%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT329+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 07:47:17 AM UTC 2026
% Result : Theorem 189.01s 70.57s
% Output : Refutation 195.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1084
% Syntax : Number of formulae : 3496 ( 651 unt; 0 typ; 67 def)
% Number of atoms : 19437 (3205 equ; 0 cnn)
% Maximal formula atoms : 58 ( 5 avg)
% Number of connectives : 65148 (5063 ~;2748 |;6923 &;45007 @)
% ( 240 <=>;5167 =>; 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 : 8043 ( 53 ^;7586 !; 337 ?;8043 :)
% ( 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(v14_lattices_decl,type,
v14_lattices: $i > $o ).
thf(r1_filter_2_decl,type,
r1_filter_2: $i > $i > $i > $o ).
thf(k2_filter_2_decl,type,
k2_filter_2: $i > $i > $i ).
thf(k22_filter_2_decl,type,
k22_filter_2: $i > $i > $i > $i ).
thf(k6_lattices_decl,type,
k6_lattices: $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(r1_binop_1_decl,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_binop_1_decl,type,
k1_binop_1: $i > $i > $i > $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(r6_binop_1_decl,type,
r6_binop_1: $i > $i > $i > $o ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(k1_realset1_decl,type,
k1_realset1: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(r4_binop_1_decl,type,
r4_binop_1: $i > $i > $i > $o ).
thf(r5_binop_1_decl,type,
r5_binop_1: $i > $i > $i > $o ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v3_binop_1_decl,type,
v3_binop_1: $i > $i > $o ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(r2_binop_1_decl,type,
r2_binop_1: $i > $i > $i > $o ).
thf(k3_relat_1_decl,type,
k3_relat_1: $i > $i ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(r3_binop_1_decl,type,
r3_binop_1: $i > $i > $i > $o ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(v3_filter_0_decl,type,
v3_filter_0: $i > $o ).
thf(v4_lattices_decl,type,
v4_lattices: $i > $o ).
thf(v5_lattices_decl,type,
v5_lattices: $i > $o ).
thf(v6_lattices_decl,type,
v6_lattices: $i > $o ).
thf(v7_lattices_decl,type,
v7_lattices: $i > $o ).
thf(v8_lattices_decl,type,
v8_lattices: $i > $o ).
thf(v9_lattices_decl,type,
v9_lattices: $i > $o ).
thf(v11_lattices_decl,type,
v11_lattices: $i > $o ).
thf(v12_lattices_decl,type,
v12_lattices: $i > $o ).
thf(k1_lattice2_decl,type,
k1_lattice2: $i > $i ).
thf(v3_lattices_decl,type,
v3_lattices: $i > $o ).
thf(l2_lattices_decl,type,
l2_lattices: $i > $o ).
thf(u2_lattices_decl,type,
u2_lattices: $i > $i ).
thf(l1_lattices_decl,type,
l1_lattices: $i > $o ).
thf(u1_lattices_decl,type,
u1_lattices: $i > $i ).
thf(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $i ).
thf(a_2_3_domain_1_decl,type,
a_2_3_domain_1: $i > $i > $i ).
thf(k2_binop_1_decl,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(v6_group_1_decl,type,
v6_group_1: $i > $o ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(v13_lattices_decl,type,
v13_lattices: $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(m1_filter_0_decl,type,
m1_filter_0: $i > $i > $o ).
thf(k8_filter_0_decl,type,
k8_filter_0: $i > $i > $i ).
thf(l2_struct_0_decl,type,
l2_struct_0: $i > $o ).
thf(v2_struct_0_decl,type,
v2_struct_0: $i > $o ).
thf(m2_lattice4_decl,type,
m2_lattice4: $i > $i > $o ).
thf(r1_lattice2_decl,type,
r1_lattice2: $i > $i > $i > $o ).
thf(k7_domain_1_decl,type,
k7_domain_1: $i > $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(k5_finsub_1_decl,type,
k5_finsub_1: $i > $i ).
thf(v1_lattice2_decl,type,
v1_lattice2: $i > $o ).
thf(k13_nat_lat_decl,type,
k13_nat_lat: $i ).
thf(k3_binop_1_decl,type,
k3_binop_1: $i > $i > $i ).
thf(k2_subset_1_decl,type,
k2_subset_1: $i > $i ).
thf(m2_nat_lat_decl,type,
m2_nat_lat: $i > $i > $o ).
thf(a_2_2_domain_1_decl,type,
a_2_2_domain_1: $i > $i > $i ).
thf(a_2_0_domain_1_decl,type,
a_2_0_domain_1: $i > $i > $i ).
thf(r8_relat_2_decl,type,
r8_relat_2: $i > $i > $o ).
thf(k1_subset_1_decl,type,
k1_subset_1: $i > $i ).
thf(k4_subset_1_decl,type,
k4_subset_1: $i > $i > $i > $i ).
thf(r3_relat_2_decl,type,
r3_relat_2: $i > $i > $o ).
thf(v15_lattices_decl,type,
v15_lattices: $i > $o ).
thf(v16_lattices_decl,type,
v16_lattices: $i > $o ).
thf(r7_binop_1_decl,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k6_nat_lat_decl,type,
k6_nat_lat: $i ).
thf(a_3_3_domain_1_decl,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(r1_relat_2_decl,type,
r1_relat_2: $i > $i > $o ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(a_1_0_domain_1_decl,type,
a_1_0_domain_1: $i > $i ).
thf(m3_realset1_decl,type,
m3_realset1: $i > $i > $i > $o ).
thf(k7_funct_2_decl,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(m2_filter_2_decl,type,
m2_filter_2: $i > $i > $o ).
thf(k21_filter_2_decl,type,
k21_filter_2: $i > $i > $i > $i ).
thf(k20_filter_2_decl,type,
k20_filter_2: $i > $i > $i > $i ).
thf(k2_lattices_decl,type,
k2_lattices: $i > $i > $i > $i ).
thf(r2_filter_2_decl,type,
r2_filter_2: $i > $i > $o ).
thf(v1_filter_0_decl,type,
v1_filter_0: $i > $i > $o ).
thf(k15_filter_2_decl,type,
k15_filter_2: $i > $i > $i ).
thf(k5_filter_0_decl,type,
k5_filter_0: $i > $i > $i > $i ).
thf(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(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(k5_lattices_decl,type,
k5_lattices: $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(r4_lattice4_decl,type,
r4_lattice4: $i > $i > $i > $o ).
thf(k4_lattices_decl,type,
k4_lattices: $i > $i > $i > $i ).
thf(m1_filter_2_decl,type,
m1_filter_2: $i > $i > $o ).
thf(k4_filter_2_decl,type,
k4_filter_2: $i > $i > $i > $i ).
thf(g2_struct_0_decl,type,
g2_struct_0: $i > $i > $i ).
thf(k2_lattice2_decl,type,
k2_lattice2: $i > $i > $i > $i > $i ).
thf(k8_funcop_1_decl,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(a_2_1_lattice4_decl,type,
a_2_1_lattice4: $i > $i > $i ).
thf(k3_lattice4_decl,type,
k3_lattice4: $i > $i > $i ).
thf(a_2_1_domain_1_decl,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k3_lattice2_decl,type,
k3_lattice2: $i > $i > $i > $i > $i ).
thf(k1_lattices_decl,type,
k1_lattices: $i > $i > $i > $i ).
thf(r1_lattices_decl,type,
r1_lattices: $i > $i > $i > $o ).
thf(k1_domain_1_decl,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(k12_filter_2_decl,type,
k12_filter_2: $i > $i > $i ).
thf(k8_filter_2_decl,type,
k8_filter_2: $i > $i > $i ).
thf(r3_lattices_decl,type,
r3_lattices: $i > $i > $i > $o ).
thf(k10_filter_2_decl,type,
k10_filter_2: $i > $i > $i ).
thf(k3_filter_0_decl,type,
k3_filter_0: $i > $i > $i ).
thf(k4_filter_0_decl,type,
k4_filter_0: $i > $i > $i > $i ).
thf(k13_filter_2_decl,type,
k13_filter_2: $i > $i > $i ).
thf(k3_filter_2_decl,type,
k3_filter_2: $i > $i > $i ).
thf(k7_filter_2_decl,type,
k7_filter_2: $i > $i > $i ).
thf(k19_filter_2_decl,type,
k19_filter_2: $i > $i > $i ).
thf(p1_s2_domain_1_decl,type,
p1_s2_domain_1: $i > $i > $o ).
thf(k5_lattice4_decl,type,
k5_lattice4: $i > $i ).
thf(k7_lattices_decl,type,
k7_lattices: $i > $i > $i ).
thf(k1_lattice4_decl,type,
k1_lattice4: $i > $i > $i ).
thf(k3_lattices_decl,type,
k3_lattices: $i > $i > $i > $i ).
thf(k7_filter_0_decl,type,
k7_filter_0: $i > $i > $i > $i ).
thf(a_0_0_domain_1_decl,type,
a_0_0_domain_1: $i ).
thf(f1_s7_domain_1_decl,type,
f1_s7_domain_1: $i ).
thf(k8_setwiseo_decl,type,
k8_setwiseo: $i > $i > $i > $i > $i ).
thf(k16_filter_2_decl,type,
k16_filter_2: $i > $i > $i ).
thf(k5_setwiseo_decl,type,
k5_setwiseo: $i > $i > $i > $i ).
thf(k2_setwiseo_decl,type,
k2_setwiseo: $i > $i > $i ).
thf(u2_struct_0_decl,type,
u2_struct_0: $i > $i ).
thf(k10_filter_0_decl,type,
k10_filter_0: $i > $i > $i ).
thf(k9_filter_0_decl,type,
k9_filter_0: $i > $i > $i > $i ).
thf(k4_lattice4_decl,type,
k4_lattice4: $i > $i > $i ).
thf(k2_lattice4_decl,type,
k2_lattice4: $i > $i > $i ).
thf(k14_filter_2_decl,type,
k14_filter_2: $i > $i > $i ).
thf(r2_lattices_decl,type,
r2_lattices: $i > $i > $i > $o ).
thf(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(r3_lattice4_decl,type,
r3_lattice4: $i > $i > $i > $o ).
thf(k11_filter_0_decl,type,
k11_filter_0: $i > $i > $i ).
thf(a_3_2_domain_1_decl,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(a_2_0_lattice4_decl,type,
a_2_0_lattice4: $i > $i > $i ).
thf(v1_lattice4_decl,type,
v1_lattice4: $i > $i > $i > $o ).
thf(m3_lattice4_decl,type,
m3_lattice4: $i > $i > $o ).
thf(m1_struct_0_decl,type,
m1_struct_0: $i > $i > $i > $o ).
thf(k7_setwiseo_decl,type,
k7_setwiseo: $i > $i > $i > $i > $i > $i ).
thf(k24_filter_2_decl,type,
k24_filter_2: $i > $i > $i ).
thf(k12_domain_1_decl,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a_1_2_domain_1_decl,type,
a_1_2_domain_1: $i > $i ).
thf(k6_filter_0_decl,type,
k6_filter_0: $i > $i > $i > $i ).
thf(a_3_6_domain_1_decl,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(f1_s4_funct_2_decl,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_decl,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_decl,type,
f3_s4_funct_2: $i > $i ).
thf(k1_finsub_1_decl,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(k2_filter_0_decl,type,
k2_filter_0: $i > $i > $i ).
thf(a_3_5_domain_1_decl,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(k18_filter_2_decl,type,
k18_filter_2: $i > $i > $i ).
thf(v3_lattice4_decl,type,
v3_lattice4: $i > $i > $i > $o ).
thf(r1_lattice4_decl,type,
r1_lattice4: $i > $i > $i > $o ).
thf(k1_filter_0_decl,type,
k1_filter_0: $i > $i ).
thf(a_3_4_domain_1_decl,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(k9_domain_1_decl,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(v2_filter_0_decl,type,
v2_filter_0: $i > $i > $o ).
thf(f1_s14_funct_2_decl,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_decl,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_decl,type,
p1_s14_funct_2: $i > $i > $o ).
thf(a_3_0_filter_0_decl,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(f1_s12_funct_2_decl,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_decl,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_decl,type,
f2_s12_funct_2: $i ).
thf(f1_s13_funct_2_decl,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_decl,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_decl,type,
f2_s13_funct_2: $i ).
thf(a_3_1_domain_1_decl,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k11_domain_1_decl,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k13_domain_1_decl,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k8_domain_1_decl,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(k11_filter_2_decl,type,
k11_filter_2: $i > $i > $i ).
thf(k12_filter_0_decl,type,
k12_filter_0: $i > $i > $i ).
thf(f1_s3_funct_2_decl,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_decl,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_decl,type,
p1_s3_funct_2: $i > $i > $o ).
thf(a_3_7_domain_1_decl,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(a_4_1_domain_1_decl,type,
a_4_1_domain_1: $i > $i > $i > $i > $i ).
thf(r1_filter_0_decl,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(r2_lattice4_decl,type,
r2_lattice4: $i > $i > $i > $o ).
thf(a_2_0_filter_0_decl,type,
a_2_0_filter_0: $i > $i > $i ).
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(a_3_2_filter_2_decl,type,
a_3_2_filter_2: $i > $i > $i > $i ).
thf(a_0_2_domain_1_decl,type,
a_0_2_domain_1: $i ).
thf(f3_s9_domain_1_decl,type,
f3_s9_domain_1: $i ).
thf(p1_s7_domain_1_decl,type,
p1_s7_domain_1: $i > $o ).
thf(r1_filter_1_decl,type,
r1_filter_1: $i > $i > $o ).
thf(f3_s11_funct_2_decl,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_decl,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_decl,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_decl,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_decl,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_decl,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_decl,type,
f7_s11_funct_2: $i > $i ).
thf(k9_filter_2_decl,type,
k9_filter_2: $i > $i > $i ).
thf(k1_struct_0_decl,type,
k1_struct_0: $i > $i > $i ).
thf(k8_subset_1_decl,type,
k8_subset_1: $i > $i ).
thf(a_0_1_domain_1_decl,type,
a_0_1_domain_1: $i ).
thf(f2_s8_domain_1_decl,type,
f2_s8_domain_1: $i ).
thf(k1_setwiseo_decl,type,
k1_setwiseo: $i > $i ).
thf(a_2_0_filter_2_decl,type,
a_2_0_filter_2: $i > $i > $i ).
thf(k7_grcat_1_decl,type,
k7_grcat_1: $i > $i ).
thf(f1_s8_domain_1_decl,type,
f1_s8_domain_1: $i ).
thf(f3_s8_domain_1_decl,type,
f3_s8_domain_1: $i > $i ).
thf(p1_s8_domain_1_decl,type,
p1_s8_domain_1: $i > $o ).
thf(k1_filter_2_decl,type,
k1_filter_2: $i > $i ).
thf(f1_s9_domain_1_decl,type,
f1_s9_domain_1: $i ).
thf(f2_s9_domain_1_decl,type,
f2_s9_domain_1: $i ).
thf(f4_s9_domain_1_decl,type,
f4_s9_domain_1: $i > $i > $i ).
thf(p1_s9_domain_1_decl,type,
p1_s9_domain_1: $i > $i > $o ).
thf(f1_s4_subset_1_decl,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_decl,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_decl,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_decl,type,
f3_s4_subset_1: $i ).
thf(a_3_0_filter_2_decl,type,
a_3_0_filter_2: $i > $i > $i > $i ).
thf(k23_filter_2_decl,type,
k23_filter_2: $i > $i > $i ).
thf(k7_funcop_1_decl,type,
k7_funcop_1: $i > $i > $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(sk251_decl,type,
sk251: $i > $i ).
thf(sk279_decl,type,
sk279: $i ).
thf(sk295_decl,type,
sk295: $i ).
thf(sk299_decl,type,
sk299: $i ).
thf(sk313_decl,type,
sk313: $i ).
thf(sk315_decl,type,
sk315: $i ).
thf(sk329_decl,type,
sk329: $o ).
thf(sk330_decl,type,
sk330: $i ).
thf(sk331_decl,type,
sk331: $i ).
thf(sk337_decl,type,
sk337: $o ).
thf(sk338_decl,type,
sk338: $i ).
thf(sk339_decl,type,
sk339: $i ).
thf(sk341_decl,type,
sk341: $i ).
thf(sk344_decl,type,
sk344: $i ).
thf(sk345_decl,type,
sk345: $o ).
thf(sk346_decl,type,
sk346: $i ).
thf(sk347_decl,type,
sk347: $i ).
thf(sk349_decl,type,
sk349: $i > $i ).
thf(sk357_decl,type,
sk357: $i ).
thf(sk358_decl,type,
sk358: $i ).
thf(sk361_decl,type,
sk361: $i ).
thf(sk366_decl,type,
sk366: $i > $i > $i ).
thf(sk367_decl,type,
sk367: $i > $i > $i ).
thf(sk372_decl,type,
sk372: $o ).
thf(sk373_decl,type,
sk373: $i ).
thf(sk374_decl,type,
sk374: $i ).
thf(sk384_decl,type,
sk384: $i > $i ).
thf(sk402_decl,type,
sk402: $i ).
thf(sk417_decl,type,
sk417: $i ).
thf(sk444_decl,type,
sk444: $o ).
thf(sk445_decl,type,
sk445: $i ).
thf(sk446_decl,type,
sk446: $i ).
thf(sk454_decl,type,
sk454: $i ).
thf(sk467_decl,type,
sk467: $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 @ v14_lattices )
=> ( A @ k6_lattices @ ( B @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k2_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
=> ( ( sk1 @ v14_lattices )
=> ( sk1 @ k6_lattices @ ( A @ ( sk1 @ k22_filter_2 ) ) @ ( A @ ( sk1 @ k2_filter_2 ) @ ( sk1 @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i,D: $i,E: $i] :
@+[F: $i] :
~ ( ( E @ ( F @ m1_subset_1 ) )
=> ~ ( ( A
= ( F @ ( B @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ k1_binop_1 ) ) )
= D ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( A @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( E @ ( D @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( C @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk8 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ( ( A @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( ( D @ ( A @ k1_funct_1 ) )
= C )
=> ( ( C @ ( B @ k1_funct_1 ) )
= D ) )
& ( ( ( C @ ( B @ k1_funct_1 ) )
= D )
=> ( ( D @ ( A @ k1_funct_1 ) )
= C ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( B @ ( A @ sk10 ) @ r2_hidden ) ) )
=> ( ( ( ( C @ ( A @ k1_funct_1 ) )
= ( B @ ( A @ sk10 ) ) )
=> ( ( B @ ( A @ sk10 ) @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( ( B @ ( A @ sk10 ) @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( B @ ( A @ sk10 ) ) ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( A @ k1_binop_1 ) ) )
= C ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ~ ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= A )
& ( ( A @ sk18 @ k1_relat_1 )
= A ) )
=> ( ( A @ sk18 )
= B ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A
= ( C @ k1_relat_1 ) ) ) ) ) ) ).
thf(sk71_def,definition,
( sk71
= ( @+[A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk80_def,definition,
( sk80
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ~ ? [C: $i] :
( ~ ? [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk81_def,definition,
( sk81
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( B @ sk80 @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk94_def,definition,
( sk94
= ( @+[A: $i] :
( ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk95_def,definition,
( sk95
= ( @+[A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk110_def,definition,
( sk110
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).
thf(sk111_def,definition,
( sk111
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).
thf(sk118_def,definition,
( sk118
= ( @+[A: $i] :
( ( A @ v1_lattice2 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk138_def,definition,
( sk138
= ( @+[A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk152_def,definition,
( sk152
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk157_def,definition,
( sk157
= ( @+[A: $i] :
( ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v12_lattices )
& ( A @ v11_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk187_def,definition,
( sk187
= ( @+[A: $i] :
( ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk188_def,definition,
( sk188
= ( @+[A: $i] :
( ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk195_def,definition,
( sk195
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk196_def,definition,
( sk196
= ( @+[A: $i] :
( ( A @ v16_lattices )
& ( A @ v15_lattices )
& ( A @ v14_lattices )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk197_def,definition,
( sk197
= ( @+[A: $i] :
( ( A @ v1_lattice2 )
& ( A @ v3_filter_0 )
& ( A @ v13_lattices )
& ( A @ v10_lattices )
& ( A @ v9_lattices )
& ( A @ v8_lattices )
& ( A @ v7_lattices )
& ( A @ v6_lattices )
& ( A @ v5_lattices )
& ( A @ v4_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk207_def,definition,
( sk207
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk216_def,definition,
( sk216
= ( @+[A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ) ) ) ).
thf(sk218_def,definition,
( sk218
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(sk235_def,definition,
( sk235
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk236_def,definition,
( sk236
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ r2_hidden ) ) ) ) ) ).
thf(sk251_def,definition,
( sk251
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk279_def,definition,
( sk279
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ) ) ) ).
thf(sk295_def,definition,
( sk295
= ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).
thf(sk299_def,definition,
( sk299
= ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).
thf(sk313_def,definition,
( sk313
= ( @+[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(sk315_def,definition,
( sk315
= ( @+[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(sk330_def,definition,
( sk330
= ( @+[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(sk331_def,definition,
( sk331
= ( @+[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(sk338_def,definition,
( sk338
= ( @+[A: $i] :
~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).
thf(sk339_def,definition,
( sk339
= ( @+[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(sk341_def,definition,
( sk341
= ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).
thf(sk344_def,definition,
( sk344
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk346_def,definition,
( sk346
= ( @+[A: $i] :
~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).
thf(sk347_def,definition,
( sk347
= ( @+[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(sk349_def,definition,
( sk349
= ( ^ [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(sk357_def,definition,
( sk357
= ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).
thf(sk358_def,definition,
( sk358
= ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).
thf(sk361_def,definition,
( sk361
= ( @+[A: $i] :
~ ( A @ v1_xboole_0 ) ) ) ).
thf(sk366_def,definition,
( sk366
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
=> ( C = B ) ) ) ) ).
thf(sk367_def,definition,
( sk367
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk373_def,definition,
( sk373
= ( @+[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(sk374_def,definition,
( sk374
= ( @+[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(sk384_def,definition,
( sk384
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).
thf(sk402_def,definition,
( sk402
= ( @+[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(sk417_def,definition,
( sk417
= ( @+[A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ) ) ) ).
thf(sk445_def,definition,
( sk445
= ( @+[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(sk446_def,definition,
( sk446
= ( @+[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(sk454_def,definition,
( sk454
= ( @+[A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ) ) ) ).
thf(sk467_def,definition,
( sk467
= ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',t2_funct_1) ).
thf(2163,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)],[193]) ).
thf(749,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5384,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(5385,plain,
! [A: $i] : ( A @ ( A @ sk384 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[5384]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',rc12_lattices) ).
thf(3053,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)],[322]) ).
thf(1015,axiom,
! [A: $i] :
( ( ( A @ l1_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(6530,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)],[1015]) ).
thf(380,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_domain_1) ).
thf(3399,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(447,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(3795,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)],[447]) ).
thf(3796,plain,
! [A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk251 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[3795]) ).
thf(3798,plain,
! [A: $i] : ( A @ sk251 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3796]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',cc2_lattice2) ).
thf(3434,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)],[387]) ).
thf(515,axiom,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(4166,plain,
! [A: $i] :
( ( A @ l1_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
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/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(1586,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(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/sandbox/benchmark/theBenchmark.p',t15_relat_1) ).
thf(1501,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(234,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(2452,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)],[234]) ).
thf(569,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/sandbox/benchmark/theBenchmark.p',t36_lattice2) ).
thf(4447,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)],[569]) ).
thf(477,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/sandbox/benchmark/theBenchmark.p',t49_lattice4) ).
thf(3962,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)],[477]) ).
