)],[1113]) ).
thf(439,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(3779,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)],[439]) ).
thf(831,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(5827,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)],[831]) ).
thf(171,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(2097,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)],[171]) ).
thf(2246,plain,
sk94 @ v7_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
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(1492,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(3106,plain,
sk196 @ v3_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(846,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(5880,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)],[846]) ).
thf(519,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(4213,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)],[519]) ).
thf(5531,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(cnf,[status(esa)],[5530]) ).
thf(8875,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)],[3197,7329]) ).
thf(8876,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8875]) ).
thf(8877,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8876:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(16863,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8877,2307]) ).
thf(16864,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16863]) ).
thf(915,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(6154,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)],[915]) ).
thf(920,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(6184,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)],[920]) ).
thf(551,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(4374,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)],[551]) ).
thf(8558,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,3166]) ).
thf(8559,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8558]) ).
thf(8561,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk152 ),
inference(simp,[status(thm)],[8559]) ).
thf(409,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(3586,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)],[409]) ).
thf(923,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(6196,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)],[923]) ).
thf(8388,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)],[1088,8292]) ).
thf(8389,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)],[8388]) ).
thf(8390,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)],[8389]) ).
thf(8392,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)],[8390]) ).
thf(16438,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)],[8392,2581]) ).
thf(16439,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)],[16438]) ).
thf(4773,plain,
sk321 @ v10_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
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(1307,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(188,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(2180,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(276,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(2742,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)],[276]) ).
thf(481,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(4009,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)],[481]) ).
thf(8826,plain,
( ( ( sk14 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3160,1243]) ).
thf(8827,plain,
( ( sk14 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8826]) ).
thf(8845,plain,
sk14 != k1_xboole_0,
inference(simp,[status(thm)],[8827]) ).
thf(34228,plain,
! [A: $i] :
( ( A != sk14 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,8845]) ).
thf(34229,plain,
! [A: $i] :
( ( A != sk14 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[34228]) ).
thf(34230,plain,
sk14 @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[34229:[bind(A,$thf( sk14 ))]]) ).
thf(2780,plain,
sk157 @ v12_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(543,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(4332,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)],[543]) ).
thf(538,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(4296,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)],[538]) ).
thf(2461,plain,
sk118 @ l3_lattices,
inference(cnfConj,[status(thm)],[2452]) ).
thf(3219,plain,
k6_nat_lat @ v8_lattices,
inference(cnfConj,[status(thm)],[3213]) ).
thf(767,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(5552,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)],[767]) ).
thf(7664,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)],[1998,7264]) ).
thf(7665,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7664]) ).
thf(7666,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7665:[bind(A,$thf( sk71 ))]]) ).
thf(7823,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)],[1088,7666]) ).
thf(7824,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)],[7823]) ).
thf(7825,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)],[7824]) ).
thf(7827,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)],[7825]) ).
thf(8734,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)],[7827,1997]) ).
thf(8735,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)],[8734]) ).
thf(555,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(4401,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)],[555]) ).
thf(698,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(5202,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)],[698]) ).
thf(433,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(3747,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)],[433]) ).
thf(8386,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)],[1090,8292]) ).
thf(8387,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)],[8386]) ).
thf(8391,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)],[8387]) ).
thf(8393,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)],[8391]) ).
thf(20111,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)],[8393,2581]) ).
thf(20112,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)],[20111]) ).
thf(558,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(4420,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(311,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(3027,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)],[311]) ).
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 ) )
=> ~ ( ! [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(5894,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)],[850]) ).
thf(586,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(4569,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)],[586]) ).
thf(13272,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[4739,8292]) ).
thf(13273,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[13272]) ).
thf(13323,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk138 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13273]) ).
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(1731,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(442,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(3800,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)],[442]) ).
thf(201,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(2261,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)],[201]) ).
thf(958,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(6353,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)],[958]) ).
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(4897,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(566,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(4452,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)],[566]) ).
thf(721,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(5286,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)],[721]) ).
thf(227,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(2446,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)],[227]) ).
thf(19731,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1978,5531]) ).
thf(19732,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[19731:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(2578,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[2577]) ).
thf(19785,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ),
inference(rewrite,[status(thm)],[19732,2578]) ).
thf(475,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(3977,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)],[475]) ).
thf(222,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(2410,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)],[222]) ).
thf(2785,plain,
sk157 @ v5_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(306,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(3006,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)],[306]) ).
thf(1033,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(6678,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)],[1033]) ).
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(4850,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(796,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(5656,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)],[796]) ).
thf(1148,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1147]) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1148]) ).
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(1556,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(243,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(2542,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)],[243]) ).
thf(886,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(6044,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)],[886]) ).
thf(2252,plain,
sk94 @ v6_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
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(1293,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(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(4993,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(293,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(2911,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)],[293]) ).
thf(4985,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk338 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
| ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk336 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk338 @ m2_relset_1 ) ) )
| ~ sk336 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk338 @ v1_funct_2 ) ) )
| ~ sk336 )
& ( ( sk338 @ v1_funct_1 )
| ~ sk336 )
& ( sk336
| ~ ( A @ ( sk337 @ p1_s14_funct_2 ) )
| ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk336
| ( f1_s14_funct_2 @ ( sk337 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4984]) ).
thf(4990,plain,
( sk336
| ( f1_s14_funct_2 @ ( sk337 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4985]) ).
thf(525,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(4232,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)],[525]) ).
thf(963,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(6377,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)],[963]) ).
thf(947,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(6288,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)],[947]) ).
thf(1173,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)],[1172]) ).
thf(1175,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)],[1173]) ).
thf(1176,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)],[1175]) ).
thf(350,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(3241,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)],[350]) ).
thf(2999,plain,
sk188 @ v4_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
thf(494,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(4067,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)],[494]) ).
thf(786,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(5619,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)],[786]) ).
thf(390,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(3480,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)],[390]) ).
thf(400,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(3539,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)],[400]) ).
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(4844,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(1191,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)],[1190]) ).
thf(1198,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)],[1191]) ).
thf(622,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(4720,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)],[622]) ).
thf(7372,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2582,7231]) ).
thf(7373,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7372]) ).
thf(7374,plain,
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7373:[bind(A,$thf( sk138 ))]]) ).
thf(7736,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 @ v12_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)],[1088,7374]) ).
thf(7737,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 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7736]) ).
thf(7744,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[7737]) ).
thf(7752,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[7744]) ).
thf(8439,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 @ v12_lattices ) ),
inference(rewrite,[status(thm)],[7752,2581]) ).
thf(8440,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[8439]) ).
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(1841,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(435,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(3759,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)],[435]) ).
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(5377,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(14206,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1978,2199]) ).
thf(14207,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[14206:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(20165,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)],[2111,20112]) ).
thf(20166,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)],[20165]) ).
thf(20187,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)],[20166]) ).
thf(20201,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)],[20187]) ).
thf(791,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(5641,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)],[791]) ).
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(1445,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(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(1528,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(1023,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(6628,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)],[1023]) ).
thf(3110,plain,
sk197 @ l3_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(180,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(2139,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)],[180]) ).
thf(711,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(5248,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)],[711]) ).
thf(8565,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,4753]) ).
thf(8566,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8565]) ).
thf(8574,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk71 ),
inference(simp,[status(thm)],[8566]) ).
thf(27571,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)],[2084,8574]) ).
thf(27572,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk71 ),
inference(pattern_uni,[status(thm)],[27571:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(27598,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk71 ),
inference(simp,[status(thm)],[27572]) ).
thf(165,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(2064,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)],[165]) ).
thf(215,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(2369,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)],[215]) ).
thf(34022,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1049]) ).
thf(34023,plain,
( ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
| ( sk2 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[34022:[bind(A,$thf( sk2 ))]]) ).
thf(371,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(3363,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)],[371]) ).
thf(799,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r3_lattices ) ) )
=> ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattices) ).
thf(5667,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)],[799]) ).
thf(4195,plain,
( ~ ( sk282 @ v3_struct_0 )
& ( sk282 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[4194]) ).
thf(4196,plain,
sk282 @ l1_struct_0,
inference(cnfConj,[status(thm)],[4195]) ).
thf(878,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(6027,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)],[878]) ).
thf(8865,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)],[3197,7300]) ).
thf(8866,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8865]) ).
thf(8867,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8866:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(16859,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8867,2307]) ).
thf(16860,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16859]) ).
thf(919,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
<=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_0) ).
thf(6180,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)],[919]) ).
thf(10014,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,4753]) ).
thf(10015,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10014]) ).
thf(10031,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk300 ),
inference(simp,[status(thm)],[10015]) ).
thf(13712,plain,
! [A: $i] :
( ( ( A @ sk254 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3865,3372]) ).
thf(13713,plain,
! [A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13712]) ).
thf(13727,plain,
! [A: $i] :
( ( A @ sk254 )
!= sk218 ),
inference(simp,[status(thm)],[13713]) ).