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/sandbox/benchmark/theBenchmark.p',t50_funct_2) ).
thf(1718,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(167,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(2043,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)],[167]) ).
thf(2044,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(cnf,[status(esa)],[2043]) ).
thf(2045,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
= ( A @ k1_tarski @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[2044]) ).
thf(261,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(2656,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(2657,plain,
( ( sk152 @ v1_relat_1 )
& ( sk152 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2656]) ).
thf(2658,plain,
sk152 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[2657]) ).
thf(610,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(4625,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(4626,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4625]) ).
thf(4627,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[4626]) ).
thf(10157,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,4627]) ).
thf(10158,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10157]) ).
thf(10163,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk152 ),
inference(simp,[status(thm)],[10158]) ).
thf(24714,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)],[2045,10163]) ).
thf(24715,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk152 ),
inference(pattern_uni,[status(thm)],[24714:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(24747,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk152 ),
inference(simp,[status(thm)],[24715]) ).
thf(771,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/sandbox/benchmark/theBenchmark.p',t41_lattices) ).
thf(5469,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)],[771]) ).
thf(986,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/sandbox/benchmark/theBenchmark.p',t31_lattices) ).
thf(6387,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)],[986]) ).
thf(462,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/sandbox/benchmark/theBenchmark.p',t20_lattice4) ).
thf(3883,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)],[462]) ).
thf(693,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/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
thf(5116,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)],[693]) ).
thf(931,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/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(6167,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)],[931]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',t66_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 @ v14_lattices )
=> ( A @ k6_lattices @ ( B @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k2_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1019,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)],[2]) ).
thf(1020,plain,
( ~ ( sk1 @ k6_lattices @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk2 @ ( sk1 @ k2_filter_2 ) @ ( sk1 @ u1_struct_0 @ r1_filter_2 ) ) )
& ( sk1 @ v14_lattices )
& ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
& ( sk1 @ l3_lattices )
& ( sk1 @ v10_lattices )
& ~ ( sk1 @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[1019]) ).
thf(1024,plain,
~ ( sk1 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[1020]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',rc10_lattices) ).
thf(2731,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)],[281]) ).
thf(2732,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)],[2731]) ).
thf(2744,plain,
sk157 @ v5_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(548,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4334,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(4335,plain,
sk295 @ v1_xboole_0,
inference(cnf,[status(esa)],[4334]) ).
thf(851,axiom,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(5827,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(5828,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[5827]) ).
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/sandbox/benchmark/theBenchmark.p',t5_realset1) ).
thf(1216,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(1217,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)],[1216]) ).
thf(1219,plain,
! [A: $i] :
( ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ ( sk14 @ ( A @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[1217]) ).
thf(40939,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)],[5828,1219]) ).
thf(40940,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[40939]) ).
thf(40941,plain,
~ ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[40940:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ k8_subset_1 ))]]) ).
thf(41150,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,40941]) ).
thf(41151,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41150]) ).
thf(41159,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk295 ),
inference(simp,[status(thm)],[41151]) ).
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/sandbox/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(1188,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(1189,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)],[1188]) ).
thf(1190,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)],[1189]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(2336,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)],[214]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).
thf(3008,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)],[312]) ).
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/sandbox/benchmark/theBenchmark.p',t19_relat_1) ).
thf(1454,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(171,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2071,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(2072,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(cnf,[status(esa)],[2071]) ).
thf(425,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).
thf(3661,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)],[425]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',rc1_lattice2) ).
thf(2412,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)],[227]) ).
thf(292,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/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).
thf(2876,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)],[292]) ).
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/sandbox/benchmark/theBenchmark.p',t157_funct_1) ).
thf(1236,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(1237,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ~ ( C @ v2_funct_1 )
| ~ ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
| ~ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1236]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(4183,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)],[520]) ).
thf(299,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/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).
thf(2921,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)],[299]) ).
thf(751,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/sandbox/benchmark/theBenchmark.p',t24_lattice2) ).
thf(5390,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)],[751]) ).
thf(955,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/sandbox/benchmark/theBenchmark.p',t40_lattice4) ).
thf(6285,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [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)],[955]) ).
thf(812,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/sandbox/benchmark/theBenchmark.p',d6_lattice4) ).
thf(5654,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)],[812]) ).
thf(965,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(6317,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)],[965]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_partfun1) ).
thf(2499,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)],[239]) ).
thf(710,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/sandbox/benchmark/theBenchmark.p',t51_filter_2) ).
thf(5205,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)],[710]) ).
thf(912,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/sandbox/benchmark/theBenchmark.p',t15_lattice4) ).
thf(6074,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)],[912]) ).
thf(246,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(2540,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(2541,plain,
( ( sk138 @ v2_funct_1 )
& ( sk138 @ v1_funct_1 )
& ( sk138 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[2540]) ).
thf(2544,plain,
sk138 @ v2_funct_1,
inference(cnfConj,[status(thm)],[2541]) ).
thf(606,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/sandbox/benchmark/theBenchmark.p',s4_funct_2) ).
thf(4609,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)],[606]) ).
thf(4610,plain,
! [A: $i] :
( ( ( ( A @ ( sk313 @ ( 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 @ ( sk313 @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ v1_funct_2 ) ) )
& ( sk313 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[4609]) ).
thf(4613,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ),
inference(cnfConj,[status(thm)],[4610]) ).
thf(349,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(3205,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(3206,plain,
( ( sk207 @ v1_funct_1 )
& ( sk207 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3205]) ).
thf(3208,plain,
sk207 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3206]) ).
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/sandbox/benchmark/theBenchmark.p',t99_partfun1) ).
thf(1051,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(1052,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)],[1051]) ).
thf(1053,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)],[1052]) ).
thf(1054,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)],[1053]) ).
thf(1021,plain,
sk1 @ v10_lattices,
inference(cnfConj,[status(thm)],[1020]) ).
thf(6760,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)],[1054,1021]) ).
thf(6761,plain,
! [A: $i] :
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6760:[bind(A,$thf( sk1 ))]]) ).
thf(7019,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)],[6761]) ).
thf(8528,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)],[3208,7019]) ).
thf(8529,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8528]) ).
thf(8530,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8529:[bind(A,$thf( sk207 ))]]) ).
thf(12281,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,8530]) ).
thf(12282,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12281]) ).
thf(12383,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12282]) ).
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/sandbox/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(1178,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(1179,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)],[1178]) ).
thf(831,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/sandbox/benchmark/theBenchmark.p',t49_lattices) ).
thf(5733,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)],[831]) ).
thf(367,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(3312,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(3313,plain,
( ( sk216 @ v1_funct_1 )
& ( sk216 @ v1_xboole_0 )
& ( sk216 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[3312]) ).
thf(3315,plain,
sk216 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[3313]) ).
thf(713,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(5224,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(5225,plain,
~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5224]) ).
thf(5226,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5225]) ).
thf(8751,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,5226]) ).
thf(8752,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8751]) ).
thf(8755,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk216 ),
inference(simp,[status(thm)],[8752]) ).
thf(896,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/sandbox/benchmark/theBenchmark.p',t12_filter_0) ).
thf(6014,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)],[896]) ).
thf(797,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/sandbox/benchmark/theBenchmark.p',d5_lattice4) ).
thf(5582,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)],[797]) ).
thf(146,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).
thf(1950,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(982,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/sandbox/benchmark/theBenchmark.p',t6_filter_0) ).
thf(6374,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)],[982]) ).
thf(207,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/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).
thf(2280,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)],[207]) ).
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/sandbox/benchmark/theBenchmark.p',t55_funct_2) ).
thf(1110,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(368,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/sandbox/benchmark/theBenchmark.p',d17_binop_1) ).
thf(3317,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)],[368]) ).
thf(562,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4391,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',rc11_lattices) ).
thf(2939,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)],[302]) ).
thf(2940,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)],[2939]) ).
thf(2947,plain,
~ ( sk187 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2940]) ).
thf(707,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/sandbox/benchmark/theBenchmark.p',t45_filter_0) ).
thf(5173,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)],[707]) ).
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/sandbox/benchmark/theBenchmark.p',t3_realset1) ).
thf(1138,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(1139,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)],[1138]) ).
thf(1142,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)],[1139]) ).
thf(722,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/sandbox/benchmark/theBenchmark.p',t49_lattice2) ).
thf(5265,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)],[722]) ).
thf(897,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/sandbox/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(6017,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)],[897]) ).
thf(218,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(2360,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)],[218]) ).
thf(2361,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)],[2360]) ).
thf(2363,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2361]) ).
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/sandbox/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(1198,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(1199,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)],[1198]) ).
thf(1200,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)],[1199]) ).
thf(765,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/sandbox/benchmark/theBenchmark.p',t14_filter_2) ).
thf(5444,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)],[765]) ).
thf(663,axiom,
? [A: $i] : ( A @ l1_lattices ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(4931,plain,
? [A: $i] : ( A @ l1_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(4611,plain,
sk313 @ v1_funct_1,
inference(cnfConj,[status(thm)],[4610]) ).
thf(6730,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)],[1054,1024]) ).
thf(6731,plain,
! [A: $i] :
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6730:[bind(A,$thf( sk1 ))]]) ).
thf(7004,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)],[6731]) ).
thf(9045,plain,
! [A: $i] :
( ( ( sk313 @ 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)],[4611,7004]) ).
thf(9046,plain,
! [A: $i] :
( ( ( sk313 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9045]) ).
thf(9047,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9046:[bind(A,$thf( sk313 ))]]) ).
thf(12330,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,9047]) ).
thf(12331,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12330]) ).
thf(12413,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk313 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12331]) ).
thf(12458,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12413]) ).
thf(908,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).
thf(6057,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)],[908]) ).
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/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
thf(1288,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(1289,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)],[1288]) ).
thf(1290,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1289]) ).
thf(1298,plain,
! [A: $i] :
( ( A @ sk18 @ v1_relat_1 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1290]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(3114,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)],[330]) ).
thf(3115,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)],[3114]) ).
thf(3116,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)],[3115]) ).
thf(3118,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3116]) ).
thf(3120,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3118]) ).
thf(3121,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[3120]) ).
thf(41096,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)],[3121,40941]) ).
thf(41097,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41096]) ).
thf(41156,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[41097]) ).
thf(42660,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)],[1298,41156]) ).
thf(42661,plain,
! [A: $i] :
( ( A
!= ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[42660]) ).
thf(42662,plain,
sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[42661:[bind(A,$thf( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ))]]) ).
thf(485,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/sandbox/benchmark/theBenchmark.p',t66_lattice2) ).
thf(3990,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)],[485]) ).
thf(494,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(4037,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(558,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/sandbox/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(4376,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)],[558]) ).
thf(323,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/sandbox/benchmark/theBenchmark.p',rc2_lattice2) ).
thf(3069,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)],[323]) ).
thf(3070,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)],[3069]) ).
thf(3072,plain,
sk197 @ v6_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
thf(150,axiom,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(1970,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(1971,plain,
( ( sk71 @ v1_xboole_0 )
& ( sk71 @ v2_funct_1 )
& ( sk71 @ v1_funct_1 )
& ( sk71 @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1970]) ).
thf(1975,plain,
sk71 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[1971]) ).
thf(40848,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk384 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5385,1219]) ).
thf(40849,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk384 @ m1_subset_1 ) )
!= ( sk14 @ ( B @ m1_subset_1 ) ) )
| ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[40848]) ).
thf(40850,plain,
~ ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[40849:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ sk384 ))]]) ).
thf(41033,plain,
( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,40850]) ).
thf(41034,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41033]) ).
thf(41081,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk71 ),
inference(simp,[status(thm)],[41034]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).
thf(2204,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)],[196]) ).
thf(2205,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)],[2204]) ).
thf(2210,plain,
sk94 @ l3_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
thf(933,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/sandbox/benchmark/theBenchmark.p',t55_filter_0) ).
thf(6177,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)],[933]) ).
thf(179,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(2104,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(828,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/sandbox/benchmark/theBenchmark.p',d11_lattices) ).
thf(5718,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)],[828]) ).
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/sandbox/benchmark/theBenchmark.p',t9_relset_1) ).
thf(1064,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(1065,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)],[1064]) ).
thf(1973,plain,
sk71 @ v1_funct_1,
inference(cnfConj,[status(thm)],[1971]) ).
thf(7128,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)],[1973,7004]) ).
thf(7129,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7128]) ).
thf(7130,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7129:[bind(A,$thf( sk71 ))]]) ).
thf(7656,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)],[1065,7130]) ).
thf(7657,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)],[7656]) ).
thf(7684,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)],[7657]) ).
thf(7694,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)],[7684]) ).
thf(1972,plain,
sk71 @ v1_relat_1,
inference(cnfConj,[status(thm)],[1971]) ).
thf(11053,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)],[7694,1972]) ).
thf(11054,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)],[11053]) ).
thf(12977,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2072,11054]) ).
thf(12978,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)],[12977]) ).
thf(12995,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)],[12978]) ).
thf(13007,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)],[12995]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',fc5_lattice2) ).
thf(2231,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)],[200]) ).
thf(1007,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lattice2) ).
thf(6495,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(469,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/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(3905,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)],[469]) ).
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/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
thf(1128,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(1129,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)],[1128]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[1129]) ).
thf(14115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,1130]) ).
thf(14116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14115]) ).
thf(14117,plain,
f1_s4_funct_2 @ ( sk313 @ k1_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[14116:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk313 ))]]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',d14_binop_1) ).
thf(2381,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)],[221]) ).
thf(203,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(2267,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(2268,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(cnf,[status(esa)],[2267]) ).
thf(15146,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)],[2268,8530]) ).
thf(15147,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)],[15146]) ).
thf(15244,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)],[15147]) ).
thf(15267,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15244]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(5069,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)],[681]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',t85_funct_2) ).
thf(2908,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)],[295]) ).
thf(408,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/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(3549,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)],[408]) ).
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/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(1808,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(2659,plain,
sk152 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2657]) ).
thf(2953,plain,
sk187 @ v7_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(728,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/sandbox/benchmark/theBenchmark.p',t29_filter_0) ).
thf(5297,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)],[728]) ).
thf(3316,plain,
sk216 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3313]) ).
thf(1026,plain,
sk1 @ v14_lattices,
inference(cnfConj,[status(thm)],[1020]) ).
thf(6820,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v14_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)],[1054,1026]) ).
thf(6821,plain,
! [A: $i] :
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6820:[bind(A,$thf( sk1 ))]]) ).
thf(7047,plain,
! [A: $i] :
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(simp,[status(thm)],[6821]) ).
thf(8772,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3316,7047]) ).
thf(8773,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8772]) ).
thf(8774,plain,
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8773:[bind(A,$thf( sk216 ))]]) ).
thf(12267,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,8774]) ).
thf(12268,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12267]) ).
thf(12371,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[12268]) ).
thf(471,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/sandbox/benchmark/theBenchmark.p',t61_filter_2) ).
thf(3912,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)],[471]) ).
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/sandbox/benchmark/theBenchmark.p',t152_relat_1) ).
thf(1073,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(807,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/sandbox/benchmark/theBenchmark.p',t8_lattice4) ).
thf(5625,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)],[807]) ).
thf(666,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(4957,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(4958,plain,
( ( sk344 @ v3_lattices )
& ( sk344 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4957]) ).
thf(4960,plain,
sk344 @ v3_lattices,
inference(cnfConj,[status(thm)],[4958]) ).
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/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
thf(1728,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(973,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/sandbox/benchmark/theBenchmark.p',d7_lattice4) ).
thf(6338,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)],[973]) ).
thf(891,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/sandbox/benchmark/theBenchmark.p',dt_k1_lattice4) ).
thf(5982,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)],[891]) ).
thf(314,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/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(3012,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)],[314]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1203,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(1204,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1203]) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1204]) ).
thf(381,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/sandbox/benchmark/theBenchmark.p',t156_relat_1) ).
thf(3402,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)],[381]) ).
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/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(1533,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(822,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/sandbox/benchmark/theBenchmark.p',t24_filter_2) ).
thf(5691,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)],[822]) ).
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/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(1793,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(609,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/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(4623,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)],[609]) ).
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 ) )
=> ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
= ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_filter_0) ).
thf(6031,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)],[901]) ).
thf(341,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(3166,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(3167,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3166]) ).
thf(3169,plain,
k1_xboole_0 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3167]) ).
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/sandbox/benchmark/theBenchmark.p',t147_relat_1) ).
thf(1049,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(1050,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)],[1049]) ).
thf(8220,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)],[3169,1050]) ).
thf(8221,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)],[8220]) ).
thf(8222,plain,
! [A: $i] : ( k1_xboole_0 @ k1_relat_1 @ ( k1_xboole_0 @ k9_relat_1 ) @ ( A @ ( k1_xboole_0 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8221:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(331,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(3122,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(3123,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3122]) ).
thf(3124,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3123]) ).
thf(21834,plain,
k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ),
inference(rewrite,[status(thm)],[8222,3124]) ).
thf(805,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/sandbox/benchmark/theBenchmark.p',d8_lattices) ).
thf(5614,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)],[805]) ).
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/sandbox/benchmark/theBenchmark.p',t132_funct_2) ).
thf(1437,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(1131,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
inference(cnfConj,[status(thm)],[1129]) ).
thf(14429,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,1131]) ).
thf(14430,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14429]) ).
thf(14431,plain,
f2_s4_funct_2 @ ( sk313 @ k2_relat_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[14430:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk313 ))]]) ).
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/sandbox/benchmark/theBenchmark.p',t60_funct_1) ).
thf(1164,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(1165,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)],[1164]) ).
thf(1169,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)],[1165]) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ~ ( A @ v2_funct_1 )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 )
| ( B
= ( A @ k2_funct_1 ) )
| ( ( A @ ( B @ sk11 ) )
!= ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) ) )
| ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
!= ( A @ ( B @ sk10 ) ) )
| ( ( A @ k2_relat_1 )
!= ( B @ k1_relat_1 ) )
| ( ( A @ k1_relat_1 )
!= ( B @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1169]) ).
thf(590,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/sandbox/benchmark/theBenchmark.p',t30_partfun1) ).
thf(4532,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)],[590]) ).
thf(958,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/sandbox/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(6295,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)],[958]) ).
thf(799,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/sandbox/benchmark/theBenchmark.p',s11_funct_2) ).
thf(5589,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)],[799]) ).
thf(332,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(3125,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(3126,plain,
~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[3125]) ).
thf(3127,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[3126]) ).
thf(8138,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,3127]) ).
thf(8139,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8138]) ).
thf(8150,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8139]) ).
thf(616,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/sandbox/benchmark/theBenchmark.p',rc13_lattices) ).
thf(4644,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)],[616]) ).
thf(4645,plain,
( ( sk315 @ v17_lattices )
& ( sk315 @ v16_lattices )
& ( sk315 @ v15_lattices )
& ( sk315 @ v14_lattices )
& ( sk315 @ v13_lattices )
& ( sk315 @ v11_lattices )
& ( sk315 @ v10_lattices )
& ( sk315 @ v9_lattices )
& ( sk315 @ v8_lattices )
& ( sk315 @ v7_lattices )
& ( sk315 @ v6_lattices )
& ( sk315 @ v5_lattices )
& ( sk315 @ v4_lattices )
& ( sk315 @ v3_lattices )
& ~ ( sk315 @ v3_struct_0 )
& ( sk315 @ l3_lattices ) ),
inference(cnf,[status(esa)],[4644]) ).
thf(4647,plain,
sk315 @ v8_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(7429,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1973,7047]) ).
thf(7430,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7429]) ).
thf(7431,plain,
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7430:[bind(A,$thf( sk71 ))]]) ).
thf(7626,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 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1065,7431]) ).
thf(7627,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 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7626]) ).
thf(7682,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[7627]) ).
thf(7692,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk71 @ v1_relat_1 )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[7682]) ).
thf(11013,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ v14_lattices ) ),
inference(rewrite,[status(thm)],[7692,1972]) ).
thf(11014,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[11013]) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',fc1_nat_lat) ).
thf(3173,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)],[343]) ).
thf(3174,plain,
( ( k6_nat_lat @ v10_lattices )
& ( k6_nat_lat @ v9_lattices )
& ( k6_nat_lat @ v8_lattices )
& ( k6_nat_lat @ v7_lattices )
& ( k6_nat_lat @ v6_lattices )
& ( k6_nat_lat @ v5_lattices )
& ( k6_nat_lat @ v4_lattices )
& ( k6_nat_lat @ v3_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[3173]) ).
thf(3175,plain,
~ ( k6_nat_lat @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3174]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(2141,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(598,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/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(4564,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)],[598]) ).
thf(316,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/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(3017,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)],[316]) ).
thf(886,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/sandbox/benchmark/theBenchmark.p',d9_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 ) ) )
=> ( ( ! [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)],[886]) ).
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/sandbox/benchmark/theBenchmark.p',t82_funct_2) ).
thf(1076,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(1077,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)],[1076]) ).
thf(1078,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)],[1077]) ).
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/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(1426,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(1009,axiom,
? [A: $i] : ( A @ l3_lattices ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(6504,plain,
? [A: $i] : ( A @ l3_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(6505,plain,
sk467 @ l3_lattices,
inference(cnf,[status(esa)],[6504]) ).
thf(386,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/sandbox/benchmark/theBenchmark.p',d8_realset1) ).
thf(3429,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)],[386]) ).
thf(794,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/sandbox/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(5565,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)],[794]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(1135,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(1136,plain,
! [A: $i] :
( ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) )
| ~ ( A @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1135]) ).
thf(1137,plain,
! [A: $i] :
( ~ ( A @ v1_relat_1 )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(lifteq,[status(thm)],[1136]) ).
thf(334,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/sandbox/benchmark/theBenchmark.p',t172_partfun1) ).
thf(3135,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)],[334]) ).
thf(489,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [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/sandbox/benchmark/theBenchmark.p',t47_lattice2) ).
thf(4011,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)],[489]) ).
thf(8522,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)],[3208,7004]) ).
thf(8523,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8522]) ).
thf(8524,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8523:[bind(A,$thf( sk207 ))]]) ).
thf(15200,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)],[2268,8524]) ).
thf(15201,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)],[15200]) ).
thf(15241,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)],[15201]) ).
thf(15263,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15241]) ).
thf(4038,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[4037]) ).
thf(4039,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[4038]) ).
thf(7550,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,4039]) ).
thf(7551,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7550]) ).
thf(7556,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk71 ),
inference(simp,[status(thm)],[7551]) ).
thf(653,axiom,
k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_nat_lat) ).
thf(4870,plain,
k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(2740,plain,
sk157 @ v9_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(29419,plain,
! [A: $i] :
( ( A != sk315 )
| ( k1_xboole_0 @ v8_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,4647]) ).
thf(29420,plain,
( ( k1_xboole_0 @ v8_lattices )
| ( sk315 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29419:[bind(A,$thf( sk315 ))]]) ).
thf(917,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ 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/sandbox/benchmark/theBenchmark.p',t7_filter_0) ).
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 ) )
=> ! [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)],[917]) ).
thf(300,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/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(2933,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)],[300]) ).
thf(4650,plain,
sk315 @ v11_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(826,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_0 )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_0) ).
thf(5713,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)],[826]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',fc3_nat_lat) ).
thf(2468,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)],[237]) ).
thf(2469,plain,
( ( k13_nat_lat @ v10_lattices )
& ( k13_nat_lat @ v9_lattices )
& ( k13_nat_lat @ v8_lattices )
& ( k13_nat_lat @ v7_lattices )
& ( k13_nat_lat @ v6_lattices )
& ( k13_nat_lat @ v5_lattices )
& ( k13_nat_lat @ v4_lattices )
& ( k13_nat_lat @ v3_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[2468]) ).
thf(2476,plain,
k13_nat_lat @ v9_lattices,
inference(cnfConj,[status(thm)],[2469]) ).
thf(817,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/sandbox/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(5674,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)],[817]) ).
thf(356,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/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(3253,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)],[356]) ).
thf(235,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/sandbox/benchmark/theBenchmark.p',fc2_lattice2) ).
thf(2459,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)],[235]) ).
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/sandbox/benchmark/theBenchmark.p',t155_relat_1) ).
thf(1342,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(673,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/sandbox/benchmark/theBenchmark.p',t5_lattice4) ).
thf(5005,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)],[673]) ).
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/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(1640,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(1022,plain,
sk1 @ l3_lattices,
inference(cnfConj,[status(thm)],[1020]) ).
thf(6862,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)],[1054,1022]) ).
thf(6863,plain,
! [A: $i] :
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 ) ),
inference(pattern_uni,[status(thm)],[6862:[bind(A,$thf( sk1 ))]]) ).
thf(7068,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)],[6863]) ).
thf(19,axiom,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(1104,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(1105,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1104]) ).
thf(1106,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[1105]) ).
thf(1108,plain,
( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1106]) ).
thf(1107,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(cnfConj,[status(thm)],[1105]) ).
thf(1109,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1107]) ).
thf(2543,plain,
sk138 @ v1_funct_1,
inference(cnfConj,[status(thm)],[2541]) ).
thf(7250,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)],[2543,7019]) ).
thf(7251,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7250]) ).
thf(7252,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7251:[bind(A,$thf( sk138 ))]]) ).
thf(7674,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1065,7252]) ).
thf(7675,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7674]) ).
thf(7681,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7675]) ).
thf(7690,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk138 @ v1_relat_1 )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[7681]) ).
thf(2542,plain,
sk138 @ v1_relat_1,
inference(cnfConj,[status(thm)],[2541]) ).
thf(10214,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[7690,2542]) ).
thf(10215,plain,
( ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[10214]) ).
thf(11579,plain,
( ( ( sk138 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[1109,10215]) ).
thf(11580,plain,
( ( ( sk138 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11579]) ).
thf(11601,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[11580]) ).
thf(13620,plain,
( ( ( sk138 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[1108,11601]) ).
thf(13623,plain,
( ( sk138 != k1_xboole_0 )
| ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13620]) ).
thf(13635,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13623]) ).
thf(13639,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(rewrite,[status(thm)],[13635,2072]) ).
thf(13640,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[13639]) ).
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/sandbox/benchmark/theBenchmark.p',t10_relset_1) ).
thf(1062,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(1063,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)],[1062]) ).
thf(7131,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)],[2543,7004]) ).
thf(7132,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7131]) ).
thf(7133,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7132:[bind(A,$thf( sk138 ))]]) ).
thf(7488,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)],[1063,7133]) ).
thf(7489,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)],[7488]) ).
thf(7519,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)],[7489]) ).
thf(7537,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)],[7519]) ).
thf(9800,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)],[7537,2542]) ).
thf(9801,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)],[9800]) ).
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/sandbox/benchmark/theBenchmark.p',t9_realset1) ).
thf(1954,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(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/sandbox/benchmark/theBenchmark.p',t28_binop_1) ).
thf(1354,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(188,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/sandbox/benchmark/theBenchmark.p',t168_funct_2) ).
thf(2146,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)],[188]) ).
thf(669,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/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(4980,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)],[669]) ).
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/sandbox/benchmark/theBenchmark.p',t2_lattice2) ).
thf(1220,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(1221,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)],[1220]) ).
thf(1222,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)],[1221]) ).
thf(29391,plain,
! [A: $i] :
( ( A != sk94 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,2210]) ).
thf(29392,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk94 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29391:[bind(A,$thf( sk94 ))]]) ).
thf(904,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/sandbox/benchmark/theBenchmark.p',redefinition_k13_filter_2) ).
thf(6046,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)],[904]) ).
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/sandbox/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(1093,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(1094,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)],[1093]) ).
thf(1095,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)],[1094]) ).
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/sandbox/benchmark/theBenchmark.p',t118_funct_1) ).
thf(1914,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(398,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(3502,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)],[398]) ).
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/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(1391,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(875,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/sandbox/benchmark/theBenchmark.p',t64_filter_0) ).
thf(5921,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)],[875]) ).
thf(730,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/sandbox/benchmark/theBenchmark.p',t25_lattices) ).
thf(5301,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)],[730]) ).
thf(865,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(5872,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(5873,plain,
( ~ ( sk417 @ v3_struct_0 )
& ( sk417 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[5872]) ).
thf(5874,plain,
sk417 @ l2_struct_0,
inference(cnfConj,[status(thm)],[5873]) ).
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/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
thf(1223,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(1224,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)],[1223]) ).
thf(1225,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)],[1224]) ).
thf(1227,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)],[1225]) ).
thf(1228,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)],[1227]) ).
thf(303,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/sandbox/benchmark/theBenchmark.p',rc1_filter_0) ).
thf(2954,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)],[303]) ).
thf(2955,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)],[2954]) ).
thf(2957,plain,
sk188 @ v3_filter_0,
inference(cnfConj,[status(thm)],[2955]) ).
thf(371,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/sandbox/benchmark/theBenchmark.p',t43_funct_2) ).
thf(3335,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)],[371]) ).
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/sandbox/benchmark/theBenchmark.p',d4_binop_1) ).
thf(1191,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(1192,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)],[1191]) ).
thf(1193,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)],[1192]) ).
thf(1196,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)],[1193]) ).
thf(369,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(3324,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(3325,plain,
( ( sk218 @ v1_relat_1 )
& ~ ( sk218 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[3324]) ).
thf(3327,plain,
sk218 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3325]) ).
thf(8832,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)],[3327,1050]) ).
thf(8833,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)],[8832]) ).
thf(8834,plain,
! [A: $i] : ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8833:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).
thf(15564,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)],[3327,1137]) ).
thf(15565,plain,
! [A: $i] :
( ( ( sk218 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15564]) ).
thf(15566,plain,
( ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) )
= ( sk218 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15565:[bind(A,$thf( sk218 ))]]) ).
thf(22379,plain,
! [A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[8834,15566]) ).
thf(942,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/sandbox/benchmark/theBenchmark.p',s4_subset_1) ).
thf(6220,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)],[942]) ).
thf(6221,plain,
( ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk446 @ r2_hidden ) )
| ~ ( sk446 @ p1_s4_subset_1 )
| sk444 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk446 @ p1_s4_subset_1 )
| ~ ( sk446 @ p1_s4_subset_1 )
| sk444 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ ( f3_s4_subset_1 @ ( sk446 @ r2_hidden ) )
| ( f3_s4_subset_1 @ ( sk446 @ r2_hidden ) )
| sk444 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk446 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk446 @ r2_hidden ) )
| sk444 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk446 @ m1_subset_1 ) )
| sk444 )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk444
| ~ ( f2_s4_subset_1 @ ( sk445 @ r2_hidden ) )
| ~ ( sk445 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk444
| ( sk445 @ p1_s4_subset_1 )
| ~ ( sk445 @ p1_s4_subset_1 ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk444
| ~ ( f2_s4_subset_1 @ ( sk445 @ r2_hidden ) )
| ( f2_s4_subset_1 @ ( sk445 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk444
| ( sk445 @ p1_s4_subset_1 )
| ( f2_s4_subset_1 @ ( sk445 @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ~ sk444
| ( f1_s4_subset_1 @ ( sk445 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[6220]) ).
thf(6229,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( f1_s4_subset_1 @ ( sk446 @ m1_subset_1 ) )
| sk444 ),
inference(cnfConj,[status(thm)],[6221]) ).
thf(6236,plain,
( ( f1_s4_subset_1 @ ( sk446 @ m1_subset_1 ) )
| sk444
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[6229]) ).
thf(642,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/sandbox/benchmark/theBenchmark.p',t85_filter_0) ).
thf(4792,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)],[642]) ).
thf(197,axiom,
? [A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_struct_0) ).
thf(2216,plain,
? [A: $i] :
( ( A @ v2_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(4343,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(714,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/sandbox/benchmark/theBenchmark.p',t18_lattices) ).
thf(5227,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)],[714]) ).
thf(1001,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k7_lattices ) )
= ( B @ ( A @ k7_lattices ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l70_filter_2) ).
thf(6466,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k7_lattices ) )
= ( B @ ( A @ k7_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(833,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/sandbox/benchmark/theBenchmark.p',t50_lattices) ).
thf(5740,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)],[833]) ).
thf(407,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/sandbox/benchmark/theBenchmark.p',t38_lattice4) ).
thf(3545,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)],[407]) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',t17_funct_2) ).
thf(2972,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)],[306]) ).
thf(509,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/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(4142,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)],[509]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).
thf(2046,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)],[168]) ).
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/sandbox/benchmark/theBenchmark.p',t59_funct_2) ).
thf(1125,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(1126,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)],[1125]) ).
thf(1127,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)],[1126]) ).
thf(951,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/sandbox/benchmark/theBenchmark.p',d7_filter_2) ).
thf(6268,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)],[951]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',t38_funct_2) ).
thf(2548,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)],[248]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(1079,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(1080,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(miniscope,[status(thm)],[1079]) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ ( B @ ( A @ r1_tarski ) ) ),
inference(cnf,[status(esa)],[1080]) ).
thf(22422,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)],[22379,1081]) ).
thf(22423,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)],[22422]) ).
thf(22424,plain,
! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[22423:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk218 @ k9_relat_1 ) )),bind(C,$thf( sk218 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(22461,plain,
! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[22424]) ).
thf(835,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/sandbox/benchmark/theBenchmark.p',t32_filter_2) ).
thf(5745,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)],[835]) ).
thf(701,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5151,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(5152,plain,
~ ! [A: $i] : ( A @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[5151]) ).
thf(5153,plain,
~ ( sk361 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[5152]) ).
thf(9010,plain,
( ( ( sk361 @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,5153]) ).
thf(9011,plain,
( ( sk361 @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9010]) ).
thf(9027,plain,
sk361 != sk295,
inference(simp,[status(thm)],[9011]) ).
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/sandbox/benchmark/theBenchmark.p',t79_funct_2) ).
thf(1046,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(618,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(4665,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)],[618]) ).
thf(14155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk313 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14117,1081]) ).
thf(14156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk313 @ k1_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14155]) ).
thf(14157,plain,
! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14156:[bind(A,$thf( sk313 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14188,plain,
! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14157]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(2136,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)],[185]) ).
thf(837,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/sandbox/benchmark/theBenchmark.p',d8_lattice4) ).
thf(5750,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)],[837]) ).
thf(29571,plain,
! [A: $i] :
( ( A != sk417 )
| ( k1_xboole_0 @ l2_struct_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,5874]) ).
thf(29572,plain,
( ( k1_xboole_0 @ l2_struct_0 )
| ( sk417 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29571:[bind(A,$thf( sk417 ))]]) ).
thf(956,axiom,
( ( k13_nat_lat @ l3_lattices )
& ( k13_nat_lat @ v10_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_nat_lat) ).
thf(6287,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)],[956]) ).
thf(6288,plain,
( ( k13_nat_lat @ l3_lattices )
& ( k13_nat_lat @ v10_lattices )
& ~ ( k13_nat_lat @ v3_struct_0 ) ),
inference(cnf,[status(esa)],[6287]) ).
thf(6291,plain,
k13_nat_lat @ l3_lattices,
inference(cnfConj,[status(thm)],[6288]) ).
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/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(1518,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(243,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/sandbox/benchmark/theBenchmark.p',t14_binop_1) ).
thf(2531,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)],[243]) ).
thf(935,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/sandbox/benchmark/theBenchmark.p',d9_lattices) ).
thf(6182,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)],[935]) ).
thf(15603,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)],[1972,1137]) ).
thf(15604,plain,
! [A: $i] :
( ( ( sk71 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15603]) ).
thf(15605,plain,
( ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) )
= ( sk71 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15604:[bind(A,$thf( sk71 ))]]) ).
thf(639,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/sandbox/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).
thf(4775,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)],[639]) ).
thf(586,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/sandbox/benchmark/theBenchmark.p',d1_filter_0) ).
thf(4511,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)],[586]) ).
thf(533,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/sandbox/benchmark/theBenchmark.p',t34_lattice4) ).
thf(4249,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)],[533]) ).
thf(739,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).
thf(5342,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)],[739]) ).
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/sandbox/benchmark/theBenchmark.p',t23_relat_1) ).
thf(1887,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(614,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/sandbox/benchmark/theBenchmark.p',t6_lattice4) ).
thf(4637,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)],[614]) ).
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/sandbox/benchmark/theBenchmark.p',d3_binop_1) ).
thf(1709,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(8513,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)],[3208,7068]) ).
thf(8514,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8513]) ).
thf(8515,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8514:[bind(A,$thf( sk207 ))]]) ).
thf(276,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).
thf(2708,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)],[276]) ).
thf(1010,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_filter_2) ).
thf(6506,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m2_filter_2 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_filter_2 ) )
=> ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) )
= ( C @ ( B @ ( A @ a_3_1_filter_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(640,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(4778,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)],[640]) ).
thf(230,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(2435,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(2436,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[2435]) ).
thf(2437,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[2436]) ).
thf(8128,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,2437]) ).
thf(8129,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8128]) ).
thf(8146,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8129]) ).
thf(2745,plain,
sk157 @ v12_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',t25_subset_1) ).
thf(2703,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)],[274]) ).
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/sandbox/benchmark/theBenchmark.p',t116_funct_2) ).
thf(1055,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(531,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/sandbox/benchmark/theBenchmark.p',t50_filter_0) ).
thf(4238,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)],[531]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(3255,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)],[357]) ).
thf(3256,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)],[3255]) ).
thf(3257,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)],[3256]) ).
thf(3259,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3257]) ).
thf(3262,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3259]) ).
thf(3263,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3262]) ).
thf(566,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/sandbox/benchmark/theBenchmark.p',t40_funct_2) ).
thf(4439,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)],[566]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(3976,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)],[481]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
thf(2603,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)],[256]) ).
thf(652,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/sandbox/benchmark/theBenchmark.p',t31_partfun1) ).
thf(4866,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)],[652]) ).
thf(943,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/sandbox/benchmark/theBenchmark.p',t23_filter_0) ).
thf(6242,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)],[943]) ).
thf(423,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/sandbox/benchmark/theBenchmark.p',t8_filter_2) ).
thf(3644,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)],[423]) ).
thf(2735,plain,
~ ( sk157 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2732]) ).
thf(11583,plain,
( ( ( sk71 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1109,11054]) ).
thf(11584,plain,
( ( ( sk71 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11583]) ).
thf(11599,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11584]) ).
thf(11919,plain,
( ( ( sk71 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1108,11599]) ).
thf(11922,plain,
( ( sk71 != k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11919]) ).
thf(11930,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[11922]) ).
thf(12942,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[11930,2072]) ).
thf(12943,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12942]) ).
thf(360,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/sandbox/benchmark/theBenchmark.p',t60_domain_1) ).
thf(3275,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)],[360]) ).
thf(902,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v13_lattices )
<=> ( A @ k1_lattice2 @ v14_lattices ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).
thf(6034,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)],[902]) ).
thf(147,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1952,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1953,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[1952]) ).
thf(191,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(2159,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(2160,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[2159]) ).
thf(13428,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1953,2160]) ).
thf(13429,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[13428:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(6710,plain,
! [B: $i,A: $i] :
( ( ( sk152 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,1050]) ).
thf(6711,plain,
! [B: $i,A: $i] :
( ( ( sk152 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[6710]) ).
thf(6712,plain,
! [A: $i] : ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6711:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).
thf(15561,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)],[2659,1137]) ).
thf(15562,plain,
! [A: $i] :
( ( ( sk152 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15561]) ).
thf(15563,plain,
( ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) )
= ( sk152 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15562:[bind(A,$thf( sk152 ))]]) ).
thf(19342,plain,
! [A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6712,15563]) ).
thf(373,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/sandbox/benchmark/theBenchmark.p',cc6_lattice2) ).
thf(3342,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)],[373]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(2269,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)],[204]) ).
thf(3054,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)],[3053]) ).
thf(3061,plain,
sk196 @ v6_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(994,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_nat_lat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_nat_lat) ).
thf(6423,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)],[994]) ).
thf(29511,plain,
! [A: $i] :
( ( A != sk315 )
| ( k1_xboole_0 @ v11_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,4650]) ).
thf(29512,plain,
( ( k1_xboole_0 @ v11_lattices )
| ( sk315 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29511:[bind(A,$thf( sk315 ))]]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(2501,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)],[240]) ).
thf(4654,plain,
sk315 @ v5_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(419,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(3617,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)],[419]) ).