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(1694,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(8554,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,3166]) ).
thf(8555,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8554]) ).
thf(8560,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk71 ),
inference(simp,[status(thm)],[8555]) ).
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(4965,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(2984,plain,
sk187 @ v9_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
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(1973,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(571,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(4481,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)],[571]) ).
thf(166,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(2069,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)],[166]) ).
thf(986,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(6476,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)],[986]) ).
thf(10126,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4737,7320]) ).
thf(10127,plain,
! [A: $i] :
( ( ( sk319 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[10126]) ).
thf(10128,plain,
( ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10127:[bind(A,$thf( sk319 ))]]) ).
thf(13259,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,10128]) ).
thf(13260,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13259]) ).
thf(13325,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk319 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[13260]) ).
thf(13371,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[13325]) ).
thf(562,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(4441,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)],[562]) ).
thf(848,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(5890,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)],[848]) ).
thf(638,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(4813,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)],[638]) ).
thf(2784,plain,
sk157 @ v14_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(16874,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,10125]) ).
thf(16875,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16874]) ).
thf(17048,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[16875]) ).
thf(17080,plain,
( ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[17048]) ).
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(1129,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(1130,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1129]) ).
thf(1132,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[1130]) ).
thf(1134,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1132]) ).
thf(7711,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)],[1088,7663]) ).
thf(7712,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)],[7711]) ).
thf(7745,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)],[7712]) ).
thf(7753,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)],[7745]) ).
thf(8476,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)],[7753,2581]) ).
thf(8477,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)],[8476]) ).
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(5003,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(396,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(3522,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)],[396]) ).
thf(307,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(3009,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)],[307]) ).
thf(9522,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3247,7231]) ).
thf(9523,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9522]) ).
thf(9524,plain,
( ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9523:[bind(A,$thf( sk207 ))]]) ).
thf(617,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(4690,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)],[617]) ).
thf(16985,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,9527]) ).
thf(16986,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16985]) ).
thf(17039,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 @ v15_lattices ) ),
inference(simp,[status(thm)],[16986]) ).
thf(17070,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[17039]) ).
thf(1166,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)],[1164]) ).
thf(847,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(5886,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)],[847]) ).
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(1203,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(1208,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)],[1206]) ).
thf(1006,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(6542,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)],[1006]) ).
thf(567,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(4458,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)],[567]) ).
thf(3864,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk254 @ m1_subset_1 ) ),
inference(cnfConj,[status(thm)],[3863]) ).
thf(19486,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( A @ sk254 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1978,3864]) ).
thf(19487,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ sk254 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[19486:[bind(A,$thf( k1_xboole_0 ))]]) ).
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(1905,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(26942,plain,
! [A: $i] :
( ( ( A @ ( A @ 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)],[3814,26923]) ).
thf(26943,plain,
! [A: $i] :
( ( ( A @ ( A @ 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)],[26942]) ).
thf(27055,plain,
! [A: $i] :
( ( A != sk1 )
| ( A
!= ( sk71 @ k1_relat_1 ) )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[26943]) ).
thf(27072,plain,
( ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[27055]) ).
thf(178,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(2124,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)],[178]) ).
thf(541,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(4319,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)],[541]) ).
thf(514,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(4177,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)],[514]) ).
thf(295,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(2927,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)],[295]) ).
thf(474,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(3975,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(195,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(2202,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)],[195]) ).
thf(616,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(4688,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)],[616]) ).
thf(212,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(2333,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)],[212]) ).
thf(251,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(2597,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)],[251]) ).
thf(590,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(4581,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)],[590]) ).
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(1958,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(511,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(4168,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)],[511]) ).
thf(607,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(4658,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)],[607]) ).
thf(935,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(6249,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)],[935]) ).
thf(724,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(5294,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)],[724]) ).
thf(3214,plain,
k6_nat_lat @ v3_lattices,
inference(cnfConj,[status(thm)],[3213]) ).
thf(181,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(2143,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(240,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(2518,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)],[240]) ).
thf(187,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(2175,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)],[187]) ).
thf(2513,plain,
k13_nat_lat @ v7_lattices,
inference(cnfConj,[status(thm)],[2508]) ).
thf(627,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(4749,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)],[627]) ).
thf(8423,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)],[1088,8295]) ).
thf(8424,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)],[8423]) ).
thf(8426,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)],[8424]) ).
thf(8428,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)],[8426]) ).
thf(31634,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)],[8428,1997]) ).
thf(31635,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)],[31634]) ).
thf(787,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(5624,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)],[787]) ).
thf(12265,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk152 ) ),
inference(paramod_ordered,[status(thm)],[1978,7802]) ).
thf(12266,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk152 ),
inference(pattern_uni,[status(thm)],[12265:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(27564,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 )
!= sk300 ) ),
inference(paramod_ordered,[status(thm)],[2084,10031]) ).
thf(27565,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk300 ),
inference(pattern_uni,[status(thm)],[27564:[bind(A,$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 )
!= sk300 ),
inference(simp,[status(thm)],[27565]) ).
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(1961,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(1035,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(6683,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)],[1035]) ).
thf(465,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(3913,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)],[465]) ).
thf(7795,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2000,4114]) ).
thf(7796,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7795]) ).
thf(7801,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk71 ),
inference(simp,[status(thm)],[7796]) ).
thf(1062,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)],[1061]) ).
thf(1069,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)],[1062]) ).
thf(1070,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)],[1069]) ).
thf(6941,plain,
( ( ( sk368 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,5293]) ).
thf(6942,plain,
( ( sk368 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6941]) ).
thf(6945,plain,
sk368 != sk152,
inference(simp,[status(thm)],[6942]) ).
thf(3112,plain,
sk197 @ v3_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(16900,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)],[2307,9512]) ).
thf(16901,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)],[16900]) ).
thf(17053,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)],[16901]) ).
thf(17087,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[17053]) ).
thf(216,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(2375,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)],[216]) ).
thf(16978,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,10128]) ).
thf(16979,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16978]) ).
thf(17030,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[16979]) ).
thf(17060,plain,
( ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[17030]) ).
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(1611,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(1225,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)],[1224]) ).
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(1743,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(759,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(5499,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)],[759]) ).
thf(32032,plain,
! [A: $i] :
( ( A != sk197 )
| ( k1_xboole_0 @ v8_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,3121]) ).
thf(32033,plain,
( ( k1_xboole_0 @ v8_lattices )
| ( sk197 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[32032:[bind(A,$thf( sk197 ))]]) ).
thf(780,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(5592,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)],[780]) ).
thf(16961,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,9524]) ).
thf(16962,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16961]) ).
thf(17025,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[16962]) ).
thf(17055,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[17025]) ).
thf(344,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(3209,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)],[344]) ).
thf(629,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(4754,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
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(1753,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(2407,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2405]) ).
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(4961,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(217,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(2386,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)],[217]) ).
thf(988,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(6481,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)],[988]) ).
thf(542,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k23_filter_2 ) @ u1_lattices )
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k23_filter_2 ) @ u2_lattices )
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_filter_2) ).
thf(4324,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k23_filter_2 ) @ u1_lattices )
= ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k23_filter_2 ) @ u2_lattices )
= ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(413,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(3608,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)],[413]) ).
thf(286,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(2831,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)],[286]) ).
thf(911,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(6146,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)],[911]) ).
thf(384,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(3448,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)],[384]) ).
thf(36293,plain,
! [A: $i] :
( ( ( sk368 @ sk18 @ 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)],[34452,1162]) ).
thf(36294,plain,
! [A: $i] :
( ( ( sk368 @ sk18 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[36293]) ).
thf(36295,plain,
( ( sk368 @ sk18 @ k1_relat_1 @ ( sk368 @ sk18 @ k9_relat_1 ) )
= ( sk368 @ sk18 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[36294:[bind(A,$thf( sk368 @ sk18 ))]]) ).
thf(1186,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)],[1185]) ).
thf(1188,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)],[1186]) ).
thf(43768,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,42659]) ).
thf(43769,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[43768]) ).
thf(43815,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk216 )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[43769]) ).
thf(367,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(3344,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)],[367]) ).
thf(26824,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)],[26815,1106]) ).
thf(26825,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)],[26824]) ).
thf(26826,plain,
! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[26825:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk218 @ k9_relat_1 ) )),bind(C,$thf( sk218 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(26904,plain,
! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[26826]) ).