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/sandbox/benchmark/theBenchmark.p',t169_partfun1) ).
thf(1826,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(12258,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,8515]) ).
thf(12259,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12258]) ).
thf(12394,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12259]) ).
thf(964,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/sandbox/benchmark/theBenchmark.p',t31_lattice4) ).
thf(6315,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)],[964]) ).
thf(554,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/sandbox/benchmark/theBenchmark.p',t52_lattices) ).
thf(4349,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)],[554]) ).
thf(7432,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2543,7047]) ).
thf(7433,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7432]) ).
thf(7434,plain,
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7433:[bind(A,$thf( sk138 ))]]) ).
thf(7571,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 @ v14_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)],[1063,7434]) ).
thf(7572,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 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7571]) ).
thf(7589,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[7572]) ).
thf(7591,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[7589]) ).
thf(10173,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 @ v14_lattices ) ),
inference(rewrite,[status(thm)],[7591,2542]) ).
thf(10174,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[10173]) ).
thf(971,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/sandbox/benchmark/theBenchmark.p',d3_filter_0) ).
thf(6332,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_filter_0 ) )
= ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(3590,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)],[418]) ).
thf(3591,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)],[3590]) ).
thf(3592,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)],[3591]) ).
thf(3597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != B )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(cnfConj,[status(thm)],[3592]) ).
thf(3601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != B )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(lifteq,[status(thm)],[3597]) ).
thf(3602,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ r2_hidden ) ),
inference(simp,[status(thm)],[3601]) ).
thf(27283,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)],[2045,3602]) ).
thf(27284,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[27283:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(27308,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
inference(simp,[status(thm)],[27284]) ).
thf(449,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/sandbox/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(3803,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)],[449]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',t69_partfun1) ).
thf(2466,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)],[236]) ).
thf(1056,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)],[1055]) ).
thf(1057,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)],[1056]) ).
thf(1059,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)],[1057]) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(1132,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(9051,plain,
! [A: $i] :
( ( ( sk313 @ 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)],[4611,7019]) ).
thf(9052,plain,
! [A: $i] :
( ( ( sk313 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9051]) ).
thf(9053,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9052:[bind(A,$thf( sk313 ))]]) ).
thf(15161,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2268,9053]) ).
thf(15162,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15161]) ).
thf(15242,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk313 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15162]) ).
thf(15264,plain,
( ( sk313 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15242]) ).
thf(270,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/sandbox/benchmark/theBenchmark.p',t7_lattice2) ).
thf(2691,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)],[270]) ).
thf(3326,plain,
~ ( sk218 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[3325]) ).
thf(8130,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,3326]) ).
thf(8131,plain,
( ( sk218 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8130]) ).
thf(8151,plain,
sk218 != k1_xboole_0,
inference(simp,[status(thm)],[8131]) ).
thf(31614,plain,
! [A: $i] :
( ( A != sk218 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,8151]) ).
thf(31615,plain,
! [A: $i] :
( ( A != sk218 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[31614]) ).
thf(31616,plain,
sk218 @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[31615:[bind(A,$thf( sk218 ))]]) ).
thf(905,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/sandbox/benchmark/theBenchmark.p',t30_lattice4) ).
thf(6049,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)],[905]) ).
thf(1025,plain,
sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ),
inference(cnfConj,[status(thm)],[1020]) ).
thf(40926,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)],[1025,1219]) ).
thf(40927,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)],[40926]) ).
thf(40977,plain,
! [A: $i] :
( ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ( sk2 != A )
| ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[40927]) ).
thf(40997,plain,
( ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[40977]) ).
thf(41462,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)],[3315,40997]) ).
thf(41463,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41462]) ).
thf(41475,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk216 )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41463]) ).
thf(712,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/sandbox/benchmark/theBenchmark.p',d1_lattice4) ).
thf(5214,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)],[712]) ).
thf(847,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/sandbox/benchmark/theBenchmark.p',t65_lattice2) ).
thf(5802,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)],[847]) ).
thf(537,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/sandbox/benchmark/theBenchmark.p',t22_lattices) ).
thf(4265,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)],[537]) ).
thf(682,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/sandbox/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(5077,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)],[682]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(1545,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(2413,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)],[2412]) ).
thf(2420,plain,
sk118 @ v6_lattices,
inference(cnfConj,[status(thm)],[2413]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(3374,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)],[377]) ).
thf(863,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/sandbox/benchmark/theBenchmark.p',t40_lattice2) ).
thf(5868,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)],[863]) ).
thf(720,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/sandbox/benchmark/theBenchmark.p',t71_lattice2) ).
thf(5256,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)],[720]) ).
thf(997,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/sandbox/benchmark/theBenchmark.p',d13_filter_0) ).
thf(6455,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)],[997]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
thf(2403,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)],[224]) ).
thf(421,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(3638,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
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/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(1514,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(523,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(4193,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(4194,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(cnf,[status(esa)],[4193]) ).
thf(697,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/sandbox/benchmark/theBenchmark.p',d8_binop_1) ).
thf(5127,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)],[697]) ).
thf(13033,plain,
! [B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,3127]) ).
thf(13034,plain,
! [B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13033]) ).
thf(13045,plain,
! [B: $i,A: $i] :
( ( A @ sk251 )
!= ( B @ ( B @ k1_funct_2 ) ) ),
inference(simp,[status(thm)],[13034]) ).
thf(806,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/sandbox/benchmark/theBenchmark.p',t79_lattice2) ).
thf(5622,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)],[806]) ).
thf(662,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/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(4928,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)],[662]) ).
thf(546,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/sandbox/benchmark/theBenchmark.p',d15_lattice4) ).
thf(4317,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)],[546]) ).
thf(324,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/sandbox/benchmark/theBenchmark.p',t71_partfun1) ).
thf(3084,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)],[324]) ).
thf(858,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/sandbox/benchmark/theBenchmark.p',t23_lattice4) ).
thf(5851,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)],[858]) ).
thf(595,axiom,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(4551,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(852,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/sandbox/benchmark/theBenchmark.p',d18_lattices) ).
thf(5829,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)],[852]) ).
thf(315,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/sandbox/benchmark/theBenchmark.p',t16_lattice2) ).
thf(3014,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)],[315]) ).
thf(829,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/sandbox/benchmark/theBenchmark.p',t74_lattice2) ).
thf(5727,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)],[829]) ).
thf(457,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/sandbox/benchmark/theBenchmark.p',t29_lattice4) ).
thf(3835,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)],[457]) ).
thf(3180,plain,
k6_nat_lat @ v10_lattices,
inference(cnfConj,[status(thm)],[3174]) ).
thf(13037,plain,
! [B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,5226]) ).
thf(13038,plain,
! [B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ k1_tarski @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13037]) ).
thf(13044,plain,
! [B: $i,A: $i] :
( ( A @ sk251 )
!= ( B @ k1_tarski ) ),
inference(simp,[status(thm)],[13038]) ).
thf(686,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(5091,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)],[686]) ).
thf(575,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/sandbox/benchmark/theBenchmark.p',d1_lattices) ).
thf(4471,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)],[575]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1873,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1874,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1873]) ).
thf(1875,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1874]) ).
thf(359,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/sandbox/benchmark/theBenchmark.p',fc3_lattice2) ).
thf(3268,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)],[359]) ).
thf(488,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/sandbox/benchmark/theBenchmark.p',t16_filter_2) ).
thf(4008,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)],[488]) ).
thf(845,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/sandbox/benchmark/theBenchmark.p',t39_lattice2) ).
thf(5792,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)],[845]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_subset_1) ).
thf(4595,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)],[604]) ).
thf(887,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/sandbox/benchmark/theBenchmark.p',t18_lattice4) ).
thf(5974,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)],[887]) ).
thf(31457,plain,
! [A: $i] :
( ( A
!= ( sk1 @ u1_struct_0 ) )
| ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,1025]) ).
thf(31458,plain,
( ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
| ( sk1 @ u1_struct_0 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31457:[bind(A,$thf( sk1 @ u1_struct_0 ))]]) ).
thf(403,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/sandbox/benchmark/theBenchmark.p',t18_binop_1) ).
thf(3524,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)],[403]) ).
thf(474,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/sandbox/benchmark/theBenchmark.p',redefinition_k10_filter_2) ).
thf(3934,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)],[474]) ).
thf(677,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/sandbox/benchmark/theBenchmark.p',t44_filter_2) ).
thf(5027,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)],[677]) ).
thf(15117,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)],[2268,8515]) ).
thf(15118,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)],[15117]) ).
thf(15239,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)],[15118]) ).
thf(15261,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[15239]) ).
thf(860,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/sandbox/benchmark/theBenchmark.p',t23_filter_2) ).
thf(5856,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)],[860]) ).
thf(404,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/sandbox/benchmark/theBenchmark.p',t58_filter_2) ).
thf(3527,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)],[404]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',t157_relat_1) ).
thf(3093,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)],[327]) ).
thf(337,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/sandbox/benchmark/theBenchmark.p',t60_partfun1) ).
thf(3152,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)],[337]) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',fc2_filter_0) ).
thf(2178,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)],[194]) ).
thf(843,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/sandbox/benchmark/theBenchmark.p',t67_filter_0) ).
thf(5787,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)],[843]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_partfun1) ).
thf(3155,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)],[338]) ).
thf(3156,plain,
( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(miniscope,[status(thm)],[3155]) ).
thf(3157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(cnf,[status(esa)],[3156]) ).
thf(3158,plain,
k1_xboole_0 @ v1_funct_1,
inference(cnfConj,[status(thm)],[3157]) ).
thf(8160,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3158,7047]) ).
thf(8161,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8160]) ).
thf(8162,plain,
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8161:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(15104,plain,
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8162,2268]) ).
thf(15105,plain,
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15104]) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(2222,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)],[199]) ).
thf(2950,plain,
sk187 @ v14_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(885,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v12_lattices )
<=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_lattices) ).
thf(5957,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) )
=> ( A @ v12_lattices ) )
& ( ( A @ v12_lattices )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( A @ r1_lattices ) ) )
=> ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
= ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(895,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/sandbox/benchmark/theBenchmark.p',d12_filter_2) ).
thf(6002,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)],[895]) ).
thf(362,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_subset_1) ).
thf(3288,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(3289,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(cnf,[status(esa)],[3288]) ).
thf(3290,plain,
! [A: $i] :
( ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) )
= ( A @ k2_subset_1 ) ),
inference(lifteq,[status(thm)],[3289]) ).
thf(247,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(2545,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(2546,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(cnf,[status(esa)],[2545]) ).
thf(2547,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(lifteq,[status(thm)],[2546]) ).
thf(326,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).
thf(3090,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(3091,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3090]) ).
thf(3092,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3091]) ).
thf(38951,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_subset_1 ) )
= A ),
inference(rewrite,[status(thm)],[3290,2547,3092]) ).
thf(1206,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1205]) ).
thf(1207,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
= A ),
inference(cnf,[status(esa)],[1206]) ).
thf(38307,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
= A ),
inference(lifteq,[status(thm)],[1207]) ).
thf(7651,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)],[1065,7133]) ).
thf(7652,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)],[7651]) ).
thf(7676,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)],[7652]) ).
thf(7704,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)],[7676]) ).
thf(28521,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)],[7704,2542]) ).
thf(28522,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)],[28521]) ).
thf(659,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/sandbox/benchmark/theBenchmark.p',s12_funct_2) ).
thf(4903,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)],[659]) ).
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/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).
thf(1811,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(183,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/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(2118,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)],[183]) ).
thf(2119,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ~ ? [C: $i] :
( ~ ? [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[2118]) ).
thf(2120,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)],[2119]) ).
thf(2124,plain,
! [A: $i] : ( A @ sk80 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2120]) ).
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/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(1238,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(1239,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)],[1238]) ).
thf(1240,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)],[1239]) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(cnfConj,[status(thm)],[1240]) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
| ( A != C ) ),
inference(lifteq,[status(thm)],[1242]) ).
thf(1245,plain,
! [B: $i,A: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ r2_hidden ) ),
inference(simp,[status(thm)],[1244]) ).
thf(38453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2124,1245]) ).
thf(38454,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[38453]) ).
thf(38468,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk80 )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[38454]) ).
thf(38478,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= ( B @ sk80 ) ),
inference(simp,[status(thm)],[38468]) ).
thf(3075,plain,
sk197 @ v3_filter_0,
inference(cnfConj,[status(thm)],[3070]) ).
thf(5590,plain,
! [A: $i] :
( ( ( ( A @ ( sk402 @ ( 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 @ ( sk402 @ ( 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 @ ( sk402 @ ( 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 @ ( sk402 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) )
& ( ( sk402 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ) ),
inference(cnf,[status(esa)],[5589]) ).
thf(5593,plain,
( ( ( f4_s11_funct_2 @ ( sk402 @ ( 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)],[5590]) ).
thf(5597,plain,
( ( ( f4_s11_funct_2 @ ( sk402 @ ( 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)],[5593]) ).
thf(651,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/sandbox/benchmark/theBenchmark.p',s14_funct_2) ).
thf(4857,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)],[651]) ).
thf(310,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/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(2996,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)],[310]) ).
thf(14469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk313 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14431,1081]) ).
thf(14470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk313 @ k2_relat_1 @ r1_tarski ) )
!= ( B @ ( A @ r1_tarski ) ) )
| ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14469]) ).
thf(14471,plain,
! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14470:[bind(A,$thf( sk313 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14495,plain,
! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14471]) ).
thf(1013,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/sandbox/benchmark/theBenchmark.p',d4_lattice4) ).
thf(6523,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)],[1013]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(3453,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)],[389]) ).
thf(1017,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t20_filter_2) ).
thf(6534,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)],[1017]) ).
thf(819,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/sandbox/benchmark/theBenchmark.p',t38_filter_0) ).
thf(5680,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)],[819]) ).
thf(960,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/sandbox/benchmark/theBenchmark.p',d12_lattice4) ).
thf(6300,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)],[960]) ).
thf(6718,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)],[1972,1050]) ).
thf(6719,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)],[6718]) ).
thf(6720,plain,
! [A: $i] : ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6719:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).
thf(21427,plain,
! [A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6720,15605]) ).
thf(21470,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)],[21427,1081]) ).
thf(21471,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)],[21470]) ).
thf(21472,plain,
! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21471:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk71 @ k9_relat_1 ) )),bind(C,$thf( sk71 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(21510,plain,
! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[21472]) ).
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/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(1828,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(480,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/sandbox/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).
thf(3973,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)],[480]) ).
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/sandbox/benchmark/theBenchmark.p',t3_filter_2) ).
thf(1146,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(1147,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r5_binop_1 ) ) )
| ( F
!= ( B @ ( D @ k1_realset1 ) ) )
| ( E
!= ( B @ ( C @ k1_realset1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
| ~ ( F @ v1_funct_1 )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
| ~ ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
| ~ ( E @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
| ~ ( D @ v1_funct_1 )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
| ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
| ~ ( C @ v1_funct_1 )
| ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
| ( B @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ( 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)],[1146]) ).
thf(1148,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
| ~ ( D @ ( C @ ( A @ r4_binop_1 ) ) )
| ( 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)],[1147]) ).
thf(1150,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)],[1148]) ).
thf(1151,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)],[1150]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',t6_relset_1) ).
thf(2034,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)],[165]) ).
thf(654,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/sandbox/benchmark/theBenchmark.p',t48_lattice4) ).
thf(4871,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)],[654]) ).
thf(506,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(4113,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(4114,plain,
( ~ ( sk279 @ v3_struct_0 )
& ( sk279 @ l1_struct_0 ) ),
inference(cnf,[status(esa)],[4113]) ).
thf(4115,plain,
sk279 @ l1_struct_0,
inference(cnfConj,[status(thm)],[4114]) ).
thf(1218,plain,
~ ( sk14 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1217]) ).
thf(8749,plain,
( ( ( sk216 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,1218]) ).
thf(8750,plain,
( ( sk216 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8749]) ).
thf(8759,plain,
sk216 != sk14,
inference(simp,[status(thm)],[8750]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',d8_filter_0) ).
thf(6438,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)],[996]) ).
thf(28523,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)],[2072,28522]) ).
thf(28524,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)],[28523]) ).
thf(28643,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)],[28524]) ).
thf(28674,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)],[28643]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',t165_funct_2) ).
thf(2073,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)],[172]) ).
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/sandbox/benchmark/theBenchmark.p',t39_partfun1) ).
thf(1180,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(1181,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
| ~ ( C @ v2_funct_1 )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( 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)],[1180]) ).
thf(1183,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)],[1181]) ).
thf(12339,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,7434]) ).
thf(12340,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12339]) ).
thf(12379,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[12340]) ).
thf(939,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/sandbox/benchmark/theBenchmark.p',d6_filter_0) ).
thf(6204,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)],[939]) ).
thf(2964,plain,
sk188 @ v8_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
thf(4660,plain,
sk315 @ v16_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(5591,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ m2_relset_1 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5590]) ).
thf(5602,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ m2_relset_1 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5591]) ).
thf(15358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ 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)],[5602,1131]) ).
thf(15359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[15358]) ).
thf(15360,plain,
( ( f2_s11_funct_2 @ ( sk402 @ k2_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[15359:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk402 ))]]) ).
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/sandbox/benchmark/theBenchmark.p',t65_funct_1) ).
thf(1351,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(208,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/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(2286,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)],[208]) ).
thf(41146,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,40941]) ).
thf(41147,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41146]) ).
thf(41155,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk216 ),
inference(simp,[status(thm)],[41147]) ).
thf(1201,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)],[1199]) ).
thf(41072,plain,
( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,40850]) ).
thf(41073,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41072]) ).
thf(41076,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk152 ),
inference(simp,[status(thm)],[41073]) ).
thf(344,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/sandbox/benchmark/theBenchmark.p',t13_binop_1) ).
thf(3184,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)],[344]) ).
thf(876,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/sandbox/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(5929,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)],[876]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',cc4_lattice2) ).
thf(2058,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)],[169]) ).
thf(406,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/sandbox/benchmark/theBenchmark.p',t2_binop_1) ).
thf(3537,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)],[406]) ).
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/sandbox/benchmark/theBenchmark.p',t4_funct_2) ).
thf(1928,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(6645,plain,
( ( ( sk152 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,1218]) ).
thf(6646,plain,
( ( sk152 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6645]) ).
thf(6648,plain,
sk152 != sk14,
inference(simp,[status(thm)],[6646]) ).
thf(497,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/sandbox/benchmark/theBenchmark.p',t17_lattice2) ).
thf(4055,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)],[497]) ).
thf(3068,plain,
sk196 @ v15_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(7611,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)],[1973,7068]) ).
thf(7612,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7611]) ).
thf(7613,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7612:[bind(A,$thf( sk71 ))]]) ).
thf(8775,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)],[3316,7004]) ).
thf(8776,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8775]) ).
thf(8777,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8776:[bind(A,$thf( sk216 ))]]) ).
thf(15183,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)],[2268,8777]) ).
thf(15184,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)],[15183]) ).
thf(15248,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)],[15184]) ).
thf(15271,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15248]) ).
thf(9036,plain,
! [A: $i] :
( ( ( sk313 @ 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)],[4611,7068]) ).
thf(9037,plain,
! [A: $i] :
( ( ( sk313 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9036]) ).
thf(9038,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9037:[bind(A,$thf( sk313 ))]]) ).
thf(12353,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,9038]) ).
thf(12354,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12353]) ).
thf(12369,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk313 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12354]) ).
thf(12430,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12369]) ).
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/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).
thf(1214,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(1215,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)],[1214]) ).
thf(809,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t2_filter_0) ).
thf(5643,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)],[809]) ).
thf(383,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/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(3421,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)],[383]) ).
thf(434,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/sandbox/benchmark/theBenchmark.p',t25_binop_1) ).
thf(3712,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)],[434]) ).
thf(744,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/sandbox/benchmark/theBenchmark.p',dt_k19_filter_2) ).
thf(5370,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)],[744]) ).
thf(451,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/sandbox/benchmark/theBenchmark.p',t63_filter_0) ).
thf(3808,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)],[451]) ).
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/sandbox/benchmark/theBenchmark.p',d5_binop_1) ).
thf(1066,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(1067,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)],[1066]) ).
thf(1070,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)],[1067]) ).
thf(1072,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)],[1070]) ).
thf(21,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(1119,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(2424,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(974,axiom,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(6344,plain,
? [A: $i] :
( ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 )
& ( A @ l3_lattices ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(6345,plain,
( ( sk454 @ v3_lattices )
& ~ ( sk454 @ v3_struct_0 )
& ( sk454 @ l3_lattices ) ),
inference(cnf,[status(esa)],[6344]) ).
thf(6347,plain,
~ ( sk454 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[6345]) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',t77_funct_2) ).
thf(2371,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)],[220]) ).
thf(735,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/sandbox/benchmark/theBenchmark.p',t24_binop_1) ).
thf(5321,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)],[735]) ).
thf(856,axiom,
! [A: $i] :
( ( ( A @ l2_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(5846,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)],[856]) ).
thf(869,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',t53_lattice2) ).
thf(5897,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)],[869]) ).
thf(6699,plain,
( ( ( sk361 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,5153]) ).
thf(6700,plain,
( ( sk361 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6699]) ).
thf(6702,plain,
sk361 != sk152,
inference(simp,[status(thm)],[6700]) ).
thf(12252,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,7431]) ).
thf(12253,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12252]) ).
thf(12411,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[12253]) ).
thf(495,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v3_lattices ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
thf(4040,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 @ l3_lattices )
& ( A @ k1_lattice2 @ v3_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(441,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/sandbox/benchmark/theBenchmark.p',t35_lattice2) ).
thf(3756,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)],[441]) ).
thf(591,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/sandbox/benchmark/theBenchmark.p',redefinition_m1_struct_0) ).
thf(4536,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)],[591]) ).
thf(898,axiom,
( ( k6_nat_lat @ l3_lattices )
& ( k6_nat_lat @ v10_lattices )
& ~ ( k6_nat_lat @ v3_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_nat_lat) ).
thf(6021,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)],[898]) ).