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(1901,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(506,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(4132,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)],[506]) ).
thf(3095,plain,
sk196 @ v7_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
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(1336,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(430,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(3715,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)],[430]) ).
thf(322,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(3080,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)],[322]) ).
thf(278,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(2747,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)],[278]) ).
thf(12255,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk216 ) ),
inference(paramod_ordered,[status(thm)],[1978,9589]) ).
thf(12256,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk216 ),
inference(pattern_uni,[status(thm)],[12255:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(964,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(6389,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)],[964]) ).
thf(22177,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)],[22169,1106]) ).
thf(22178,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)],[22177]) ).
thf(22179,plain,
! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[22178:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk71 @ k9_relat_1 ) )),bind(C,$thf( sk71 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(22256,plain,
! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[22179]) ).
thf(584,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(4561,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)],[584]) ).
thf(546,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(4346,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)],[546]) ).
thf(33206,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( B @ k1_funct_2 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,8846]) ).
thf(33207,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( B @ k1_funct_2 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[33206]) ).
thf(33208,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[33207:[bind(A,$thf( D @ ( D @ k1_funct_2 ) )),bind(B,$thf( D ))]]) ).
thf(35231,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[33208]) ).
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(4905,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(933,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(6244,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)],[933]) ).
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 ) )
=> ( ( A @ v14_lattices )
=> ( A @ k6_lattices @ ( B @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k2_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_2) ).
thf(6036,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 )
=> ( A @ k6_lattices @ ( B @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k2_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(2454,plain,
sk118 @ v8_lattices,
inference(cnfConj,[status(thm)],[2452]) ).
thf(3114,plain,
sk197 @ v5_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(403,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(3554,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)],[403]) ).
thf(16885,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)],[2307,9657]) ).
thf(16886,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)],[16885]) ).
thf(17042,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)],[16886]) ).
thf(17073,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[17042]) ).
thf(521,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(4222,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)],[521]) ).
thf(28960,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 @ sk254 ) ) ),
inference(paramod_ordered,[status(thm)],[2084,13720]) ).
thf(28961,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ k1_zfmisc_1 )
!= ( A @ sk254 ) ),
inference(pattern_uni,[status(thm)],[28960:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 )),bind(D,$thf( E @ k1_tarski ))]]) ).
thf(28976,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ k1_zfmisc_1 )
!= ( A @ sk254 ) ),
inference(simp,[status(thm)],[28961]) ).
thf(389,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(3475,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)],[389]) ).
thf(224,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(2429,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)],[224]) ).
thf(633,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(4768,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)],[633]) ).
thf(446,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(3823,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)],[446]) ).
thf(769,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(5560,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)],[769]) ).
thf(997,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(6508,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)],[997]) ).
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(5030,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(906,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(6125,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)],[906]) ).
thf(179,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(2128,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)],[179]) ).
thf(693,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(5154,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(871,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(5995,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)],[871]) ).
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(1763,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(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(5001,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(449,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(3847,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)],[449]) ).
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(4982,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(418,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(3623,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)],[418]) ).
thf(4781,plain,
sk321 @ v5_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(336,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(3174,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)],[336]) ).
thf(790,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(5638,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)],[790]) ).
thf(951,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(6330,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)],[951]) ).
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(4959,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(576,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(4510,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)],[576]) ).
thf(376,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(3388,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)],[376]) ).
thf(998,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
=> ( ( 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(6511,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)],[998]) ).
thf(781,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(5596,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)],[781]) ).
thf(729,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(5319,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)],[729]) ).
thf(2247,plain,
sk94 @ v5_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
thf(16971,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,10080]) ).
thf(16972,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16971]) ).
thf(17027,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16972]) ).
thf(17057,plain,
( ( sk319 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[17027]) ).
thf(1027,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(6650,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)],[1027]) ).
thf(1039,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(6701,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)],[1039]) ).
thf(921,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(6188,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)],[921]) ).
thf(967,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(6415,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)],[967]) ).
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(1543,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(3107,plain,
sk196 @ v14_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(704,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(5223,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)],[704]) ).
thf(2992,plain,
sk187 @ v4_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(27555,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)],[2084,9594]) ).
thf(27556,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk216 ),
inference(pattern_uni,[status(thm)],[27555:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(27591,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk216 ),
inference(simp,[status(thm)],[27556]) ).
thf(732,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(5347,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)],[732]) ).
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 ) )
=> ( ( ( 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(6318,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)],[950]) ).
thf(597,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(4611,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)],[597]) ).
thf(560,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(4436,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)],[560]) ).
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 @ v13_lattices )
=> ( B @ ( A @ k5_lattices @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k18_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_filter_2) ).
thf(6369,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v13_lattices )
=> ( B @ ( A @ k5_lattices @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k18_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(13702,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk254 @ v1_xboole_0 )
!= ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3865,2476]) ).
thf(13703,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
!= ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13702]) ).
thf(13724,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk254 )
!= ( C @ ( B @ k4_tarski ) ) ),
inference(simp,[status(thm)],[13703]) ).
thf(1218,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)],[1217]) ).
thf(1221,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)],[1218]) ).
thf(303,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(2975,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)],[303]) ).
thf(268,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(2711,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)],[268]) ).
thf(500,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(4106,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)],[500]) ).
thf(922,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(6193,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)],[922]) ).
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 @ ( 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(6213,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)],[926]) ).
thf(10016,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,3166]) ).
thf(10017,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10016]) ).
thf(10028,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk300 ),
inference(simp,[status(thm)],[10017]) ).
thf(486,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(4046,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)],[486]) ).
thf(1094,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)],[1092]) ).
thf(2511,plain,
~ ( k13_nat_lat @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2508]) ).
thf(600,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(4634,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)],[600]) ).
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 @ 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(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 ) )
=> ( ( 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)],[895]) ).
thf(3117,plain,
sk197 @ v9_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(13166,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,10125]) ).
thf(13167,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13166]) ).
thf(13332,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk319 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[13167]) ).
thf(13374,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[13332]) ).
thf(522,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(4225,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)],[522]) ).
thf(545,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(4342,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)],[545]) ).
thf(6937,plain,
( ( ( sk152 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,1243]) ).
thf(6938,plain,
( ( sk152 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6937]) ).
thf(6943,plain,
sk152 != sk14,
inference(simp,[status(thm)],[6938]) ).
thf(807,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(5717,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)],[807]) ).
thf(40162,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk356 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5110,1270]) ).
thf(40163,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk356 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[40162]) ).
thf(40167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk356 )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[40163]) ).
thf(40189,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= ( B @ sk356 ) ),
inference(simp,[status(thm)],[40167]) ).
thf(640,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(4819,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)],[640]) ).
thf(969,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(6420,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)],[969]) ).
thf(16980,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,7374]) ).
thf(16981,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16980]) ).
thf(17036,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[16981]) ).
thf(17067,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[17036]) ).
thf(1240,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)],[1239]) ).
thf(520,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(4217,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)],[520]) ).
thf(946,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_0) ).
thf(6286,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)],[946]) ).
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(1839,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(2458,plain,
sk118 @ v5_lattices,
inference(cnfConj,[status(thm)],[2452]) ).
thf(234,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(2479,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)],[234]) ).
thf(377,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(3401,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)],[377]) ).
thf(885,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(6041,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)],[885]) ).
thf(632,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(4763,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)],[632]) ).
thf(301,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(2960,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)],[301]) ).
thf(13251,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[4739,8295]) ).
thf(13252,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[13251]) ).
thf(13357,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk71 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13252]) ).
thf(210,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(2325,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)],[210]) ).
thf(580,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(4548,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)],[580]) ).
thf(536,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(4289,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)],[536]) ).
thf(535,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(4278,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)],[535]) ).
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(1649,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(7702,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 @ v12_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)],[1088,7377]) ).
thf(7703,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 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7702]) ).
thf(7750,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[7703]) ).
thf(7760,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[7750]) ).
thf(8697,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 @ v12_lattices ) ),
inference(rewrite,[status(thm)],[7760,1997]) ).
thf(8698,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[8697]) ).
thf(1084,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)],[1082]) ).
thf(795,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(5653,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)],[795]) ).
thf(797,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(5660,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)],[797]) ).
thf(10026,plain,
( ( ( sk368 @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,5293]) ).
thf(10027,plain,
( ( sk368 @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10026]) ).
thf(10033,plain,
sk368 != sk300,
inference(simp,[status(thm)],[10027]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(4656,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
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(1844,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(775,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(5573,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)],[775]) ).
thf(670,axiom,
k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_nat_lat) ).
thf(4997,plain,
k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(401,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(3548,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)],[401]) ).
thf(4738,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[4736]) ).
thf(4780,plain,
sk321 @ v3_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(1122,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)],[1121]) ).
thf(1124,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)],[1122]) ).
thf(1126,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)],[1124]) ).
thf(604,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(4646,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)],[604]) ).
thf(431,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( A @ ( B @ m2_nat_lat ) )
<=> ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) )
= ( E @ ( D @ ( C @ g3_lattices ) ) ) )
& ( E
= ( C @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( C @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( A @ ( C @ m2_lattice4 ) )
& ~ ( C @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_filter_2) ).
thf(3725,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] :
( ? [D: $i] :
( ? [E: $i] :
( ( ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) )
= ( E @ ( D @ ( C @ g3_lattices ) ) ) )
& ( E
= ( C @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( C @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( A @ ( C @ m2_lattice4 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( A @ ( B @ m2_nat_lat ) ) )
& ( ( A @ ( B @ m2_nat_lat ) )
=> ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) )
= ( E @ ( D @ ( C @ g3_lattices ) ) ) )
& ( E
= ( C @ ( A @ u1_lattices @ k1_realset1 ) ) )
& ( D
= ( C @ ( A @ u2_lattices @ k1_realset1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( A @ ( C @ m2_lattice4 ) )
& ~ ( C @ v1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(727,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(5308,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)],[727]) ).
thf(2997,plain,
sk188 @ v6_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
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(1390,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(318,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(3056,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)],[318]) ).
thf(756,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(5485,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)],[756]) ).
thf(259,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(2658,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)],[259]) ).
thf(2775,plain,
sk157 @ l3_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(42792,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2697,42607]) ).
thf(42793,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42792]) ).
thf(42825,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk152 ),
inference(simp,[status(thm)],[42793]) ).
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(1734,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(491,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(4061,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)],[491]) ).
thf(292,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(2907,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)],[292]) ).
thf(612,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(4678,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)],[612]) ).
thf(313,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(3039,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)],[313]) ).
thf(17006,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[2307,7666]) ).
thf(17007,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[17006]) ).
thf(17054,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 @ v10_lattices ) ),
inference(simp,[status(thm)],[17007]) ).
thf(17088,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[17054]) ).
thf(587,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(4574,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)],[587]) ).
thf(40140,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)],[28421,1270]) ).
thf(40141,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)],[40140]) ).
thf(40174,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)],[40141]) ).
thf(40196,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( k1_xboole_0 @ k1_tarski @ ( B @ k4_xboole_0 ) ) ),
inference(simp,[status(thm)],[40174]) ).
thf(33192,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v15_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1050]) ).
thf(33193,plain,
( ( k1_xboole_0 @ v15_lattices )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[33192:[bind(A,$thf( sk1 ))]]) ).
thf(2251,plain,
sk94 @ v8_lattices,
inference(cnfConj,[status(thm)],[2244]) ).
thf(689,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(5132,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)],[689]) ).
thf(1037,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(6694,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)],[1037]) ).
thf(715,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(5258,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)],[715]) ).
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(5055,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(12257,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk300 ) ),
inference(paramod_ordered,[status(thm)],[1978,10029]) ).
thf(12258,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk300 ),
inference(pattern_uni,[status(thm)],[12257:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(1252,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 ) ),
inference(cnfConj,[status(thm)],[1250]) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
| ~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ( ( A @ ( B @ sk15 ) )
!= ( C @ ( B @ k1_funct_1 ) ) ) ),
inference(lifteq,[status(thm)],[1252]) ).
thf(16881,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)],[2307,7850]) ).
thf(16882,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)],[16881]) ).
thf(17033,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)],[16882]) ).
thf(17063,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[17033]) ).
thf(2988,plain,
sk187 @ v15_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(218,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(2389,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)],[218]) ).
thf(13290,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[4739,9479]) ).
thf(13291,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[13290]) ).
thf(13303,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk207 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13291]) ).
thf(569,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(4468,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)],[569]) ).
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(5382,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(614,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(4683,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)],[614]) ).
thf(3220,plain,
~ ( k6_nat_lat @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3213]) ).
thf(578,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(4542,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)],[578]) ).
thf(636,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(4791,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)],[636]) ).
thf(3104,plain,
sk196 @ v16_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
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(2004,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(830,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(5813,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)],[830]) ).
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(5368,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(34026,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1049]) ).
thf(34027,plain,
( ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[34026:[bind(A,$thf( sk1 ))]]) ).
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(2026,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(252,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(2608,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)],[252]) ).
thf(348,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(3235,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)],[348]) ).
thf(13178,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[4739,9657]) ).
thf(13179,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ 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)],[13178]) ).
thf(13318,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13179]) ).
thf(393,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(3501,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)],[393]) ).
thf(3003,plain,
sk188 @ v8_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
thf(32030,plain,
! [A: $i] :
( ( A != sk118 )
| ( k1_xboole_0 @ v6_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,2459]) ).
thf(32031,plain,
( ( k1_xboole_0 @ v6_lattices )
| ( sk118 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[32030:[bind(A,$thf( sk118 ))]]) ).
thf(9575,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,3166]) ).
thf(9576,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9575]) ).
thf(9591,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk216 ),
inference(simp,[status(thm)],[9576]) ).
thf(818,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(5756,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)],[818]) ).
thf(281,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(2764,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
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(4834,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(13714,plain,
! [B: $i,A: $i] :
( ( ( A @ sk254 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3865,5364]) ).
thf(13715,plain,
! [B: $i,A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13714]) ).
thf(13721,plain,
! [B: $i,A: $i] :
( ( A @ sk254 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[13715]) ).
thf(4495,plain,
sk304 @ l1_struct_0,
inference(cnf,[status(esa)],[4494]) ).
thf(5087,plain,
sk351 @ v3_lattices,
inference(cnfConj,[status(thm)],[5085]) ).
thf(7724,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 @ v16_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)],[1088,7485]) ).
thf(7725,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 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7724]) ).
thf(7748,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[7725]) ).
thf(7757,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[7748]) ).
thf(8616,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 @ v16_lattices ) ),
inference(rewrite,[status(thm)],[7757,1997]) ).
thf(8617,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[8616]) ).
thf(12267,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk71 ) ),
inference(paramod_ordered,[status(thm)],[1978,7801]) ).
thf(12268,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk71 ),
inference(pattern_uni,[status(thm)],[12267:[bind(A,$thf( k1_xboole_0 ))]]) ).
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(1558,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(183,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(2152,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)],[183]) ).
thf(626,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(4745,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)],[626]) ).
thf(300,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(2956,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)],[300]) ).
thf(834,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(5837,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)],[834]) ).
thf(553,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(4387,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)],[553]) ).
thf(1005,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(6536,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)],[1005]) ).
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(1661,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(34687,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v12_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,1045]) ).
thf(34688,plain,
( ( k1_xboole_0 @ v12_lattices )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[34687:[bind(A,$thf( sk1 ))]]) ).
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(2036,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(688,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(5128,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)],[688]) ).
thf(275,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(2739,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)],[275]) ).
thf(380,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(3420,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)],[380]) ).
thf(284,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(2786,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)],[284]) ).
thf(4197,plain,
~ ( sk282 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4195]) ).
thf(364,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(3324,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)],[364]) ).
thf(696,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(5164,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)],[696]) ).
thf(971,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(6430,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)],[971]) ).
thf(537,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(4293,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)],[537]) ).
thf(764,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(5532,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)],[764]) ).
thf(904,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(6118,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)],[904]) ).
thf(804,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(5692,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)],[804]) ).
thf(4774,plain,
~ ( sk321 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4771]) ).
thf(2462,plain,
sk118 @ v4_lattices,
inference(cnfConj,[status(thm)],[2452]) ).