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/sandbox/benchmark/theBenchmark.p',t25_partfun1) ).
thf(1433,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(778,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/sandbox/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).
thf(5489,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)],[778]) ).
thf(2965,plain,
sk188 @ v3_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
thf(808,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/sandbox/benchmark/theBenchmark.p',t54_filter_2) ).
thf(5629,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)],[808]) ).
thf(410,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/sandbox/benchmark/theBenchmark.p',dt_k4_filter_2) ).
thf(3559,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)],[410]) ).
thf(611,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(4628,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(9016,plain,
( ( ( sk295 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,1218]) ).
thf(9017,plain,
( ( sk295 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9016]) ).
thf(9024,plain,
sk295 != sk14,
inference(simp,[status(thm)],[9017]) ).
thf(823,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/sandbox/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(5695,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)],[823]) ).
thf(9014,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,3127]) ).
thf(9015,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9014]) ).
thf(9026,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk295 ),
inference(simp,[status(thm)],[9015]) ).
thf(31248,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,1022]) ).
thf(31249,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31248:[bind(A,$thf( sk1 ))]]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',t81_lattice2) ).
thf(3582,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)],[415]) ).
thf(703,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/sandbox/benchmark/theBenchmark.p',t46_lattice2) ).
thf(5157,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)],[703]) ).
thf(1003,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) )
=> ( ( A @ k6_lattices )
= ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_lattice2) ).
thf(6482,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) )
=> ( ( A @ k6_lattices )
= ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(2364,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2361]) ).
thf(13039,plain,
! [B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,4039]) ).
thf(13040,plain,
! [B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13039]) ).
thf(13049,plain,
! [B: $i,A: $i] :
( ( A @ sk251 )
!= ( B @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[13040]) ).
thf(525,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/sandbox/benchmark/theBenchmark.p',t24_filter_0) ).
thf(4199,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)],[525]) ).
thf(5875,plain,
~ ( sk417 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[5873]) ).
thf(31455,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,1025]) ).
thf(31456,plain,
( ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
| ( sk2 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31455:[bind(A,$thf( sk2 ))]]) ).
thf(564,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/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).
thf(4407,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)],[564]) ).
thf(2473,plain,
k13_nat_lat @ v4_lattices,
inference(cnfConj,[status(thm)],[2469]) ).
thf(12948,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)],[2072,9801]) ).
thf(12949,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)],[12948]) ).
thf(12989,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)],[12949]) ).
thf(13019,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)],[12989]) ).
thf(757,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(5411,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)],[757]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(3984,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(3260,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3257]) ).
thf(3264,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3260]) ).
thf(3265,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[3264]) ).
thf(1149,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)],[1147]) ).
thf(1152,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)],[1149]) ).
thf(1153,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)],[1152]) ).
thf(824,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/sandbox/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(5697,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)],[824]) ).
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/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(1338,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(699,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/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).
thf(5142,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)],[699]) ).
thf(358,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(3266,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(3267,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(cnf,[status(esa)],[3266]) ).
thf(18645,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
inference(rewrite,[status(thm)],[3267,2547]) ).
thf(3596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != A )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(cnfConj,[status(thm)],[3592]) ).
thf(3603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ r2_hidden ) )
| ( D != A )
| ( C
!= ( B @ ( A @ k2_tarski ) ) ) ),
inference(lifteq,[status(thm)],[3596]) ).
thf(3604,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[3603]) ).
thf(317,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(3026,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)],[317]) ).
thf(3027,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)],[3026]) ).
thf(3028,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)],[3027]) ).
thf(3029,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3028]) ).
thf(3031,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3029]) ).
thf(3032,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[3031]) ).
thf(27398,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)],[3604,3032]) ).
thf(27399,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[27398]) ).
thf(27425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) )
!= k1_xboole_0 )
| ( A != C ) ),
inference(simp,[status(thm)],[27399]) ).
thf(27431,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k2_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[27425]) ).
thf(30945,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)],[1298,27431]) ).
thf(30946,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ k2_tarski ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[30945]) ).
thf(30947,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[30946:[bind(A,$thf( E @ ( D @ k2_tarski ) )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).
thf(32254,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[30947]) ).
thf(777,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(5487,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)],[777]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(1783,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(10159,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,4627]) ).
thf(10160,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10159]) ).
thf(10165,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk295 ),
inference(simp,[status(thm)],[10160]) ).
thf(501,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/sandbox/benchmark/theBenchmark.p',dt_m1_lattice4) ).
thf(4076,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)],[501]) ).
thf(2737,plain,
sk157 @ v6_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(1311,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(8781,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)],[3316,7019]) ).
thf(8782,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8781]) ).
thf(8783,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8782:[bind(A,$thf( sk216 ))]]) ).
thf(15144,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)],[2268,8783]) ).
thf(15145,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)],[15144]) ).
thf(15236,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)],[15145]) ).
thf(15258,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15236]) ).
thf(862,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/sandbox/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(5862,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)],[862]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',t8_relset_1) ).
thf(2083,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)],[175]) ).
thf(492,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/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(4031,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)],[492]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(2660,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)],[262]) ).
thf(13041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,4627]) ).
thf(13042,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13041]) ).
thf(13047,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk251 )
!= ( C @ ( B @ k2_tarski ) ) ),
inference(simp,[status(thm)],[13042]) ).
thf(28128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( D @ ( C @ k2_tarski ) ) )
| ( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( B @ sk251 ) ) ),
inference(paramod_ordered,[status(thm)],[2045,13047]) ).
thf(28129,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ k1_zfmisc_1 )
!= ( A @ sk251 ) ),
inference(pattern_uni,[status(thm)],[28128:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 )),bind(D,$thf( E @ k1_tarski ))]]) ).
thf(28130,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ k1_zfmisc_1 )
!= ( A @ sk251 ) ),
inference(simp,[status(thm)],[28129]) ).
thf(517,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/sandbox/benchmark/theBenchmark.p',t52_domain_1) ).
thf(4172,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)],[517]) ).
thf(7996,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,2437]) ).
thf(7997,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7996]) ).
thf(7999,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk152 ),
inference(simp,[status(thm)],[7997]) ).
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/sandbox/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(1636,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(1000,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/sandbox/benchmark/theBenchmark.p',t65_filter_2) ).
thf(6464,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)],[1000]) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',t168_partfun1) ).
thf(3037,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)],[319]) ).
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/sandbox/benchmark/theBenchmark.p',t169_funct_2) ).
thf(1159,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(1160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 ) )
& ( ( ( 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)],[1159]) ).
thf(1161,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)],[1160]) ).
thf(1163,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)],[1161]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_partfun1) ).
thf(2409,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)],[226]) ).
thf(456,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/sandbox/benchmark/theBenchmark.p',t22_filter_0) ).
thf(3827,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)],[456]) ).
thf(2733,plain,
sk157 @ v7_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).
thf(2277,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)],[206]) ).
thf(16156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( sk402 @ 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)],[15360,1081]) ).
thf(16157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( sk402 @ 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)],[16156]) ).
thf(16158,plain,
! [A: $i] :
( ( f2_s11_funct_2 @ ( A @ ( sk402 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[16157:[bind(A,$thf( sk402 @ k2_relat_1 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( C ))]]) ).
thf(16205,plain,
! [A: $i] :
( ( f2_s11_funct_2 @ ( A @ ( sk402 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[16158]) ).
thf(4661,plain,
sk315 @ v15_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(4981,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)],[4980]) ).
thf(4982,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk349 @ ( E @ r2_hidden ) )
| ( A @ sk349 @ ( E @ r2_tarski ) )
| ~ ( A @ sk349 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk349 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk349 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk349 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk349 @ ( B @ r2_hidden ) ) )
& ( A @ sk349 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[4981]) ).
thf(4983,plain,
! [A: $i] : ( A @ sk349 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[4982]) ).
thf(16972,plain,
! [B: $i,A: $i] :
( ( ( A @ sk349 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4983,3032]) ).
thf(16973,plain,
! [B: $i,A: $i] :
( ( A @ sk349 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[16972]) ).
thf(16989,plain,
! [B: $i,A: $i] :
( ( ( A @ sk349 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[16973]) ).
thf(16997,plain,
! [A: $i] :
( ( A @ sk349 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16989]) ).
thf(30783,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk349 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,16997]) ).
thf(30784,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk349 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[30783]) ).
thf(30785,plain,
! [A: $i] : ( A @ sk349 @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[30784:[bind(A,$thf( C @ sk349 )),bind(B,$thf( C ))]]) ).
thf(32237,plain,
! [A: $i] : ( A @ sk349 @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[30785]) ).
thf(627,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/sandbox/benchmark/theBenchmark.p',t45_lattice2) ).
thf(4712,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)],[627]) ).
thf(574,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/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(4466,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)],[574]) ).
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/sandbox/benchmark/theBenchmark.p',t23_binop_1) ).
thf(1082,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(1083,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)],[1082]) ).
thf(1084,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)],[1083]) ).
thf(1091,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)],[1084]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(1255,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(846,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/sandbox/benchmark/theBenchmark.p',t36_filter_2) ).
thf(5794,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)],[846]) ).
thf(8747,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,3127]) ).
thf(8748,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8747]) ).
thf(8756,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk216 ),
inference(simp,[status(thm)],[8748]) ).
thf(796,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/sandbox/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
thf(5579,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)],[796]) ).
thf(1014,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/sandbox/benchmark/theBenchmark.p',fc3_filter_2) ).
thf(6528,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)],[1014]) ).
thf(670,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/sandbox/benchmark/theBenchmark.p',d16_lattices) ).
thf(4989,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)],[670]) ).
thf(1171,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)],[1165]) ).
thf(1174,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)],[1171]) ).
thf(743,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t87_filter_0) ).
thf(5366,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)],[743]) ).
thf(440,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/sandbox/benchmark/theBenchmark.p',dt_m1_filter_2) ).
thf(3752,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)],[440]) ).
thf(353,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/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).
thf(3233,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)],[353]) ).
thf(376,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/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(3371,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)],[376]) ).
thf(570,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/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(4449,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)],[570]) ).
thf(582,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/sandbox/benchmark/theBenchmark.p',t48_lattice2) ).
thf(4493,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)],[582]) ).
thf(684,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(5085,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(2150,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)],[189]) ).
thf(452,axiom,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s7_domain_1) ).
thf(3816,plain,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
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/sandbox/benchmark/theBenchmark.p',d7_binop_1) ).
thf(1619,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(308,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/sandbox/benchmark/theBenchmark.p',t31_lattice2) ).
thf(2986,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)],[308]) ).
thf(752,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/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(5396,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)],[752]) ).
thf(2414,plain,
sk118 @ v1_lattice2,
inference(cnfConj,[status(thm)],[2413]) ).
thf(647,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/sandbox/benchmark/theBenchmark.p',t44_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] :
( ( 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)],[647]) ).
thf(1011,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k17_filter_2 @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_filter_2) ).
thf(6509,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k17_filter_2 @ m2_filter_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(3207,plain,
sk207 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3206]) ).
thf(7559,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,5226]) ).
thf(7560,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7559]) ).
thf(7565,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk71 ),
inference(simp,[status(thm)],[7560]) ).
thf(428,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/sandbox/benchmark/theBenchmark.p',dt_k10_filter_2) ).
thf(3682,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)],[428]) ).
thf(491,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/sandbox/benchmark/theBenchmark.p',t45_filter_2) ).
thf(4021,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)],[491]) ).
thf(372,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/sandbox/benchmark/theBenchmark.p',t58_partfun1) ).
thf(3339,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)],[372]) ).
thf(496,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/sandbox/benchmark/theBenchmark.p',t43_lattice4) ).
thf(4044,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)],[496]) ).
thf(854,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/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(5843,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)],[854]) ).
thf(2958,plain,
sk188 @ v6_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
thf(345,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/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(3191,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)],[345]) ).
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/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(1920,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(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/sandbox/benchmark/theBenchmark.p',t15_funct_1) ).
thf(1457,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(405,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/sandbox/benchmark/theBenchmark.p',t26_filter_2) ).
thf(3535,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)],[405]) ).
thf(2211,plain,
sk94 @ v8_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
thf(6715,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)],[2542,1050]) ).
thf(6716,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)],[6715]) ).
thf(6717,plain,
! [A: $i] : ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[6716:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).
thf(15596,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)],[2542,1137]) ).
thf(15597,plain,
! [A: $i] :
( ( ( sk138 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15596]) ).
thf(15598,plain,
( ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) )
= ( sk138 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15597:[bind(A,$thf( sk138 ))]]) ).
thf(21332,plain,
! [A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[6717,15598]) ).
thf(21374,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)],[21332,1081]) ).
thf(21375,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)],[21374]) ).
thf(21376,plain,
! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21375:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk138 @ k9_relat_1 ) )),bind(C,$thf( sk138 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(21409,plain,
! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[21376]) ).
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/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(1910,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(388,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/sandbox/benchmark/theBenchmark.p',t14_lattice2) ).
thf(3445,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)],[388]) ).
thf(961,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/sandbox/benchmark/theBenchmark.p',dt_k20_filter_2) ).
thf(6303,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)],[961]) ).
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/sandbox/benchmark/theBenchmark.p',t24_relat_1) ).
thf(1027,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(1028,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
| ( E
!= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
| ~ ( E @ v1_relat_1 ) )
& ( ( ( 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)],[1027]) ).
thf(1029,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)],[1028]) ).
thf(1031,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)],[1029]) ).
thf(1032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 )
| ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) ) ),
inference(simp,[status(thm)],[1031]) ).
thf(482,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/sandbox/benchmark/theBenchmark.p',t11_filter_2) ).
thf(3980,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)],[482]) ).
thf(779,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/sandbox/benchmark/theBenchmark.p',t19_filter_2) ).
thf(5492,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)],[779]) ).
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/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(1365,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(258,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_subset_1) ).
thf(2628,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(2477,plain,
k13_nat_lat @ v8_lattices,
inference(cnfConj,[status(thm)],[2469]) ).
thf(3314,plain,
sk216 @ v1_relat_1,
inference(cnfConj,[status(thm)],[3313]) ).
thf(8618,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)],[3314,1050]) ).
thf(8619,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)],[8618]) ).
thf(8620,plain,
! [A: $i] : ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8619:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).
thf(15575,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)],[3314,1137]) ).
thf(15576,plain,
! [A: $i] :
( ( ( sk216 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15575]) ).
thf(15577,plain,
( ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) )
= ( sk216 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15576:[bind(A,$thf( sk216 ))]]) ).
thf(22284,plain,
! [A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[8620,15577]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',t12_lattice2) ).
thf(2663,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)],[263]) ).
thf(29632,plain,
! [A: $i] :
( ( A != sk196 )
| ( k1_xboole_0 @ v6_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,3061]) ).
thf(29633,plain,
( ( k1_xboole_0 @ v6_lattices )
| ( sk196 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29632:[bind(A,$thf( sk196 ))]]) ).
thf(3065,plain,
sk196 @ v13_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(8154,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)],[3158,7068]) ).
thf(8155,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8154]) ).
thf(8156,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8155:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(15102,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8156,2268]) ).
thf(15103,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15102]) ).
thf(14608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( A @ ( sk313 @ 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)],[14495,1081]) ).
thf(14609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( A @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14608]) ).
thf(14610,plain,
! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14609:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f2_s4_funct_2 )),bind(D,$thf( D ))]]) ).
thf(14643,plain,
! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14610]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',t32_relat_1) ).
thf(2872,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)],[291]) ).
thf(1951,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(cnf,[status(esa)],[1950]) ).
thf(957,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/sandbox/benchmark/theBenchmark.p',t43_lattices) ).
thf(6292,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)],[957]) ).
thf(4552,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(cnf,[status(esa)],[4551]) ).
thf(4553,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(lifteq,[status(thm)],[4552]) ).
thf(466,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/sandbox/benchmark/theBenchmark.p',t56_filter_0) ).
thf(3894,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)],[466]) ).
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/sandbox/benchmark/theBenchmark.p',t51_funct_2) ).
thf(1819,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(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/sandbox/benchmark/theBenchmark.p',t8_lattice2) ).
thf(1624,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(8132,plain,
( ( ( sk361 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,5153]) ).
thf(8133,plain,
( ( sk361 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8132]) ).
thf(8147,plain,
sk361 != k1_xboole_0,
inference(simp,[status(thm)],[8133]) ).
thf(32117,plain,
! [A: $i] :
( ( A != sk361 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,8147]) ).
thf(32118,plain,
! [A: $i] :
( ( A != sk361 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[32117]) ).
thf(32119,plain,
sk361 @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[32118:[bind(A,$thf( sk361 ))]]) ).
thf(33231,plain,
! [A: $i] :
( ( ( sk361 @ 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)],[32119,1137]) ).
thf(33232,plain,
! [A: $i] :
( ( ( sk361 @ sk18 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[33231]) ).
thf(33233,plain,
( ( sk361 @ sk18 @ k1_relat_1 @ ( sk361 @ sk18 @ k9_relat_1 ) )
= ( sk361 @ sk18 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[33232:[bind(A,$thf( sk361 @ sk18 ))]]) ).
thf(521,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/sandbox/benchmark/theBenchmark.p',t59_lattice2) ).
thf(4187,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)],[521]) ).
thf(738,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(5340,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(5341,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(cnf,[status(esa)],[5340]) ).
thf(790,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/sandbox/benchmark/theBenchmark.p',t40_lattices) ).
thf(5551,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)],[790]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',d12_binop_1) ).
thf(3144,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)],[336]) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',t27_relset_1) ).
thf(2327,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)],[212]) ).
thf(2213,plain,
sk94 @ v6_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
thf(29338,plain,
! [A: $i] :
( ( A != sk207 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,15267]) ).
thf(29339,plain,
! [A: $i] :
( ( A != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[29338]) ).
thf(29340,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( sk207 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29339:[bind(A,$thf( sk207 ))]]) ).
thf(2741,plain,
sk157 @ v14_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(573,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/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(4461,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)],[573]) ).
thf(631,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/sandbox/benchmark/theBenchmark.p',t55_lattice2) ).
thf(4732,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)],[631]) ).
thf(736,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/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
thf(5330,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)],[736]) ).
thf(448,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ( ( A @ v3_struct_0 )
<=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
thf(3799,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)],[448]) ).
thf(593,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/sandbox/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
thf(4544,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)],[593]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(2631,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)],[259]) ).
thf(3078,plain,
~ ( sk197 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3070]) ).
thf(8144,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,4039]) ).
thf(8145,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8144]) ).
thf(8149,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8145]) ).
thf(11563,plain,
( ( ( sk71 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(paramod_ordered,[status(thm)],[1109,11014]) ).
thf(11564,plain,
( ( ( sk71 @ k2_relat_1 )
!= ( k1_xboole_0 @ k2_relat_1 ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[11563]) ).
thf(11592,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[11564]) ).
thf(11683,plain,
( ( ( sk71 @ k1_relat_1 )
!= ( k1_xboole_0 @ k1_relat_1 ) )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(paramod_ordered,[status(thm)],[1108,11592]) ).
thf(11685,plain,
( ( sk71 != k1_xboole_0 )
| ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[11683]) ).
thf(11689,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[11685]) ).
thf(12944,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v14_lattices ) ),
inference(rewrite,[status(thm)],[11689,2072]) ).
thf(12945,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[12944]) ).
thf(1111,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)],[1110]) ).
thf(1114,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)],[1111]) ).
thf(1118,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)],[1114]) ).
thf(478,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/sandbox/benchmark/theBenchmark.p',t68_lattice2) ).
thf(3968,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)],[478]) ).
thf(859,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ m2_nat_lat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_nat_lat) ).
thf(5854,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)],[859]) ).
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/sandbox/benchmark/theBenchmark.p',cc1_filter_0) ).
thf(1936,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(8519,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3208,7047]) ).
thf(8520,plain,
! [A: $i] :
( ( ( sk207 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8519]) ).
thf(8521,plain,
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8520:[bind(A,$thf( sk207 ))]]) ).
thf(12347,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,8521]) ).
thf(12348,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12347]) ).
thf(12414,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk207 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[12348]) ).
thf(1089,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)],[1083]) ).
thf(470,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/sandbox/benchmark/theBenchmark.p',abstractness_v2_struct_0) ).
thf(3909,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)],[470]) ).
thf(991,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/sandbox/benchmark/theBenchmark.p',dt_k7_filter_2) ).
thf(6413,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)],[991]) ).
thf(871,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/sandbox/benchmark/theBenchmark.p',t26_lattice4) ).
thf(5904,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)],[871]) ).
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/sandbox/benchmark/theBenchmark.p',t3_funct_2) ).
thf(1231,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(1232,plain,
! [A: $i] :
( ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) )
& ( ( A @ v1_funct_1 )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ) ),
inference(cnf,[status(esa)],[1231]) ).
thf(1234,plain,
! [A: $i] :
( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1232]) ).