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(5409,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(6397,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk453 @ m1_subset_1 ) )
| sk451 ),
inference(cnfConj,[status(thm)],[6394]) ).
thf(6412,plain,
( ( f1_s4_subset_1 @ ( sk453 @ m1_subset_1 ) )
| sk451
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[6397]) ).
thf(398,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(3529,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)],[398]) ).
thf(6521,plain,
sk461 @ v3_lattices,
inference(cnfConj,[status(thm)],[6518]) ).
thf(766,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(5549,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)],[766]) ).
thf(189,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(2183,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)],[189]) ).
thf(1210,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)],[1209]) ).
thf(1211,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)],[1210]) ).
thf(1212,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)],[1211]) ).
thf(842,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(5869,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)],[842]) ).
thf(917,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(6166,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)],[917]) ).
thf(564,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(4446,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1011,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(6569,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)],[1011]) ).
thf(16479,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)],[2111,16439]) ).
thf(16480,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)],[16479]) ).
thf(16491,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)],[16480]) ).
thf(16514,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)],[16491]) ).
thf(550,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(4372,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)],[550]) ).
thf(16883,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,9672]) ).
thf(16884,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16883]) ).
thf(17051,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 @ v15_lattices ) ),
inference(simp,[status(thm)],[16884]) ).
thf(17084,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[17051]) ).
thf(697,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(5194,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)],[697]) ).
thf(994,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(6499,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)],[994]) ).
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(4927,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(2779,plain,
sk157 @ v8_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
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 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_0) ).
thf(6198,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)],[924]) ).
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(4917,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(13192,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,10113]) ).
thf(13193,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk319 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13192]) ).
thf(13307,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk319 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13193]) ).
thf(13413,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk319 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13307]) ).
thf(2517,plain,
k13_nat_lat @ v6_lattices,
inference(cnfConj,[status(thm)],[2508]) ).
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(1280,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(395,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(3511,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)],[395]) ).
thf(42841,plain,
! [A: $i] :
( ( A
!= ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,42747]) ).
thf(42842,plain,
! [A: $i] :
( ( A
!= ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[42841]) ).
thf(42843,plain,
sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[42842:[bind(A,$thf( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ))]]) ).
thf(13226,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,7485]) ).
thf(13227,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13226]) ).
thf(13314,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[13227]) ).
thf(913,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(6150,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)],[913]) ).
thf(589,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(4579,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)],[589]) ).
thf(819,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(5760,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)],[819]) ).
thf(342,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(3203,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)],[342]) ).
thf(1112,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)],[1108]) ).
thf(1116,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)],[1112]) ).
thf(31974,plain,
! [A: $i] :
( ( A != k6_nat_lat )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,3217]) ).
thf(31975,plain,
( ( k1_xboole_0 @ v10_lattices )
| ( k6_nat_lat @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31974:[bind(A,$thf( k6_nat_lat ))]]) ).
thf(1040,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ 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(6703,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)],[1040]) ).
thf(2258,plain,
sk95 @ v2_struct_0,
inference(cnfConj,[status(thm)],[2256]) ).
thf(1131,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[1130]) ).
thf(1133,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1131]) ).
thf(483,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(4014,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)],[483]) ).
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(1578,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(925,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(6201,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)],[925]) ).
thf(554,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(4399,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)],[554]) ).
thf(184,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(2155,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)],[184]) ).
thf(480,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(3997,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)],[480]) ).
thf(975,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(6439,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)],[975]) ).
thf(463,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(3907,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)],[463]) ).
thf(2983,plain,
sk187 @ v8_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(271,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(2719,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)],[271]) ).
thf(1095,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)],[1092]) ).
thf(1097,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)],[1095]) ).
thf(250,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(2587,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)],[250]) ).
thf(594,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(4596,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)],[594]) ).
thf(908,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(6131,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)],[908]) ).
thf(959,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(6361,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)],[959]) ).
thf(33006,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk80 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,16847]) ).
thf(33007,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk80 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[33006]) ).
thf(33008,plain,
! [A: $i] : ( A @ sk80 @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[33007:[bind(A,$thf( C @ sk80 )),bind(B,$thf( C ))]]) ).
thf(35213,plain,
! [A: $i] : ( A @ sk80 @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[33008]) ).
thf(478,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(3987,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)],[478]) ).
thf(888,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(6050,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)],[888]) ).
thf(3100,plain,
sk196 @ v13_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(751,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(5430,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)],[751]) ).
thf(274,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(2736,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)],[274]) ).
thf(4787,plain,
sk321 @ v17_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
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(2008,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(441,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(3790,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)],[441]) ).
thf(366,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(3337,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)],[366]) ).
thf(329,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(3132,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)],[329]) ).
thf(990,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(6490,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)],[990]) ).
thf(762,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(5527,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(163,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 @ k23_filter_2 ) @ v10_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v9_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v8_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v7_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v6_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v5_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v4_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v3_lattices )
& ~ ( B @ ( A @ k23_filter_2 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_filter_2) ).
thf(2050,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 @ k23_filter_2 ) @ v10_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v9_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v8_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v7_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v6_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v5_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v4_lattices )
& ( B @ ( A @ k23_filter_2 ) @ v3_lattices )
& ~ ( B @ ( A @ k23_filter_2 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1015,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(6580,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)],[1015]) ).
thf(16876,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,7377]) ).
thf(16877,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v12_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16876]) ).
thf(17029,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 @ v12_lattices ) ),
inference(simp,[status(thm)],[16877]) ).
thf(17059,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v12_lattices ) ),
inference(simp,[status(thm)],[17029]) ).
thf(948,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(6294,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)],[948]) ).
thf(456,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(3875,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)],[456]) ).
thf(42699,plain,
( ( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,42553]) ).
thf(42700,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42699]) ).
thf(42753,plain,
( ( sk14 @ sk395 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk300 ),
inference(simp,[status(thm)],[42700]) ).
thf(214,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(2366,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)],[214]) ).
thf(1165,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)],[1164]) ).
thf(2783,plain,
sk157 @ v9_lattices,
inference(cnfConj,[status(thm)],[2771]) ).
thf(3305,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3303]) ).
thf(3308,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3305]) ).
thf(3309,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3308]) ).
thf(331,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(3145,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)],[331]) ).
thf(4777,plain,
sk321 @ v7_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(488,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(4051,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)],[488]) ).
thf(726,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(5300,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)],[726]) ).
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(1363,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(548,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(4350,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)],[548]) ).
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(1816,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(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(4895,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(902,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(6114,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)],[902]) ).
thf(404,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(3558,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)],[404]) ).
thf(869,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(5990,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)],[869]) ).
thf(6520,plain,
~ ( sk461 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[6518]) ).
thf(337,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(3177,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)],[337]) ).
thf(1025,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(6644,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)],[1025]) ).
thf(496,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(4083,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)],[496]) ).
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(5413,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(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(1561,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(1018,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(6590,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)],[1018]) ).
thf(771,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(5564,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)],[771]) ).
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 @ ( 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(6258,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [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)],[939]) ).
thf(1196,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)],[1190]) ).
thf(1197,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)],[1196]) ).
thf(5867,plain,
k6_nat_lat @ v13_lattices,
inference(cnfConj,[status(thm)],[5864]) ).
thf(712,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(5251,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)],[712]) ).
thf(5031,plain,
! [A: $i] :
( ( ( ( A @ ( sk346 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s12_funct_2 ) )
| ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk344 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk346 @ m2_relset_1 ) ) )
| ~ sk344 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk346 @ v1_funct_2 ) ) )
| ~ sk344 )
& ( ( sk346 @ v1_funct_1 )
| ~ sk344 )
& ( sk344
| ~ ( f2_s12_funct_2 @ ( sk345 @ f3_s12_funct_2 @ r2_hidden ) ) )
& ( sk344
| ( f1_s12_funct_2 @ ( sk345 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[5030]) ).
thf(5036,plain,
( sk344
| ( f1_s12_funct_2 @ ( sk345 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[5031]) ).
thf(419,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(3633,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)],[419]) ).
thf(702,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ 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(5215,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)],[702]) ).
thf(720,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(5283,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)],[720]) ).
thf(1151,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)],[1150]) ).
thf(1152,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)],[1151]) ).
thf(10010,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4440,2476]) ).
thf(10011,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk300 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10010]) ).
thf(10032,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk300 ),
inference(simp,[status(thm)],[10011]) ).
thf(2583,plain,
sk138 @ v2_funct_1,
inference(cnfConj,[status(thm)],[2580]) ).
thf(572,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(4484,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)],[572]) ).
thf(980,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(6452,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)],[980]) ).
thf(703,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 @ ( C @ m1_filter_2 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_filter_2 ) )
=> ( ( ( 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 @ k8_filter_0 ) )
= ( D @ ( B @ k8_filter_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_2) ).
thf(5219,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 @ ( C @ m1_filter_2 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_filter_2 ) )
=> ( ( ( 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 @ k8_filter_0 ) )
= ( D @ ( B @ k8_filter_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(262,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(2687,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)],[262]) ).
thf(264,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(2699,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)],[264]) ).
thf(8896,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)],[3197,7264]) ).
thf(8897,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8896]) ).
thf(8898,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8897:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(16855,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8898,2307]) ).
thf(16856,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16855]) ).
thf(957,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(6351,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)],[957]) ).
thf(719,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(5275,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)],[719]) ).
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(4923,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(699,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(5204,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)],[699]) ).
thf(16949,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,9627]) ).
thf(16950,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v16_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16949]) ).
thf(17026,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 @ v16_lattices ) ),
inference(simp,[status(thm)],[16950]) ).
thf(17056,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v16_lattices ) ),
inference(simp,[status(thm)],[17026]) ).
thf(828,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(5803,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)],[828]) ).
thf(310,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(3025,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)],[310]) ).
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(1261,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(949,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(6316,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)],[949]) ).
thf(899,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(6099,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)],[899]) ).
thf(291,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(2898,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)],[291]) ).
thf(406,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(3570,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)],[406]) ).
thf(235,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(2485,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)],[235]) ).
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(1537,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(973,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(6435,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)],[973]) ).
thf(1976,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(cnf,[status(esa)],[1975]) ).
thf(866,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(5975,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)],[866]) ).
thf(984,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(6471,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)],[984]) ).
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(5060,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(556,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(4410,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)],[556]) ).
thf(309,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(3020,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)],[309]) ).
thf(527,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(4239,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)],[527]) ).
thf(16945,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2307,8112]) ).
thf(16946,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16945]) ).
thf(17032,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[16946]) ).
thf(17062,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[17032]) ).
thf(956,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(6348,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)],[956]) ).
thf(518,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(4206,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)],[518]) ).
thf(24550,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)],[24541,1106]) ).
thf(24551,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)],[24550]) ).
thf(24552,plain,
! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[24551:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk207 @ k9_relat_1 ) )),bind(C,$thf( sk207 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(24632,plain,
! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[24552]) ).
thf(321,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(3076,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)],[321]) ).
thf(3113,plain,
sk197 @ v10_lattices,
inference(cnfConj,[status(thm)],[3109]) ).
thf(16902,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[2307,7663]) ).
thf(16903,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[16902]) ).
thf(17040,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[16903]) ).
thf(17071,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[17040]) ).
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(1505,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(202,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(2270,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)],[202]) ).
thf(13708,plain,
! [B: $i,A: $i] :
( ( ( A @ sk254 @ v1_xboole_0 )
!= ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3865,3166]) ).
thf(13709,plain,
! [B: $i,A: $i] :
( ( A @ sk254 @ v1_xboole_0 )
!= ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13708]) ).
thf(13723,plain,
! [B: $i,A: $i] :
( ( A @ sk254 )
!= ( B @ ( B @ k1_funct_2 ) ) ),
inference(simp,[status(thm)],[13709]) ).
thf(1029,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(6658,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)],[1029]) ).
thf(835,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ r3_lattices ) ) )
& ( A @ v3_filter_0 ) )
=> ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ v3_filter_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_filter_2) ).
thf(5845,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ ( A @ r3_lattices ) ) )
& ( A @ v3_filter_0 ) )
=> ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ v3_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(470,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(3960,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)],[470]) ).
thf(4779,plain,
sk321 @ v15_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
thf(853,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(5913,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)],[853]) ).
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(1367,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(244,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(2563,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)],[244]) ).
thf(36087,plain,
! [A: $i] :
( ( ( sk14 @ sk18 @ 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)],[34230,1162]) ).
thf(36088,plain,
! [A: $i] :
( ( ( sk14 @ sk18 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[36087]) ).
thf(36089,plain,
( ( sk14 @ sk18 @ k1_relat_1 @ ( sk14 @ sk18 @ k9_relat_1 ) )
= ( sk14 @ sk18 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[36088:[bind(A,$thf( sk14 @ sk18 ))]]) ).
thf(5782,plain,
( ( ( f3_s11_funct_2 @ ( sk413 @ ( 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)],[5781]) ).
thf(5788,plain,
( ( ( f3_s11_funct_2 @ ( sk413 @ ( 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)],[5782]) ).
thf(253,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(2615,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)],[253]) ).
thf(2453,plain,
sk118 @ v1_lattice2,
inference(cnfConj,[status(thm)],[2452]) ).
thf(513,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k23_filter_2 ) )
= ( B @ ( A @ k10_filter_2 ) @ ( A @ k1_lattice2 @ k23_filter_2 ) @ ( A @ k1_lattice2 @ k24_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_2) ).
thf(4174,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k23_filter_2 ) )
= ( B @ ( A @ k10_filter_2 ) @ ( A @ k1_lattice2 @ k23_filter_2 ) @ ( A @ k1_lattice2 @ k24_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(42777,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3361,42607]) ).
thf(42778,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[42777]) ).
thf(42829,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk216 ),
inference(simp,[status(thm)],[42778]) ).
thf(582,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(4552,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)],[582]) ).
thf(17145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s11_funct_2 @ ( sk413 @ 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)],[15600,1106]) ).
thf(17146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s11_funct_2 @ ( sk413 @ 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)],[17145]) ).
thf(17147,plain,
! [A: $i] :
( ( f1_s11_funct_2 @ ( A @ ( sk413 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[17146:[bind(A,$thf( sk413 @ k1_relat_1 )),bind(B,$thf( f1_s11_funct_2 )),bind(C,$thf( C ))]]) ).
thf(17205,plain,
! [A: $i] :
( ( f1_s11_funct_2 @ ( A @ ( sk413 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[17147]) ).
thf(591,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(4584,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)],[591]) ).
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(1945,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(22272,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)],[22264,1106]) ).
thf(22273,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)],[22272]) ).
thf(22274,plain,
! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[22273:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk152 @ k9_relat_1 ) )),bind(C,$thf( sk152 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(22341,plain,
! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[22274]) ).
thf(359,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(3299,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)],[359]) ).
thf(793,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(5649,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)],[793]) ).
thf(583,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(4555,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)],[583]) ).
thf(3096,plain,
sk196 @ v5_lattices,
inference(cnfConj,[status(thm)],[3093]) ).
thf(5787,plain,
( ( sk413 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5781]) ).
thf(5789,plain,
( ( sk413 @ v1_funct_1 )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5787]) ).
thf(4784,plain,
sk321 @ v8_lattices,
inference(cnfConj,[status(thm)],[4771]) ).
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(1565,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(2998,plain,
sk188 @ v9_lattices,
inference(cnfConj,[status(thm)],[2994]) ).
thf(16969,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[2307,8295]) ).
thf(16970,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ 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)],[16969]) ).
thf(17045,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[16970]) ).
thf(17076,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[17045]) ).
thf(773,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(5569,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)],[773]) ).
thf(31847,plain,
! [A: $i] :
( ( A != sk157 )
| ( k1_xboole_0 @ v13_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1322,2778]) ).
thf(31848,plain,
( ( k1_xboole_0 @ v13_lattices )
| ( sk157 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31847:[bind(A,$thf( sk157 ))]]) ).
thf(625,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(4742,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)],[625]) ).
thf(714,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(5255,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)],[714]) ).
thf(752,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(5445,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)],[752]) ).
thf(6711,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ l3_lattices )
!= ( sk1 @ l3_lattices ) )
| ~ $true
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v15_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[1047,1051]) ).
thf(6712,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ l3_lattices )
!= ( sk1 @ l3_lattices ) )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v15_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6711]) ).
thf(6719,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v15_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6712]) ).
thf(6735,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v15_lattices )
!= ( sk1 @ v15_lattices ) )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ $true
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[1050,6719]) ).
thf(6736,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v15_lattices )
!= ( sk1 @ v15_lattices ) )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6735]) ).
thf(6741,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6736]) ).
thf(6744,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6741]) ).
thf(6749,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
!= ( sk1 @ v10_lattices ) )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ~ $true
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[1046,6744]) ).
thf(6750,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v10_lattices )
!= ( sk1 @ v10_lattices ) )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6749]) ).
thf(6752,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6750]) ).
thf(6753,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6752]) ).
thf(6791,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
!= ( sk1 @ v16_lattices ) )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ~ $true
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(paramod_ordered,[status(thm)],[1044,6753]) ).
thf(6792,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v16_lattices )
!= ( sk1 @ v16_lattices ) )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6791]) ).
thf(6793,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6792]) ).
thf(6794,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 ) ),
inference(simp,[status(thm)],[6793]) ).
thf(6801,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 )
!= ( sk1 @ v3_struct_0 ) )
| ~ $true
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[6794,1048]) ).
thf(6802,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) @ v3_struct_0 )
!= ( sk1 @ v3_struct_0 ) )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6801]) ).
thf(6809,plain,
( ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6802]) ).
thf(6810,plain,
( ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ k23_filter_2 ) )
!= sk1 ),
inference(simp,[status(thm)],[6809]) ).