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 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_binop_1) ).
thf(1983,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)],[154]) ).
thf(968,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/sandbox/benchmark/theBenchmark.p',dt_k23_filter_2) ).
thf(6324,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)],[968]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',t1_realset1) ).
thf(2157,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)],[190]) ).
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/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).
thf(1143,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(700,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/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).
thf(5145,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)],[700]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(2100,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)],[178]) ).
thf(382,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/sandbox/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(3404,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)],[382]) ).
thf(3405,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)],[3404]) ).
thf(3406,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)],[3405]) ).
thf(3410,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[3406]) ).
thf(3412,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[3410]) ).
thf(3413,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[3412]) ).
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/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(1270,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(12972,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[2072,10215]) ).
thf(12973,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) ) )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12972]) ).
thf(12994,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12973]) ).
thf(13006,plain,
( ( ( sk138 @ k1_relat_1 )
!= k1_xboole_0 )
| ( ( sk138 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12994]) ).
thf(2946,plain,
sk187 @ v9_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(724,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/sandbox/benchmark/theBenchmark.p',t68_filter_0) ).
thf(5270,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)],[724]) ).
thf(285,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/sandbox/benchmark/theBenchmark.p',d3_relat_2) ).
thf(2801,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)],[285]) ).
thf(972,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/sandbox/benchmark/theBenchmark.p',d6_filter_2) ).
thf(6335,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)],[972]) ).
thf(816,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/sandbox/benchmark/theBenchmark.p',t60_nat_lat) ).
thf(5668,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)],[816]) ).
thf(5669,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)],[5668]) ).
thf(5673,plain,
k6_nat_lat @ l3_lattices,
inference(cnfConj,[status(thm)],[5669]) ).
thf(7247,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)],[1973,7019]) ).
thf(7248,plain,
! [A: $i] :
( ( ( sk71 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7247]) ).
thf(7249,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7248:[bind(A,$thf( sk71 ))]]) ).
thf(1120,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[1119]) ).
thf(1121,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[1120]) ).
thf(580,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/sandbox/benchmark/theBenchmark.p',t76_lattice2) ).
thf(4486,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)],[580]) ).
thf(998,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/sandbox/benchmark/theBenchmark.p',t37_lattice4) ).
thf(6459,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)],[998]) ).
thf(780,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_lattice4) ).
thf(5502,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)],[780]) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',t56_subset_1) ).
thf(2694,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)],[271]) ).
thf(622,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/sandbox/benchmark/theBenchmark.p',t25_filter_2) ).
thf(4693,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)],[622]) ).
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/sandbox/benchmark/theBenchmark.p',t72_partfun1) ).
thf(1096,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(760,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v14_lattices )
<=> ( A @ k1_lattice2 @ v13_lattices ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_lattice2) ).
thf(5428,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)],[760]) ).
thf(7477,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)],[1063,7249]) ).
thf(7478,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)],[7477]) ).
thf(7516,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)],[7478]) ).
thf(7532,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)],[7516]) ).
thf(8013,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)],[7532,1972]) ).
thf(8014,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)],[8013]) ).
thf(530,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/sandbox/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(4233,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)],[530]) ).
thf(8766,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)],[3316,7068]) ).
thf(8767,plain,
! [A: $i] :
( ( ( sk216 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8766]) ).
thf(8768,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8767:[bind(A,$thf( sk216 ))]]) ).
thf(742,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/sandbox/benchmark/theBenchmark.p',dt_k22_filter_2) ).
thf(5362,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)],[742]) ).
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/sandbox/benchmark/theBenchmark.p',d11_binop_1) ).
thf(1540,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(889,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/sandbox/benchmark/theBenchmark.p',t48_filter_2) ).
thf(5978,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)],[889]) ).
thf(10145,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,4627]) ).
thf(10146,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10145]) ).
thf(10162,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10146]) ).
thf(24730,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)],[2045,10162]) ).
thf(24731,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[24730:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(24754,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[24731]) ).
thf(3060,plain,
sk196 @ v4_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(3176,plain,
k6_nat_lat @ v3_lattices,
inference(cnfConj,[status(thm)],[3174]) ).
thf(941,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/sandbox/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(6218,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)],[941]) ).
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/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(1397,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(29727,plain,
! [A: $i] :
( ( A != sk313 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,15264]) ).
thf(29728,plain,
! [A: $i] :
( ( A != sk313 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[29727]) ).
thf(29729,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( sk313 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29728:[bind(A,$thf( sk313 ))]]) ).
thf(678,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/sandbox/benchmark/theBenchmark.p',t5_filter_2) ).
thf(5031,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)],[678]) ).
thf(4858,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk331 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
| ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk329 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk331 @ m2_relset_1 ) ) )
| ~ sk329 )
& ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk331 @ v1_funct_2 ) ) )
| ~ sk329 )
& ( ( sk331 @ v1_funct_1 )
| ~ sk329 )
& ( sk329
| ~ ( A @ ( sk330 @ p1_s14_funct_2 ) )
| ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk329
| ( f1_s14_funct_2 @ ( sk330 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4857]) ).
thf(4860,plain,
( sk329
| ( f1_s14_funct_2 @ ( sk330 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4858]) ).
thf(952,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/sandbox/benchmark/theBenchmark.p',t39_lattice4) ).
thf(6271,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)],[952]) ).
thf(880,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/sandbox/benchmark/theBenchmark.p',t32_lattices) ).
thf(5941,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)],[880]) ).
thf(4653,plain,
sk315 @ v13_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(849,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/sandbox/benchmark/theBenchmark.p',dt_m2_nat_lat) ).
thf(5818,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)],[849]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',t57_filter_2) ).
thf(3922,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)],[473]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',t10_lattice2) ).
thf(3000,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)],[311]) ).
thf(3179,plain,
k6_nat_lat @ v5_lattices,
inference(cnfConj,[status(thm)],[3174]) ).
thf(29248,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,1024]) ).
thf(29249,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29248:[bind(A,$thf( sk1 ))]]) ).
thf(708,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/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(5181,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)],[708]) ).
thf(638,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/sandbox/benchmark/theBenchmark.p',d4_lattice2) ).
thf(4772,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)],[638]) ).
thf(15125,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)],[2268,7613]) ).
thf(15126,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)],[15125]) ).
thf(15243,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)],[15126]) ).
thf(15265,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[15243]) ).
thf(9020,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,4039]) ).
thf(9021,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9020]) ).
thf(9025,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk295 ),
inference(simp,[status(thm)],[9021]) ).
thf(11624,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk295 ) ),
inference(paramod_ordered,[status(thm)],[1953,9025]) ).
thf(11625,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk295 ),
inference(pattern_uni,[status(thm)],[11624:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(5107,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)],[689]) ).
thf(1182,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)],[1181]) ).
thf(7464,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 @ v14_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)],[1063,7431]) ).
thf(7465,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 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[7464]) ).
thf(7512,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[7465]) ).
thf(7527,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[7512]) ).
thf(7845,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 @ v14_lattices ) ),
inference(rewrite,[status(thm)],[7527,1972]) ).
thf(7846,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[7845]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',t27_binop_1) ).
thf(2868,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)],[290]) ).
thf(561,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/sandbox/benchmark/theBenchmark.p',dt_k7_domain_1) ).
thf(4389,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)],[561]) ).
thf(7992,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,2437]) ).
thf(7993,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7992]) ).
thf(7998,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk71 ),
inference(simp,[status(thm)],[7993]) ).
thf(2419,plain,
sk118 @ v5_lattices,
inference(cnfConj,[status(thm)],[2413]) ).
thf(1074,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)],[1073]) ).
thf(1075,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)],[1074]) ).
thf(834,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/sandbox/benchmark/theBenchmark.p',t11_lattice4) ).
thf(5743,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)],[834]) ).
thf(8005,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,3127]) ).
thf(8006,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8005]) ).
thf(8008,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk152 ),
inference(simp,[status(thm)],[8006]) ).
thf(565,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/sandbox/benchmark/theBenchmark.p',fc4_filter_2) ).
thf(4421,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)],[565]) ).
thf(545,axiom,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(4315,plain,
! [A: $i] :
( ( A @ l2_lattices )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun1) ).
thf(3010,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)],[313]) ).
thf(769,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/sandbox/benchmark/theBenchmark.p',t13_filter_0) ).
thf(5464,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)],[769]) ).
thf(634,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(4750,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)],[634]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relat_1) ).
thf(1229,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(1230,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(cnf,[status(esa)],[1229]) ).
thf(43976,plain,
! [B: $i,A: $i] :
( ( ( sk207 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3207,1230]) ).
thf(43977,plain,
! [B: $i,A: $i] :
( ( ( sk207 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[43976]) ).
thf(43978,plain,
! [A: $i] : ( A @ ( sk207 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[43977:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).
thf(719,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/sandbox/benchmark/theBenchmark.p',s3_funct_2) ).
thf(5247,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)],[719]) ).
thf(5248,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk374 @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) )
| ~ ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
| ~ sk372 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk374 @ m2_relset_1 ) ) )
| ~ sk372 )
& ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk374 @ v1_funct_2 ) ) )
| ~ sk372 )
& ( ( sk374 @ v1_funct_1 )
| ~ sk372 )
& ( sk372
| ~ ( A @ ( sk373 @ p1_s3_funct_2 ) )
| ~ ( f2_s3_funct_2 @ ( A @ m1_subset_1 ) ) )
& ( sk372
| ( f1_s3_funct_2 @ ( sk373 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[5247]) ).
thf(5253,plain,
( sk372
| ( f1_s3_funct_2 @ ( sk373 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[5248]) ).
thf(737,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(5337,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(8142,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,5226]) ).
thf(8143,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8142]) ).
thf(8152,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8143]) ).
thf(31080,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)],[1298,8152]) ).
thf(31081,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_tarski ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[31080]) ).
thf(31082,plain,
! [A: $i] : ( A @ k1_tarski @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[31081:[bind(A,$thf( C @ k1_tarski )),bind(B,$thf( C ))]]) ).
thf(32297,plain,
! [A: $i] : ( A @ k1_tarski @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[31082]) ).
thf(14132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk313 @ 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)],[14117,1095]) ).
thf(14133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( sk313 @ 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)],[14132]) ).
thf(14134,plain,
! [A: $i] : ( sk313 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14133:[bind(A,$thf( sk313 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14189,plain,
! [A: $i] : ( sk313 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14134]) ).
thf(788,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/sandbox/benchmark/theBenchmark.p',dt_k8_filter_2) ).
thf(5547,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)],[788]) ).
thf(18015,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( B @ k1_zfmisc_1 ) )
| ( ( A @ sk251 )
!= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1953,13049]) ).
thf(18016,plain,
! [A: $i] :
( ( A @ sk251 )
!= ( k1_xboole_0 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[18015:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
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/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(1791,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(4648,plain,
sk315 @ v14_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(15154,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)],[2268,7249]) ).
thf(15155,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)],[15154]) ).
thf(15247,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)],[15155]) ).
thf(15270,plain,
( ( sk71 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[15247]) ).
thf(813,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/sandbox/benchmark/theBenchmark.p',t66_filter_0) ).
thf(5662,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)],[813]) ).
thf(13025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,2437]) ).
thf(13026,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13025]) ).
thf(13046,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk251 )
!= ( C @ ( B @ k4_tarski ) ) ),
inference(simp,[status(thm)],[13026]) ).
thf(9042,plain,
! [A: $i] :
( ( ( sk313 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4611,7047]) ).
thf(9043,plain,
! [A: $i] :
( ( ( sk313 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[9042]) ).
thf(9044,plain,
( ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[9043:[bind(A,$thf( sk313 ))]]) ).
thf(12297,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,9044]) ).
thf(12298,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12297]) ).
thf(12405,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk313 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[12298]) ).
thf(12454,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[12405]) ).
thf(1008,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_filter_2 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_filter_2) ).
thf(6501,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_filter_2 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(15229,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2268,9038]) ).
thf(15230,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15229]) ).
thf(15251,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk313 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[15230]) ).
thf(15275,plain,
( ( sk313 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[15251]) ).
thf(426,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/sandbox/benchmark/theBenchmark.p',redefinition_k12_filter_2) ).
thf(3671,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)],[426]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',t31_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 ) )
=> ( ( ( 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)],[176]) ).
thf(436,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/sandbox/benchmark/theBenchmark.p',t5_lattice2) ).
thf(3723,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)],[436]) ).
thf(8140,plain,
( ( ( sk14 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,1218]) ).
thf(8141,plain,
( ( sk14 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8140]) ).
thf(8148,plain,
sk14 != k1_xboole_0,
inference(simp,[status(thm)],[8141]) ).
thf(31539,plain,
! [A: $i] :
( ( A != sk14 )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,8148]) ).
thf(31540,plain,
! [A: $i] :
( ( A != sk14 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[31539]) ).
thf(31541,plain,
sk14 @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[31540:[bind(A,$thf( sk14 ))]]) ).
thf(44047,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ sk18 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31541,1230]) ).
thf(44048,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ sk18 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[44047]) ).
thf(44049,plain,
! [A: $i] : ( A @ ( sk14 @ sk18 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[44048:[bind(A,$thf( A )),bind(B,$thf( sk14 @ sk18 ))]]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',t26_relset_1) ).
thf(2666,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)],[264]) ).
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/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(1644,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(954,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/sandbox/benchmark/theBenchmark.p',t75_filter_0) ).
thf(6275,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)],[954]) ).
thf(2472,plain,
~ ( k13_nat_lat @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2469]) ).
thf(519,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/sandbox/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).
thf(4180,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)],[519]) ).
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/sandbox/benchmark/theBenchmark.p',t5_funct_2) ).
thf(1035,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(1036,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)],[1035]) ).
thf(1039,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)],[1036]) ).
thf(12311,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,8777]) ).
thf(12312,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12311]) ).
thf(12408,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk216 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12312]) ).
thf(920,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/sandbox/benchmark/theBenchmark.p',d17_lattices) ).
thf(6097,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)],[920]) ).
thf(746,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/sandbox/benchmark/theBenchmark.p',t49_filter_2) ).
thf(5374,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)],[746]) ).
thf(1974,plain,
sk71 @ v2_funct_1,
inference(cnfConj,[status(thm)],[1971]) ).
thf(454,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/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(3819,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)],[454]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',s2_domain_1) ).
thf(2006,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)],[159]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(2813,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)],[286]) ).
thf(850,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/sandbox/benchmark/theBenchmark.p',t29_filter_2) ).
thf(5823,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)],[850]) ).
thf(472,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(3920,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(3083,plain,
sk197 @ v1_lattice2,
inference(cnfConj,[status(thm)],[3070]) ).
thf(975,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/sandbox/benchmark/theBenchmark.p',t34_lattice2) ).
thf(6349,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)],[975]) ).
thf(882,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/sandbox/benchmark/theBenchmark.p',t45_lattices) ).
thf(5947,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)],[882]) ).
thf(649,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/sandbox/benchmark/theBenchmark.p',d5_lattices) ).
thf(4846,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)],[649]) ).
thf(29692,plain,
! [A: $i] :
( ( A != sk71 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,12943]) ).
thf(29693,plain,
! [A: $i] :
( ( A != sk71 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[29692]) ).
thf(29694,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( sk71 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29693:[bind(A,$thf( sk71 ))]]) ).
thf(396,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/sandbox/benchmark/theBenchmark.p',d15_binop_1) ).
thf(3486,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)],[396]) ).
thf(12351,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,7252]) ).
thf(12352,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12351]) ).
thf(12410,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12352]) ).
thf(585,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/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(4508,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)],[585]) ).
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/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).
thf(1368,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(1369,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)],[1368]) ).
thf(1370,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)],[1369]) ).
thf(1377,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1370]) ).
thf(1381,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk25 ) @ k1_relat_1 )
= B )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1377]) ).
thf(1382,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk25 ) @ k1_relat_1 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1381]) ).
thf(254,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(2598,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(3059,plain,
sk196 @ v8_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(748,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/sandbox/benchmark/theBenchmark.p',t25_lattice4) ).
thf(5380,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)],[748]) ).
thf(29393,plain,
! [A: $i] :
( ( A != sk187 )
| ( k1_xboole_0 @ v7_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,2953]) ).
thf(29394,plain,
( ( k1_xboole_0 @ v7_lattices )
| ( sk187 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29393:[bind(A,$thf( sk187 ))]]) ).
thf(668,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(4970,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)],[668]) ).
thf(698,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/sandbox/benchmark/theBenchmark.p',d20_binop_1) ).
thf(5134,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)],[698]) ).
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/sandbox/benchmark/theBenchmark.p',d9_binop_1) ).
thf(1799,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(475,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(3937,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)],[475]) ).
thf(840,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/sandbox/benchmark/theBenchmark.p',d10_filter_2) ).
thf(5766,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)],[840]) ).
thf(6346,plain,
sk454 @ l3_lattices,
inference(cnfConj,[status(thm)],[6345]) ).
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 @ 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/sandbox/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(5683,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)],[820]) ).
thf(430,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/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(3692,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)],[430]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',t175_partfun1) ).
thf(2697,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)],[272]) ).
thf(3064,plain,
sk196 @ v10_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(800,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/sandbox/benchmark/theBenchmark.p',redefinition_k9_filter_2) ).
thf(5603,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)],[800]) ).
thf(535,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(4259,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
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/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(1979,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(3074,plain,
sk197 @ v10_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
thf(621,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/sandbox/benchmark/theBenchmark.p',d2_lattice4) ).
thf(4689,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)],[621]) ).
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/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(1627,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(556,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/sandbox/benchmark/theBenchmark.p',dt_k24_filter_2) ).
thf(4361,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)],[556]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(3476,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)],[393]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',d14_filter_2) ).
thf(5544,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)],[787]) ).
thf(1202,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)],[1199]) ).
thf(635,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ k1_lattice2 )
= ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice2) ).
thf(4765,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)],[635]) ).
thf(2629,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(cnf,[status(esa)],[2628]) ).
thf(2630,plain,
! [A: $i] :
( ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) )
= ( A @ k1_subset_1 ) ),
inference(lifteq,[status(thm)],[2629]) ).
thf(38935,plain,
! [A: $i] :
( ( A @ ( A @ k3_subset_1 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[2630,2547,3092]) ).
thf(459,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/sandbox/benchmark/theBenchmark.p',t15_filter_2) ).
thf(3841,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)],[459]) ).
thf(601,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/sandbox/benchmark/theBenchmark.p',t12_funct_2) ).
thf(4572,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)],[601]) ).
thf(706,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( C @ l3_lattices )
& ( C @ v13_lattices )
& ( C @ v10_lattices )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( 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/sandbox/benchmark/theBenchmark.p',t69_lattice2) ).
thf(5170,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)],[706]) ).
thf(39036,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)],[2045,3413]) ).
thf(39037,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[39036:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(39078,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[39037]) ).
thf(39140,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)],[39078,1081]) ).
thf(39141,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)],[39140]) ).
thf(39142,plain,
! [B: $i,A: $i] : ( B @ k1_tarski @ k1_zfmisc_1 @ ( A @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[39141:[bind(A,$thf( G )),bind(B,$thf( k1_xboole_0 @ k1_tarski )),bind(C,$thf( G @ k1_tarski @ k1_zfmisc_1 )),bind(D,$thf( D ))]]) ).
thf(39182,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)],[39142]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(3903,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(836,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k17_filter_2 )
= ( A @ u1_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_2) ).
thf(5747,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)],[836]) ).
thf(733,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/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).
thf(5310,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)],[733]) ).
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/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(1814,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(1086,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)],[1083]) ).
thf(541,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/sandbox/benchmark/theBenchmark.p',t61_lattice2) ).
thf(4288,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)],[541]) ).
thf(10155,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,4627]) ).
thf(10156,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10155]) ).
thf(10161,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk216 ),
inference(simp,[status(thm)],[10156]) ).
thf(24736,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)],[2045,10161]) ).
thf(24737,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk216 ),
inference(pattern_uni,[status(thm)],[24736:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(24743,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk216 ),
inference(simp,[status(thm)],[24737]) ).
thf(524,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/sandbox/benchmark/theBenchmark.p',t59_filter_0) ).
thf(4195,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)],[524]) ).
thf(599,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/sandbox/benchmark/theBenchmark.p',t80_lattice2) ).
thf(4567,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)],[599]) ).
thf(8169,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)],[3158,7019]) ).
thf(8170,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8169]) ).
thf(8171,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8170:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(15100,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8171,2268]) ).
thf(15101,plain,
( ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15100]) ).
thf(502,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/sandbox/benchmark/theBenchmark.p',d3_filter_2) ).
thf(4081,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)],[502]) ).
thf(41466,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,40997]) ).
thf(41467,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41466]) ).
thf(41474,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk295 )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41467]) ).
thf(2208,plain,
sk94 @ v5_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
thf(417,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/sandbox/benchmark/theBenchmark.p',t50_lattice4) ).
thf(3587,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)],[417]) ).
thf(3183,plain,
k6_nat_lat @ v6_lattices,
inference(cnfConj,[status(thm)],[3174]) ).
thf(577,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_domain_1) ).
thf(4476,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)],[577]) ).
thf(365,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/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
thf(3306,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)],[365]) ).