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(1416,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(798,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(5664,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)],[798]) ).
thf(809,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(5732,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)],[809]) ).
thf(1204,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)],[1203]) ).
thf(941,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(6265,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)],[941]) ).
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(4858,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(314,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(3047,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)],[314]) ).
thf(13176,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,9672]) ).
thf(13177,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk319 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v15_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[13176]) ).
thf(13311,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk319 != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v15_lattices ) ),
inference(simp,[status(thm)],[13177]) ).
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(1912,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(852,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ v11_lattices )
=> ( B @ ( A @ k23_filter_2 ) @ v11_lattices ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_2) ).
thf(5911,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ m2_lattice4 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ v11_lattices )
=> ( B @ ( A @ k23_filter_2 ) @ v11_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(2980,plain,
sk187 @ v5_lattices,
inference(cnfConj,[status(thm)],[2979]) ).
thf(312,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(3035,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)],[312]) ).
thf(48486,plain,
$false,
inference(e,[status(thm)],[2163,1501,3962,5116,4094,17072,4899,42828,3167,2463,35548,1083,1110,5385,2199,1322,1665,2630,3873,1411,5365,5088,1369,6669,1168,2306,3053,4464,36192,6530,2778,34452,5260,1995,6544,1237,6283,4183,3698,6448,5778,6555,1179,2331,1818,1295,1686,2250,1750,6576,4075,3153,3108,5669,4614,1305,1437,4479,40493,3680,4043,4037,2512,2117,43818,5225,6944,6495,7377,1068,3858,4311,6106,3762,9590,3230,2776,1808,3417,2953,5297,3460,1422,2947,1939,2248,5878,3098,1073,3910,5793,6338,16862,5982,1205,2114,1142,7850,10125,6031,4973,3217,1655,15632,5146,1233,4564,4247,6336,1063,31835,2146,1458,40692,1705,6522,5967,6391,1608,3120,6505,3049,4739,5589,13317,3004,13722,6246,15600,31945,1999,2316,17079,2448,17068,6089,4856,4440,4650,2476,2627,2168,3253,3826,2459,3121,6680,1222,2360,6046,9672,3370,3836,17081,5745,1046,5921,1935,3281,5750,4775,3103,8851,6466,5740,31977,8848,2972,2046,6251,2432,5393,1127,6268,2491,1243,2985,4496,5723,5770,4198,2082,31882,14969,6102,2516,4963,2825,9657,6483,4665,4156,3880,1228,1482,1254,26802,5024,5352,5797,1709,4348,4422,2708,6066,2217,3612,3803,2745,12254,3891,4637,3248,31864,5953,3442,17075,14909,4439,13313,3221,5585,4524,4866,6552,6242,3644,3275,6034,2698,3131,3116,2667,4151,1871,3574,4761,6423,4778,15881,3776,3125,5150,4130,1313,42748,2185,5160,3744,6332,6519,5289,4984,1462,1059,6240,1147,6626,3216,2730,2024,40022,2989,5091,3866,5231,8849,2420,3099,6253,2713,4119,1379,3374,3385,5868,6470,5214,5605,4788,2403,3638,1087,4194,1247,4358,6502,19414,1479,4492,5397,4622,17085,3084,1115,3470,5851,35186,34025,13393,3312,7965,6025,6734,2852,1100,5617,4253,3268,3788,5792,2456,9593,5892,3966,2782,2259,2122,6176,1978,5156,4115,2017,5682,6081,15878,2950,5957,5264,6002,42607,3524,15500,3199,6227,28563,4443,5084,6670,5861,4258,7300,1373,2996,13382,16018,13312,27070,3163,5856,14423,2451,6410,3473,6534,4847,1383,2254,2540,5805,5311,2034,2777,4783,1283,2073,1051,42754,4810,5773,3712,2772,5629,16858,6474,5045,5572,5059,4718,4751,42553,5738,33881,6631,24541,4055,4230,9616,5379,13305,6685,1215,6221,17058,5343,1526,3361,3955,6021,2286,2639,2750,1405,4643,1201,5137,6156,3870,3588,4892,1104,4379,13725,9589,10113,6860,2586,2982,1975,10029,4065,1863,3582,5406,32087,3567,17655,1470,2307,6092,1074,3899,2011,3097,3011,4604,5012,3450,5875,3301,4753,5530,4589,5751,2574,8233,5411,26815,3984,1153,6139,6064,6058,6588,5291,9588,3995,5562,4059,26923,6442,2061,3550,2773,2000,6464,1047,1057,1163,6652,2705,1042,2277,5794,1570,35499,28963,3610,35220,4785,1824,2396,6620,17061,1900,1723,1223,4712,22169,5611,5734,1091,42751,2733,3972,2249,6000,6371,6528,36406,3239,4449,3134,3814,2986,14484,4836,4661,3664,15439,1238,2015,3889,15886,2670,2477,1178,3894,2200,1159,10035,1407,1128,4680,3445,3166,3958,7663,3191,6926,2758,3980,41301,4608,9512,1920,3314,6445,4757,3499,3065,4776,3600,1836,35528,6096,5566,6060,1079,8847,4732,5936,2228,2112,5993,3408,42827,4063,6709,1106,2515,5615,3119,17065,5081,3205,2245,5854,3105,3467,42747,3615,1541,1089,2498,7329,44205,5714,2157,2840,1143,1270,1851,3122,2990,5270,4668,1953,40194,7249,5423,22264,3862,40676,2895,1121,6603,2577,3381,6133,1064,1111,5577,1227,3218,4048,1096,2509,3102,5428,9624,5362,5583,1719,5978,6624,5847,4012,6128,4109,1118,6148,5497,3001,4817,4263,4676,2460,16847,5915,3094,3596,6256,3194,2108,13309,2978,24470,1329,1160,3311,1942,3922,5694,3000,18132,13308,5651,4772,6116,5107,1182,5791,6661,6363,5743,1075,17074,3441,2312,2455,34374,4545,2080,5253,1414,2196,5213,37619,1207,3671,2085,1644,6275,6271,1155,2781,6065,1114,1263,41205,7966,4259,13340,1150,5481,1451,6033,1539,1456,6433,2243,5973,7485,4244,1060,1050,2581,2465,2505,3819,3222,2006,5058,20028,17064,1984,6450,3115,3247,2862,4135,2766,3692,4902,2697,6418,17069,5801,1979,6152,3074,3005,4086,6224,1759,1393,3215,16854,5245,1333,3755,5544,1202,5402,4782,3856,5571,1170,5417,7802,26708,32675,8846,5747,1086,33584,1241,2702,4889,3183,5833,20096,5964,6260,6647,1286,3321,5447,1071,2402,1187,2915,2408,1663,5930,3508,1167,2189,6038,2995,5872,4308,6497,8234,4550,3807,6524,1273,2570,5960,9594,4577,5647,27582,5679,1135,3660,2001,1251,4919,6437,4685,1146,40016,13726,1103,3358,2253,31874,4594,1219,6699,4874,5508,10030,3491,1927,6578,8112,13372,3289,4340,3888,6454,6546,3111,6492,6052,42659,5241,4786,3372,4998,1833,5933,17083,1652,9471,2991,5097,2716,5239,5799,9627,3636,3925,5488,4494,8580,2981,5627,3266,2514,5962,5831,6229,4709,1226,2695,1256,28421,3051,2308,5908,3695,3123,5449,5997,2474,3355,2319,6016,5556,3223,4251,5039,1669,9587,3118,10034,4096,10083,4112,4149,4171,4236,17077,3208,2935,3002,4822,42826,4413,1107,5086,1239,1997,2442,5207,1090,3619,2457,4640,3641,6123,7482,3532,4716,6478,3101,6572,2774,2257,6340,1144,32054,1376,2510,6585,1209,3352,4228,2538,1853,5671,2478,2642,9592,2084,5244,3764,27594,2987,5520,2637,1117,3779,1048,5827,2097,2246,1492,3106,5880,4213,3197,5531,4667,16864,6154,6184,4374,8561,3586,6196,16439,4773,3160,1307,2180,2742,4009,34230,2780,4332,4296,2461,3219,5552,8735,4401,5202,3747,20112,1080,4420,3027,5894,4569,13323,2111,1731,3800,5863,2261,6353,4897,1162,4452,5286,2446,19785,3977,2410,2785,3006,6678,4850,5656,1149,1556,2542,6044,2252,40010,1293,4993,5780,2911,4990,2578,4232,6377,6288,1176,3241,2999,4067,5619,3480,1171,3539,2770,4844,1198,4720,8440,1841,1213,3759,5377,14207,8573,1044,20201,1245,5641,1445,1528,6628,3110,2139,5248,27598,2064,2369,34023,3363,5667,4196,6027,16860,6180,10031,13727,6029,1694,8560,4965,2984,1973,4481,2069,6476,1076,13371,4441,5890,4813,2784,17080,1134,8477,5003,3522,3009,9524,4690,17070,1166,5886,1203,1208,6542,4458,19487,3161,4735,1905,27072,2124,4319,4177,2927,3975,2202,6517,4688,2333,2597,4581,1958,4168,2582,37419,1049,4658,6249,5294,14485,3214,2143,3462,2518,2175,1098,10080,2513,4749,31635,5624,12266,27595,1961,6683,3913,7801,1070,6945,3112,17087,2375,5388,1156,17060,1611,1225,1743,5499,32033,5592,3129,17055,3209,4754,1753,2407,4961,2386,6481,4324,8295,3608,1230,2831,6146,3448,36295,1188,43815,3344,26904,1901,4132,3095,1336,3715,3080,2747,12256,6389,3246,22256,4561,4346,35231,4905,6244,7264,6036,2454,3114,3334,3554,17073,4222,28976,3475,2429,4768,8845,3823,5560,6508,5030,6125,2128,5154,5995,1763,5001,3847,4982,3623,4781,3174,4737,5638,6330,7847,1898,4959,4510,3388,6511,5596,5319,2247,17057,6650,6701,6188,6415,1543,3107,5223,2992,27591,5347,10128,6318,4611,4436,6369,13724,1221,2975,1052,2711,4106,6193,6213,2579,10028,4046,7374,1094,8850,2511,4634,6086,3117,5364,13374,4225,4342,6943,5717,3071,40189,2584,4257,4819,6420,17067,1240,4217,6286,1839,2458,2479,3401,3092,4770,6041,4763,2960,13357,2325,1216,4548,4289,4278,1649,8844,8698,1084,9527,5653,5660,1157,10033,4656,1844,5573,4997,3548,4738,4780,1126,4646,3725,5308,2997,1189,2110,1390,3056,5485,2658,2775,42825,1734,4061,2907,4678,3039,17088,1998,4574,40196,40281,33193,2251,5132,6694,5258,5055,12258,15869,10072,1253,17063,2988,3864,2389,13303,4468,5382,6030,4683,8292,1101,9482,3220,4542,4791,3104,2004,5813,5368,34027,2026,2608,3235,13318,3501,3003,1244,32031,9591,5756,2764,4834,13721,4495,5087,5243,8617,12268,1558,2152,4745,2956,5837,4387,6536,1661,34688,2036,5128,2739,3420,14970,2786,4197,3324,5164,6430,4293,5532,2399,9669,6118,5692,4774,2462,5409,2198,6412,3529,6521,15875,5549,6062,2183,1212,5869,6166,4446,6569,16514,4372,17084,5194,6499,4927,5336,2779,6198,1045,8115,4917,13413,2517,1280,3511,42843,13314,3373,6150,4579,5760,3203,3164,1116,31975,6703,2258,1133,4014,1578,4114,6201,4399,2155,2255,3997,6439,3907,2983,3865,2719,1097,7231,2587,7666,4596,6131,6361,35213,3987,6050,3100,5430,2736,4787,2008,3790,3337,3132,1248,6490,5527,2050,8574,6580,17059,6294,3875,42753,2366,2404,6393,1165,5110,2783,3309,3145,4777,4051,5300,1363,4350,1816,4895,6114,3558,5990,6520,3177,6644,4083,5413,1561,6590,5564,6258,1197,5867,5251,5036,3633,5215,5283,5322,3362,1152,10032,2583,4484,6452,5219,2687,2699,1120,16856,6351,5275,4923,3244,5204,17056,1977,1129,5803,3025,1261,6316,6099,2898,3570,2485,1537,6435,3360,15845,1976,5975,6471,5060,4410,3020,4239,2507,17062,6348,13720,4206,24632,3076,3113,17071,1505,2270,13723,6658,5845,3960,4779,5913,1367,2563,36089,1184,5788,9479,2615,2453,5293,4174,42829,4552,17205,4584,1945,22341,3212,3299,5649,4555,3096,5789,4784,1565,7320,2998,17076,5569,31848,4742,5255,5445,6810,1416,5664,28420,5732,1088,2993,6668,1204,6265,4858,3047,13311,1912,5911,2980,3035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT336+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
% 0.12/0.40 % Computer : n017.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Fri Sep 25 20:56:20 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.18/1.66 % [INFO] Parsing done (677ms).
% 3.18/1.68 % [INFO] Running in sequential loop mode.
% 4.07/1.96 % [INFO] eprover registered as external prover.
% 4.07/1.96 % [INFO] Scanning for conjecture ...
% 4.89/2.15 % [INFO] Found a conjecture (or negated_conjecture) and 3024 axioms. Running axiom selection ...
% 7.67/2.95 % [INFO] Axiom selection finished. Selected 1039 axioms (removed 1985 axioms).
% 10.41/3.75 % [INFO] Problem is first-order (TPTP FOF).
% 10.73/3.82 % [INFO] Type checking passed.
% 10.73/3.83 % [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 ...
% 164.99/46.38 % External prover 'e' found a proof!
% 164.99/46.38 % [INFO] Killing All external provers ...
% 164.99/46.38 % Time passed: 45833ms (effective reasoning time: 44692ms)
% 164.99/46.38 % 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)>
% 164.99/46.39 % Axioms used in derivation (1039): 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, t70_filter_2, 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, 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, t68_filter_2, t50_funct_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, 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, t71_filter_2, s13_funct_2, fraenkel_a_2_2_domain_1, t129_zfmisc_1, d4_subset_1, t2_binop_1, t80_filter_2, t17_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, 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, t66_filter_2, fraenkel_a_3_0_filter_0, 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, t31_partfun1, dt_k7_lattices, t3_funct_2, rc2_subset_1, existence_l2_lattices, l59_filter_2, t75_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, dt_k11_filter_2, d15_filter_2, d13_relat_1, t74_filter_2, 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, d6_tarski, t82_filter_2, t32_partfun1, t4_relat_1, t26_binop_1, t28_subset_1, d12_lattices, d17_lattice4, fc3_subset_1, t128_zfmisc_1, t39_partfun1, t75_zfmisc_1, redefinition_k4_filter_2, t8_lattice4, rc1_filter_0, d2_realset1, d16_filter_2, 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, t65_filter_2, t40_funct_2, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t24_binop_1, t27_lattice4, 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, t75_lattice2, t67_filter_2, t47_lattices, d7_filter_2, d20_lattices, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t38_filter_0, d3_lattices, t77_filter_2, 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_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, existence_m2_realset1, fc5_filter_2, 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, 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, dt_k3_lattice2, t78_filter_2, 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, fraenkel_a_2_0_filter_2, 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, t79_filter_2, t11_relset_1, t155_relat_1, t27_filter_2, t15_subset_1, 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, t44_filter_0, t73_filter_2, 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, t76_filter_2, 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, t69_filter_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, t84_filter_2, 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, 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, t54_funct_1, t81_filter_2, 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, t72_filter_2, t29_lattices, t88_filter_0, d1_relat_2, 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, t82_filter_0, t83_filter_2, 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
% 164.99/46.39 % No. of inferences in proof: 3493
% 164.99/46.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 45833 ms resp. 44692 ms w/o parsing
% 171.43/47.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 171.43/47.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------