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/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(1846,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(762,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/sandbox/benchmark/theBenchmark.p',t19_filter_0) ).
thf(5434,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)],[762]) ).
thf(38322,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)],[1121,38307]) ).
thf(38323,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ sk13 ) )
= A ),
inference(pattern_uni,[status(thm)],[38322:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(948,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/sandbox/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(6260,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)],[948]) ).
thf(910,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/sandbox/benchmark/theBenchmark.p',t26_lattice2) ).
thf(6070,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)],[910]) ).
thf(6643,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,3326]) ).
thf(6644,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6643]) ).
thf(6647,plain,
sk218 != sk152,
inference(simp,[status(thm)],[6644]) ).
thf(2963,plain,
~ ( sk188 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2955]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(2365,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)],[219]) ).
thf(2366,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)],[2365]) ).
thf(2368,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_relat_1 ),
inference(cnfConj,[status(thm)],[2366]) ).
thf(1068,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)],[1067]) ).
thf(1071,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)],[1068]) ).
thf(984,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ 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/sandbox/benchmark/theBenchmark.p',t18_filter_2) ).
thf(6378,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)],[984]) ).
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/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(1184,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(1185,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)],[1184]) ).
thf(1186,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)],[1185]) ).
thf(1187,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)],[1186]) ).
thf(4904,plain,
! [A: $i] :
( ( ( ( A @ ( sk339 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s12_funct_2 ) )
| ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk337 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk339 @ m2_relset_1 ) ) )
| ~ sk337 )
& ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk339 @ v1_funct_2 ) ) )
| ~ sk337 )
& ( ( sk339 @ v1_funct_1 )
| ~ sk337 )
& ( sk337
| ~ ( f2_s12_funct_2 @ ( sk338 @ f3_s12_funct_2 @ r2_hidden ) ) )
& ( sk337
| ( f1_s12_funct_2 @ ( sk338 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4903]) ).
thf(4906,plain,
( sk337
| ( f1_s12_funct_2 @ ( sk338 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4904]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fc2_realset1) ).
thf(2440,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)],[232]) ).
thf(711,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/sandbox/benchmark/theBenchmark.p',t77_lattice2) ).
thf(5209,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)],[711]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',cc3_lattice2) ).
thf(2089,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)],[177]) ).
thf(400,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/sandbox/benchmark/theBenchmark.p',t49_filter_0) ).
thf(3508,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)],[400]) ).
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/sandbox/benchmark/theBenchmark.p',t115_funct_2) ).
thf(1895,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(195,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/sandbox/benchmark/theBenchmark.p',t25_funct_2) ).
thf(2189,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)],[195]) ).
thf(903,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/sandbox/benchmark/theBenchmark.p',t65_filter_0) ).
thf(6038,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)],[903]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',t32_lattice2) ).
thf(1996,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)],[157]) ).
thf(544,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/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
thf(4308,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)],[544]) ).
thf(2423,plain,
sk118 @ v4_lattices,
inference(cnfConj,[status(thm)],[2413]) ).
thf(815,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/sandbox/benchmark/theBenchmark.p',t38_filter_2) ).
thf(5666,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)],[815]) ).
thf(268,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/sandbox/benchmark/theBenchmark.p',t7_funct_2) ).
thf(2677,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)],[268]) ).
thf(741,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/sandbox/benchmark/theBenchmark.p',t66_funct_2) ).
thf(5359,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)],[741]) ).
thf(4657,plain,
sk315 @ v3_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(597,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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(4562,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)],[597]) ).
thf(906,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/sandbox/benchmark/theBenchmark.p',t39_lattices) ).
thf(6052,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)],[906]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(2144,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)],[187]) ).
thf(937,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/sandbox/benchmark/theBenchmark.p',t21_lattice2) ).
thf(6192,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) )
= C ) )
=> ( B
= ( A @ k5_lattices ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(980,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/sandbox/benchmark/theBenchmark.p',t5_filter_0) ).
thf(6368,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)],[980]) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',t119_funct_2) ).
thf(2936,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)],[301]) ).
thf(782,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/sandbox/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
thf(5524,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)],[782]) ).
thf(15409,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ 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)],[5602,1130]) ).
thf(15410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ m2_relset_1 ) ) )
!= ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
| ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[15409]) ).
thf(15411,plain,
( ( f1_s11_funct_2 @ ( sk402 @ k1_relat_1 @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[15410:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk402 ))]]) ).
thf(16645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s11_funct_2 @ ( sk402 @ 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)],[15411,1081]) ).
thf(16646,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f1_s11_funct_2 @ ( sk402 @ 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)],[16645]) ).
thf(16647,plain,
! [A: $i] :
( ( f1_s11_funct_2 @ ( A @ ( sk402 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(pattern_uni,[status(thm)],[16646:[bind(A,$thf( sk402 @ k1_relat_1 )),bind(B,$thf( f1_s11_funct_2 )),bind(C,$thf( C ))]]) ).
thf(16694,plain,
! [A: $i] :
( ( f1_s11_funct_2 @ ( A @ ( sk402 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(simp,[status(thm)],[16647]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relat_1) ).
thf(2292,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)],[209]) ).
thf(899,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/sandbox/benchmark/theBenchmark.p',t44_lattices) ).
thf(6026,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)],[899]) ).
thf(8743,plain,
( ( ( sk361 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,5153]) ).
thf(8744,plain,
( ( sk361 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8743]) ).
thf(8760,plain,
sk361 != sk216,
inference(simp,[status(thm)],[8744]) ).
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/sandbox/benchmark/theBenchmark.p',t24_partfun1) ).
thf(1680,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(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/sandbox/benchmark/theBenchmark.p',d2_binop_1) ).
thf(1698,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(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/sandbox/benchmark/theBenchmark.p',fc6_lattice2) ).
thf(1959,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(4116,plain,
~ ( sk279 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4114]) ).
thf(18,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(1102,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1103,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(cnf,[status(esa)],[1102]) ).
thf(41070,plain,
( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,40850]) ).
thf(41071,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41070]) ).
thf(41077,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk216 ),
inference(simp,[status(thm)],[41071]) ).
thf(465,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(3890,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(33025,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)],[31541,1137]) ).
thf(33026,plain,
! [A: $i] :
( ( ( sk14 @ sk18 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[33025]) ).
thf(33027,plain,
( ( sk14 @ sk18 @ k1_relat_1 @ ( sk14 @ sk18 @ k9_relat_1 ) )
= ( sk14 @ sk18 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[33026:[bind(A,$thf( sk14 @ sk18 ))]]) ).
thf(655,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/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
thf(4874,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)],[655]) ).
thf(916,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/sandbox/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(6084,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)],[916]) ).
thf(715,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(5230,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)],[715]) ).
thf(3079,plain,
sk197 @ v4_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
thf(29347,plain,
! [A: $i] :
( ( A != sk344 )
| ( k1_xboole_0 @ v3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,4960]) ).
thf(29348,plain,
( ( k1_xboole_0 @ v3_lattices )
| ( sk344 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29347:[bind(A,$thf( sk344 ))]]) ).
thf(2941,plain,
sk187 @ v13_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(27412,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)],[2045,3604]) ).
thf(27413,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[27412:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(27438,plain,
! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
inference(simp,[status(thm)],[27413]) ).
thf(38459,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)],[27438,1245]) ).
thf(38460,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)],[38459]) ).
thf(38462,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)],[38460]) ).
thf(38496,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= ( k1_xboole_0 @ k1_tarski @ ( B @ k4_xboole_0 ) ) ),
inference(simp,[status(thm)],[38462]) ).
thf(563,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/sandbox/benchmark/theBenchmark.p',d11_filter_2) ).
thf(4393,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)],[563]) ).
thf(802,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/sandbox/benchmark/theBenchmark.p',t42_filter_0) ).
thf(5608,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)],[802]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_filter_0 ) )
& ( B @ ( C @ m1_filter_0 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(6469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_filter_0 ) )
& ( B @ ( C @ m1_filter_0 ) )
& ( B @ l3_lattices )
& ( B @ v10_lattices )
& ~ ( B @ v3_struct_0 ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
& ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
& ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
& ( A = E )
& ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(464,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/sandbox/benchmark/theBenchmark.p',t56_lattice2) ).
thf(3888,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)],[464]) ).
thf(2734,plain,
sk157 @ l3_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(539,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/sandbox/benchmark/theBenchmark.p',t15_subset_1) ).
thf(4269,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)],[539]) ).
thf(810,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/sandbox/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(5647,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)],[810]) ).
thf(429,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/sandbox/benchmark/theBenchmark.p',d20_lattices) ).
thf(3686,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)],[429]) ).
thf(839,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/sandbox/benchmark/theBenchmark.p',d21_lattices) ).
thf(5758,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)],[839]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(4365,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)],[557]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',t39_subset_1) ).
thf(2524,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)],[242]) ).
thf(379,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/sandbox/benchmark/theBenchmark.p',t61_funct_2) ).
thf(3396,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)],[379]) ).
thf(754,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/sandbox/benchmark/theBenchmark.p',t88_filter_0) ).
thf(5400,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)],[754]) ).
thf(5594,plain,
( ( ( f3_s11_funct_2 @ ( sk402 @ ( 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)],[5590]) ).
thf(5598,plain,
( ( ( f3_s11_funct_2 @ ( sk402 @ ( 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)],[5594]) ).
thf(717,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(5241,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
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/sandbox/benchmark/theBenchmark.p',t131_funct_2) ).
thf(1154,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(487,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/sandbox/benchmark/theBenchmark.p',l48_filter_2) ).
thf(4000,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)],[487]) ).
thf(1006,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k2_lattice4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattice4) ).
thf(6493,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
& ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( B @ ( A @ k2_lattice4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(289,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/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
thf(2859,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)],[289]) ).
thf(11614,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk71 ) ),
inference(paramod_ordered,[status(thm)],[1953,7556]) ).
thf(11615,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk71 ),
inference(pattern_uni,[status(thm)],[11614:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(2981,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)],[307]) ).
thf(695,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_filter_2) ).
thf(5121,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)],[695]) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1370]) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_relat_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1376]) ).
thf(1388,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_relat_1 ),
inference(simp,[status(thm)],[1387]) ).
thf(804,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v11_lattices ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_0) ).
thf(5612,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)],[804]) ).
thf(467,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/sandbox/benchmark/theBenchmark.p',t22_lattice4) ).
thf(3900,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)],[467]) ).
thf(1226,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)],[1225]) ).
thf(584,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/sandbox/benchmark/theBenchmark.p',t50_lattice2) ).
thf(4505,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)],[584]) ).
thf(2959,plain,
sk188 @ v9_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
thf(617,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/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(4662,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)],[617]) ).
thf(767,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/sandbox/benchmark/theBenchmark.p',t1_filter_0) ).
thf(5456,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)],[767]) ).
thf(551,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/sandbox/benchmark/theBenchmark.p',t43_lattice2) ).
thf(4341,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)],[551]) ).
thf(280,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(2727,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)],[280]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(2970,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)],[305]) ).
thf(19040,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
inference(paramod_ordered,[status(thm)],[1953,5341]) ).
thf(19041,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_tarski ),
inference(pattern_uni,[status(thm)],[19040:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(245,axiom,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(2538,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(2539,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[2538]) ).
thf(19086,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ),
inference(rewrite,[status(thm)],[19041,2539]) ).
thf(773,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/sandbox/benchmark/theBenchmark.p',t90_filter_0) ).
thf(5474,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)],[773]) ).
thf(399,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/sandbox/benchmark/theBenchmark.p',t33_filter_2) ).
thf(3504,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)],[399]) ).
thf(540,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/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).
thf(4283,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)],[540]) ).
thf(963,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_lattices) ).
thf(6312,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
= ( A @ k5_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(22327,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)],[22284,1081]) ).
thf(22328,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)],[22327]) ).
thf(22329,plain,
! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[22328:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk216 @ k9_relat_1 ) )),bind(C,$thf( sk216 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(22377,plain,
! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[22329]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',t49_funct_2) ).
thf(2393,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)],[223]) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(3086,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)],[325]) ).
thf(438,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/sandbox/benchmark/theBenchmark.p',t32_partfun1) ).
thf(3736,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)],[438]) ).
thf(3081,plain,
sk197 @ v5_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_realset1) ).
thf(2674,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(41020,plain,
( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,40850]) ).
thf(41021,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41020]) ).
thf(41082,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[41021]) ).
thf(42048,plain,
! [A: $i] :
( ( A
!= ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,41082]) ).
thf(42049,plain,
! [A: $i] :
( ( A
!= ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[42048]) ).
thf(42050,plain,
sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[42049:[bind(A,$thf( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ))]]) ).
thf(866,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/sandbox/benchmark/theBenchmark.p',d4_filter_0) ).
thf(5876,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)],[866]) ).
thf(892,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).
thf(5984,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)],[892]) ).
thf(687,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/sandbox/benchmark/theBenchmark.p',t32_filter_0) ).
thf(5097,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)],[687]) ).
thf(8594,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)],[1065,8524]) ).
thf(8595,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)],[8594]) ).
thf(8597,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)],[8595]) ).
thf(8605,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)],[8597]) ).
thf(37988,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)],[8605,3207]) ).
thf(37989,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)],[37988]) ).
thf(37990,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)],[2072,37989]) ).
thf(37991,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)],[37990]) ).
thf(38157,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)],[37991]) ).
thf(38187,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)],[38157]) ).
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 ) )
=> ( ! [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/sandbox/benchmark/theBenchmark.p',t57_lattice2) ).
thf(4381,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)],[560]) ).
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 ) )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',t64_filter_2) ).
thf(6407,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)],[989]) ).
thf(716,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/sandbox/benchmark/theBenchmark.p',t41_subset_1) ).
thf(5239,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)],[716]) ).
thf(41464,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,40997]) ).
thf(41465,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41464]) ).
thf(41473,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk152 )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41465]) ).
thf(4612,plain,
f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ v1_funct_2 ) ),
inference(cnfConj,[status(thm)],[4610]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(1122,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(1123,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[1122]) ).
thf(1124,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1123]) ).
thf(43981,plain,
! [B: $i,A: $i] :
( ( ( sk216 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3314,1230]) ).
thf(43982,plain,
! [B: $i,A: $i] :
( ( ( sk216 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[43981]) ).
thf(43983,plain,
! [A: $i] : ( A @ ( sk216 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[43982:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',t5_relat_1) ).
thf(2220,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)],[198]) ).
thf(504,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/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).
thf(4096,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)],[504]) ).
thf(772,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/sandbox/benchmark/theBenchmark.p',t48_filter_0) ).
thf(5471,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)],[772]) ).
thf(5086,plain,
sk357 @ l2_struct_0,
inference(cnf,[status(esa)],[5085]) ).
thf(1088,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)],[1083]) ).
thf(1092,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)],[1088]) ).
thf(1087,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)],[1083]) ).
thf(1090,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)],[1087]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(2161,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)],[192]) ).
thf(534,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/sandbox/benchmark/theBenchmark.p',t82_lattice2) ).
thf(4251,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)],[534]) ).
thf(588,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/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(4526,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)],[588]) ).
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/sandbox/benchmark/theBenchmark.p',t11_binop_1) ).
thf(1503,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(680,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/sandbox/benchmark/theBenchmark.p',t9_filter_0) ).
thf(5039,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)],[680]) ).
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/sandbox/benchmark/theBenchmark.p',t31_funct_2) ).
thf(1669,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(3077,plain,
sk197 @ v9_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
thf(643,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/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).
thf(4796,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)],[643]) ).
thf(977,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ 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/sandbox/benchmark/theBenchmark.p',t42_filter_2) ).
thf(6357,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)],[977]) ).
thf(38437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk349 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4983,1245]) ).
thf(38438,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk349 @ ( A @ r2_hidden ) )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[38437]) ).
thf(38466,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk349 )
!= ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[38438]) ).
thf(38476,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= ( B @ sk349 ) ),
inference(simp,[status(thm)],[38466]) ).
thf(1016,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(6532,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)],[1016]) ).
thf(431,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/sandbox/benchmark/theBenchmark.p',t53_filter_0) ).
thf(3695,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)],[431]) ).
thf(2738,plain,
sk157 @ v4_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(510,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/sandbox/benchmark/theBenchmark.p',t167_funct_2) ).
thf(4149,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)],[510]) ).
thf(727,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(5282,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)],[727]) ).
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 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_lattice4) ).
thf(6091,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)],[918]) ).
thf(1058,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)],[1057]) ).
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 @ ( 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/sandbox/benchmark/theBenchmark.p',d5_filter_0) ).
thf(4060,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)],[499]) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',t70_partfun1) ).
thf(2706,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)],[275]) ).
thf(422,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/sandbox/benchmark/theBenchmark.p',t60_lattice2) ).
thf(3641,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)],[422]) ).
thf(925,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/sandbox/benchmark/theBenchmark.p',t19_lattices) ).
thf(6123,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)],[925]) ).
thf(945,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/sandbox/benchmark/theBenchmark.p',d19_lattices) ).
thf(6248,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)],[945]) ).
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/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(1258,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(842,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/sandbox/benchmark/theBenchmark.p',t72_filter_0) ).
thf(5784,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)],[842]) ).
thf(2474,plain,
k13_nat_lat @ v7_lattices,
inference(cnfConj,[status(thm)],[2469]) ).
thf(981,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/sandbox/benchmark/theBenchmark.p',t27_filter_0) ).
thf(6372,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)],[981]) ).
thf(413,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/sandbox/benchmark/theBenchmark.p',l59_filter_2) ).
thf(3568,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)],[413]) ).
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/sandbox/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(1638,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(374,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/sandbox/benchmark/theBenchmark.p',fc4_lattice2) ).
thf(3355,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)],[374]) ).
thf(761,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/sandbox/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(5432,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)],[761]) ).
thf(342,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/sandbox/benchmark/theBenchmark.p',t55_subset_1) ).
thf(3170,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)],[342]) ).
thf(29509,plain,
! [A: $i] :
( ( A != sk157 )
| ( k1_xboole_0 @ v9_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,2740]) ).
thf(29510,plain,
( ( k1_xboole_0 @ v9_lattices )
| ( sk157 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29509:[bind(A,$thf( sk157 ))]]) ).
thf(1194,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)],[1192]) ).
thf(43902,plain,
! [B: $i,A: $i] :
( ( ( sk152 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2659,1230]) ).
thf(43903,plain,
! [B: $i,A: $i] :
( ( ( sk152 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[43902]) ).
thf(43904,plain,
! [A: $i] : ( A @ ( sk152 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[43903:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).
thf(2415,plain,
sk118 @ v8_lattices,
inference(cnfConj,[status(thm)],[2413]) ).
thf(857,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/sandbox/benchmark/theBenchmark.p',t28_lattice2) ).
thf(5848,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)],[857]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',t9_lattice2) ).
thf(2669,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)],[265]) ).
thf(864,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/sandbox/benchmark/theBenchmark.p',t78_filter_0) ).
thf(5870,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)],[864]) ).
thf(641,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/sandbox/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(4790,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)],[641]) ).
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/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
thf(1282,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(2478,plain,
k13_nat_lat @ v6_lattices,
inference(cnfConj,[status(thm)],[2469]) ).
thf(355,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/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(3251,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)],[355]) ).
thf(2214,plain,
sk94 @ v10_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
thf(718,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/sandbox/benchmark/theBenchmark.p',t83_lattice2) ).
thf(5244,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)],[718]) ).
thf(409,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/sandbox/benchmark/theBenchmark.p',t18_lattice2) ).
thf(3551,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)],[409]) ).
thf(2422,plain,
sk118 @ l3_lattices,
inference(cnfConj,[status(thm)],[2413]) ).
thf(543,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/sandbox/benchmark/theBenchmark.p',redefinition_k4_filter_2) ).
thf(4305,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)],[543]) ).
thf(1113,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)],[1111]) ).
thf(1117,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)],[1113]) ).
thf(927,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( ( 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/sandbox/benchmark/theBenchmark.p',t74_filter_0) ).
thf(6147,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)],[927]) ).
thf(44088,plain,
! [B: $i,A: $i] :
( ( ( sk71 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1972,1230]) ).
thf(44089,plain,
! [B: $i,A: $i] :
( ( ( sk71 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[44088]) ).
thf(44090,plain,
! [A: $i] : ( A @ ( sk71 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[44089:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).
thf(1047,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)],[1046]) ).
thf(1048,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)],[1047]) ).
thf(922,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_filter_0) ).
thf(6112,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)],[922]) ).
thf(731,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(5303,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)],[731]) ).
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/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
thf(1933,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(870,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/sandbox/benchmark/theBenchmark.p',t62_filter_0) ).
thf(5901,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)],[870]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(3106,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)],[329]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(2116,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)],[182]) ).
thf(803,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_2) ).
thf(5610,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)],[803]) ).
thf(2943,plain,
sk187 @ v10_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(7493,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)],[1063,7130]) ).
thf(7494,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)],[7493]) ).
thf(7514,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)],[7494]) ).
thf(7529,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)],[7514]) ).
thf(7882,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)],[7529,1972]) ).
thf(7883,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)],[7882]) ).
thf(12981,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2072,7883]) ).
thf(12982,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12981]) ).
thf(12993,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12982]) ).
thf(13005,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12993]) ).
thf(756,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/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(5407,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)],[756]) ).
thf(2945,plain,
sk187 @ v8_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(607,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/sandbox/benchmark/theBenchmark.p',t7_filter_2) ).
thf(4616,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)],[607]) ).
thf(1041,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)],[1036]) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ sk3 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ r2_hidden ) )
| ~ ( C @ v1_funct_1 )
| ~ ( C @ v1_relat_1 )
| ( ( C @ k1_relat_1 )
!= A ) ),
inference(lifteq,[status(thm)],[1041]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ k1_relat_1 @ ( B @ sk3 ) ) )
| ( B @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ ( B @ sk4 ) ) @ r2_hidden ) )
| ~ ( B @ v1_funct_1 )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[1042]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(2856,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)],[288]) ).
thf(29581,plain,
! [A: $i] :
( ( A != k13_nat_lat )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,6291]) ).
thf(29582,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( k13_nat_lat @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29581:[bind(A,$thf( k13_nat_lat ))]]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(3138,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)],[335]) ).
thf(3182,plain,
k6_nat_lat @ v9_lattices,
inference(cnfConj,[status(thm)],[3174]) ).
thf(3066,plain,
~ ( sk196 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[3054]) ).
thf(294,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/sandbox/benchmark/theBenchmark.p',cc1_lattice2) ).
thf(2896,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)],[294]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [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/sandbox/benchmark/theBenchmark.p',t2_realset1) ).
thf(3160,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)],[339]) ).
thf(940,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/sandbox/benchmark/theBenchmark.p',t82_filter_0) ).
thf(6216,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)],[940]) ).
thf(1166,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)],[1165]) ).
thf(1175,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)],[1166]) ).
thf(848,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/sandbox/benchmark/theBenchmark.p',t72_lattice2) ).
thf(5816,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)],[848]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ 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/sandbox/benchmark/theBenchmark.p',d2_realset1) ).
thf(2025,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)],[163]) ).
thf(3055,plain,
sk196 @ v14_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(763,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/sandbox/benchmark/theBenchmark.p',t71_filter_0) ).
thf(5439,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)],[763]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',t9_domain_1) ).
thf(2446,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)],[233]) ).
thf(15065,plain,
! [B: $i,A: $i] :
( ( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2124,3032]) ).
thf(15066,plain,
! [B: $i,A: $i] :
( ( A @ sk80 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[15065]) ).
thf(15081,plain,
! [B: $i,A: $i] :
( ( ( A @ sk80 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[15066]) ).
thf(15088,plain,
! [A: $i] :
( ( A @ sk80 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[15081]) ).
thf(31844,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk80 ) )
| ( k1_xboole_0 != k1_xboole_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,15088]) ).
thf(31845,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk80 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[31844]) ).
thf(31846,plain,
! [A: $i] : ( A @ sk80 @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[31845:[bind(A,$thf( C @ sk80 )),bind(B,$thf( C ))]]) ).
thf(32471,plain,
! [A: $i] : ( A @ sk80 @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[31846]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(1838,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(613,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4635,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(692,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/sandbox/benchmark/theBenchmark.p',dt_k3_lattice2) ).
thf(5114,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)],[692]) ).
thf(930,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/sandbox/benchmark/theBenchmark.p',dt_k2_filter_2) ).
thf(6165,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)],[930]) ).
thf(679,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/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(5035,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)],[679]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(3740,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)],[439]) ).
thf(3741,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)],[3740]) ).
thf(3742,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)],[3741]) ).
thf(3743,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[3742]) ).
thf(3746,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r1_tarski ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[3743]) ).
thf(3747,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(simp,[status(thm)],[3746]) ).
thf(13027,plain,
! [A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,3326]) ).
thf(13028,plain,
! [A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13027]) ).
thf(13050,plain,
! [A: $i] :
( ( A @ sk251 )
!= sk218 ),
inference(simp,[status(thm)],[13028]) ).
thf(2742,plain,
sk157 @ v10_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(568,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/sandbox/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(4445,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)],[568]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(2129,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)],[184]) ).
thf(15181,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)],[2268,7133]) ).
thf(15182,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)],[15181]) ).
thf(15237,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)],[15182]) ).
thf(15259,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15237]) ).
thf(830,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/sandbox/benchmark/theBenchmark.p',t26_filter_0) ).
thf(5730,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)],[830]) ).
thf(868,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/sandbox/benchmark/theBenchmark.p',d9_filter_2) ).
thf(5894,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)],[868]) ).
thf(41148,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,40941]) ).
thf(41149,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41148]) ).
thf(41157,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk152 ),
inference(simp,[status(thm)],[41149]) ).
thf(600,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/sandbox/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
thf(4569,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)],[600]) ).
thf(893,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/sandbox/benchmark/theBenchmark.p',t10_filter_0) ).
thf(5994,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)],[893]) ).
thf(3073,plain,
sk197 @ v8_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
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/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(1630,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(7563,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,5226]) ).
thf(7564,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7563]) ).
thf(7566,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk152 ),
inference(simp,[status(thm)],[7564]) ).
thf(414,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/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(3572,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)],[414]) ).
thf(658,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/sandbox/benchmark/theBenchmark.p',t18_funct_2) ).
thf(4897,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)],[658]) ).
thf(1162,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)],[1160]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(4452,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)],[571]) ).
thf(966,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/sandbox/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
thf(6319,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)],[966]) ).
thf(914,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/sandbox/benchmark/theBenchmark.p',t30_lattice2) ).
thf(6080,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)],[914]) ).
thf(364,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/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
thf(3298,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)],[364]) ).
thf(4652,plain,
sk315 @ v10_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(542,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/sandbox/benchmark/theBenchmark.p',d14_lattice4) ).
thf(4296,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)],[542]) ).
thf(44056,plain,
! [B: $i,A: $i] :
( ( ( sk138 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2542,1230]) ).
thf(44057,plain,
! [B: $i,A: $i] :
( ( ( sk138 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[44056]) ).
thf(44058,plain,
! [A: $i] : ( A @ ( sk138 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[44057:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).
thf(395,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/sandbox/benchmark/theBenchmark.p',redefinition_k21_filter_2) ).
thf(3483,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)],[395]) ).
thf(479,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/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
thf(3971,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)],[479]) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(1344,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(630,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/sandbox/benchmark/theBenchmark.p',t113_funct_2) ).
thf(4726,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)],[630]) ).
thf(6551,plain,
( ( ( sk71 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,1218]) ).
thf(6552,plain,
( ( sk71 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6551]) ).
thf(6553,plain,
sk71 != sk14,
inference(simp,[status(thm)],[6552]) ).
thf(12309,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,7133]) ).
thf(12310,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12309]) ).
thf(12381,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk138 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12310]) ).
thf(619,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/sandbox/benchmark/theBenchmark.p',t47_lattice4) ).
thf(4684,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)],[619]) ).
thf(1060,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)],[1057]) ).
thf(1061,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)],[1060]) ).
thf(296,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/sandbox/benchmark/theBenchmark.p',t33_subset_1) ).
thf(2911,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)],[296]) ).
thf(596,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(4554,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)],[596]) ).
thf(983,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_filter_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_2) ).
thf(6376,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)],[983]) ).
thf(29389,plain,
! [A: $i] :
( ( A != sk197 )
| ( k1_xboole_0 @ v6_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,3072]) ).
thf(29390,plain,
( ( k1_xboole_0 @ v6_lattices )
| ( sk197 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29389:[bind(A,$thf( sk197 ))]]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(2350,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)],[216]) ).
thf(775,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( 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/sandbox/benchmark/theBenchmark.p',t35_filter_2) ).
thf(5482,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)],[775]) ).
thf(450,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/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(3806,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)],[450]) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',t13_lattice2) ).
thf(2535,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)],[244]) ).
thf(2207,plain,
sk94 @ v7_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
thf(900,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/sandbox/benchmark/theBenchmark.p',dt_k3_filter_2) ).
thf(6029,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)],[900]) ).
thf(8001,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,3127]) ).
thf(8002,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8001]) ).
thf(8007,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= sk71 ),
inference(simp,[status(thm)],[8002]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(2075,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)],[173]) ).
thf(2418,plain,
sk118 @ v9_lattices,
inference(cnfConj,[status(thm)],[2413]) ).
thf(664,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(4933,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)],[664]) ).
thf(946,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
= ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_lattices) ).
thf(6255,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)],[946]) ).
thf(645,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/sandbox/benchmark/theBenchmark.p',dt_k3_lattices) ).
thf(4832,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)],[645]) ).
thf(628,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/sandbox/benchmark/theBenchmark.p',t52_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 @ ( 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)],[628]) ).
thf(24701,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 )
!= sk295 ) ),
inference(paramod_ordered,[status(thm)],[2045,10165]) ).
thf(24702,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk295 ),
inference(pattern_uni,[status(thm)],[24701:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(24757,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk295 ),
inference(simp,[status(thm)],[24702]) ).
thf(231,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relat_1) ).
thf(2438,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(2439,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(cnf,[status(esa)],[2438]) ).
thf(2962,plain,
sk188 @ v5_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
thf(877,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/sandbox/benchmark/theBenchmark.p',t10_filter_2) ).
thf(5931,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)],[877]) ).
thf(279,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(2725,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(745,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/sandbox/benchmark/theBenchmark.p',t41_lattice2) ).
thf(5372,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)],[745]) ).
thf(764,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/sandbox/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(5442,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)],[764]) ).
thf(2212,plain,
sk94 @ v4_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
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/sandbox/benchmark/theBenchmark.p',t174_partfun1) ).
thf(1208,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(1209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
!= ( C @ k1_tarski ) )
| ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) )
| ~ ( C @ v1_funct_1 ) )
& ( ( ( 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)],[1208]) ).
thf(1211,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)],[1209]) ).
thf(1213,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)],[1211]) ).
thf(442,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/sandbox/benchmark/theBenchmark.p',t37_filter_2) ).
thf(3759,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)],[442]) ).
thf(458,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/sandbox/benchmark/theBenchmark.p',redefinition_k16_filter_2) ).
thf(3838,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)],[458]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(1445,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(2369,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_funct_1 ),
inference(cnfConj,[status(thm)],[2366]) ).
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 ) )
=> ( ! [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/sandbox/benchmark/theBenchmark.p',t62_lattice2) ).
thf(3674,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)],[427]) ).
thf(354,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/sandbox/benchmark/theBenchmark.p',t8_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 ) )
=> ( ( 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)],[354]) ).
thf(888,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/sandbox/benchmark/theBenchmark.p',t7_lattice4) ).
thf(5976,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)],[888]) ).
thf(661,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(4918,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)],[661]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',t51_partfun1) ).
thf(2022,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)],[162]) ).
thf(665,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/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(4954,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)],[665]) ).
thf(304,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
thf(2967,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)],[304]) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',t65_partfun1) ).
thf(2390,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)],[222]) ).
thf(729,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/sandbox/benchmark/theBenchmark.p',dt_k14_filter_2) ).
thf(5299,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)],[729]) ).
thf(29414,plain,
! [A: $i] :
( ( A != sk467 )
| ( k1_xboole_0 @ l3_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,6505]) ).
thf(29415,plain,
( ( k1_xboole_0 @ l3_lattices )
| ( sk467 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29414:[bind(A,$thf( sk467 ))]]) ).
thf(934,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/sandbox/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(6180,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)],[934]) ).
thf(401,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/sandbox/benchmark/theBenchmark.p',d16_nat_lat) ).
thf(3512,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)],[401]) ).
thf(3178,plain,
k6_nat_lat @ v8_lattices,
inference(cnfConj,[status(thm)],[3174]) ).
thf(1004,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v1_lattice2 )
<=> ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lattice2) ).
thf(6485,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) )
=> ( A @ v1_lattice2 ) )
& ( ( A @ v1_lattice2 )
=> ( ( A @ v13_lattices )
& ( A @ v3_filter_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(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/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(1694,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(579,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/sandbox/benchmark/theBenchmark.p',dt_k5_lattice4) ).
thf(4481,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)],[579]) ).
thf(512,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/sandbox/benchmark/theBenchmark.p',t45_lattice4) ).
thf(4158,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)],[512]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',t158_relat_1) ).
thf(2069,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)],[170]) ).
thf(29521,plain,
! [A: $i] :
( ( A != sk138 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,13640]) ).
thf(29522,plain,
! [A: $i] :
( ( A != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[29521]) ).
thf(29523,plain,
( ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ( sk138 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29522:[bind(A,$thf( sk138 ))]]) ).
thf(547,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/sandbox/benchmark/theBenchmark.p',t58_lattice2) ).
thf(4331,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)],[547]) ).
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/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).
thf(1948,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(1030,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)],[1028]) ).
thf(1033,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)],[1030]) ).
thf(1034,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)],[1033]) ).
thf(2952,plain,
sk187 @ v4_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(572,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/sandbox/benchmark/theBenchmark.p',t17_filter_2) ).
thf(4458,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)],[572]) ).
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/sandbox/benchmark/theBenchmark.p',d10_binop_1) ).
thf(1467,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(2471,plain,
k13_nat_lat @ v3_lattices,
inference(cnfConj,[status(thm)],[2469]) ).
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/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(1420,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(589,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/sandbox/benchmark/theBenchmark.p',t17_lattices) ).
thf(4529,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)],[589]) ).
thf(1133,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)],[1132]) ).
thf(1134,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)],[1133]) ).
thf(390,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/sandbox/benchmark/theBenchmark.p',t63_partfun1) ).
thf(3455,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)],[390]) ).
thf(361,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/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(3278,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)],[361]) ).
thf(516,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/sandbox/benchmark/theBenchmark.p',t19_lattice4) ).
thf(4168,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)],[516]) ).
thf(8488,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)],[3207,1050]) ).
thf(8489,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)],[8488]) ).
thf(8490,plain,
! [A: $i] : ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8489:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).
thf(15570,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)],[3207,1137]) ).
thf(15571,plain,
! [A: $i] :
( ( ( sk207 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[15570]) ).
thf(15572,plain,
( ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) )
= ( sk207 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[15571:[bind(A,$thf( sk207 ))]]) ).
thf(21901,plain,
! [A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
inference(rewrite,[status(thm)],[8490,15572]) ).
thf(297,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(2914,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
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/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).
thf(1583,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(785,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/sandbox/benchmark/theBenchmark.p',t54_lattice2) ).
thf(5538,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)],[785]) ).
thf(798,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v3_filter_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_filter_0) ).
thf(5587,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)],[798]) ).
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/sandbox/benchmark/theBenchmark.p',t29_relat_1) ).
thf(1304,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(385,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(3427,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)],[385]) ).
thf(1018,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/sandbox/benchmark/theBenchmark.p',t27_filter_2) ).
thf(6540,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) )
=> ( A @ v13_lattices ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(2107,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)],[180]) ).
thf(15212,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2268,7434]) ).
thf(15213,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15212]) ).
thf(15252,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[15213]) ).
thf(15276,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[15252]) ).
thf(12289,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,8768]) ).
thf(12290,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12289]) ).
thf(12368,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12290]) ).
thf(378,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(3395,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(241,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/sandbox/benchmark/theBenchmark.p',t34_funct_2) ).
thf(2503,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)],[241]) ).
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/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(1684,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(1144,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)],[1143]) ).
thf(1145,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)],[1144]) ).
thf(555,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(4355,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)],[555]) ).
thf(7614,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)],[2543,7068]) ).
thf(7615,plain,
! [A: $i] :
( ( ( sk138 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[7614]) ).
thf(7616,plain,
( ( k1_xboole_0 @ l3_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7615:[bind(A,$thf( sk138 ))]]) ).
thf(12349,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,7616]) ).
thf(12350,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12349]) ).
thf(12377,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk138 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12350]) ).
thf(549,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/sandbox/benchmark/theBenchmark.p',dt_m1_struct_0) ).
thf(4336,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)],[549]) ).
thf(672,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/sandbox/benchmark/theBenchmark.p',t33_lattice4) ).
thf(5003,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)],[672]) ).
thf(9006,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,2437]) ).
thf(9007,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9006]) ).
thf(9022,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk295 ),
inference(simp,[status(thm)],[9007]) ).
thf(827,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/sandbox/benchmark/theBenchmark.p',dt_k9_filter_2) ).
thf(5716,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)],[827]) ).
thf(29268,plain,
! [A: $i] :
( ( A != sk138 )
| ( k1_xboole_0 @ v2_funct_1 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,2544]) ).
thf(29269,plain,
( ( k1_xboole_0 @ v2_funct_1 )
| ( sk138 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29268:[bind(A,$thf( sk138 ))]]) ).
thf(696,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/sandbox/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(5125,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)],[696]) ).
thf(774,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/sandbox/benchmark/theBenchmark.p',t85_lattice2) ).
thf(5478,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)],[774]) ).
thf(351,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/sandbox/benchmark/theBenchmark.p',cc5_lattice2) ).
thf(3214,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)],[351]) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',t57_domain_1) ).
thf(2588,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)],[252]) ).
thf(881,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/sandbox/benchmark/theBenchmark.p',d13_lattice4) ).
thf(5944,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)],[881]) ).
thf(391,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/sandbox/benchmark/theBenchmark.p',t176_partfun1) ).
thf(3462,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)],[391]) ).
thf(890,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/sandbox/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(5980,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)],[890]) ).
thf(350,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/sandbox/benchmark/theBenchmark.p',d6_realset1) ).
thf(3209,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)],[350]) ).
thf(985,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/sandbox/benchmark/theBenchmark.p',t36_lattice4) ).
thf(6384,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)],[985]) ).
thf(4658,plain,
sk315 @ l3_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(2942,plain,
sk187 @ v5_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(3988,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(978,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/sandbox/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(6362,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)],[978]) ).
thf(924,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/sandbox/benchmark/theBenchmark.p',t78_lattice2) ).
thf(6120,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)],[924]) ).
thf(88,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(1516,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(15223,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2268,8521]) ).
thf(15224,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15223]) ).
thf(15246,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[15224]) ).
thf(15269,plain,
( ( sk207 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[15246]) ).
thf(41425,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)],[1975,40997]) ).
thf(41426,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41425]) ).
thf(41471,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk71 )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41426]) ).
thf(8572,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)],[1063,8524]) ).
thf(8573,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)],[8572]) ).
thf(8596,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)],[8573]) ).
thf(8604,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)],[8596]) ).
thf(35469,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)],[8604,3207]) ).
thf(35470,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)],[35469]) ).
thf(35471,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ 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)],[2072,35470]) ).
thf(35472,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk207 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[35471]) ).
thf(35629,plain,
! [A: $i] :
( ( A != 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)],[35472]) ).
thf(35654,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)],[35629]) ).
thf(11616,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1953,8149]) ).
thf(11617,plain,
( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[11616:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(31590,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)],[1298,11617]) ).
thf(31591,plain,
! [A: $i] :
( ( A
!= ( k1_xboole_0 @ k1_tarski ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[31590]) ).
thf(31592,plain,
k1_xboole_0 @ k1_tarski @ sk18 @ v1_relat_1,
inference(pattern_uni,[status(thm)],[31591:[bind(A,$thf( k1_xboole_0 @ k1_tarski ))]]) ).
thf(33334,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)],[31592,1137]) ).
thf(33335,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski @ sk18 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[33334]) ).
thf(33336,plain,
( ( k1_xboole_0 @ k1_tarski @ sk18 @ k1_relat_1 @ ( k1_xboole_0 @ k1_tarski @ sk18 @ k9_relat_1 ) )
= ( k1_xboole_0 @ k1_tarski @ sk18 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[33335:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ sk18 ))]]) ).
thf(691,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/sandbox/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(5111,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)],[691]) ).
thf(3082,plain,
sk197 @ v3_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',t27_lattice2) ).
thf(2407,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)],[225]) ).
thf(667,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/sandbox/benchmark/theBenchmark.p',s13_funct_2) ).
thf(4961,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)],[667]) ).
thf(3058,plain,
sk196 @ l3_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(683,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/sandbox/benchmark/theBenchmark.p',t34_filter_0) ).
thf(5079,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)],[683]) ).
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/sandbox/benchmark/theBenchmark.p',t112_partfun1) ).
thf(1531,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(603,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_struct_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_struct_0) ).
thf(4593,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)],[603]) ).
thf(293,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/sandbox/benchmark/theBenchmark.p',t120_funct_2) ).
thf(2888,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)],[293]) ).
thf(250,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/sandbox/benchmark/theBenchmark.p',t11_funct_2) ).
thf(2569,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)],[250]) ).
thf(553,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/sandbox/benchmark/theBenchmark.p',d3_lattice2) ).
thf(4346,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)],[553]) ).
thf(3063,plain,
sk196 @ v3_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(1038,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)],[1036]) ).
thf(726,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/sandbox/benchmark/theBenchmark.p',t21_lattices) ).
thf(5276,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)],[726]) ).
thf(1235,plain,
! [A: $i] :
( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
| ~ ( A @ v1_funct_1 )
| ~ ( A @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1232]) ).
thf(793,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/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
thf(5560,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)],[793]) ).
thf(443,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).
thf(3769,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)],[443]) ).
thf(514,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/sandbox/benchmark/theBenchmark.p',t38_lattice2) ).
thf(4164,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)],[514]) ).
thf(3080,plain,
sk197 @ v13_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
thf(282,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/sandbox/benchmark/theBenchmark.p',d6_tarski) ).
thf(2747,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)],[282]) ).
thf(884,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/sandbox/benchmark/theBenchmark.p',t56_filter_2) ).
thf(5955,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)],[884]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',t29_lattice2) ).
thf(1987,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)],[155]) ).
thf(758,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/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
thf(5420,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)],[758]) ).
thf(31459,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,1025]) ).
thf(31460,plain,
( ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[31459:[bind(A,$thf( sk1 ))]]) ).
thf(770,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/sandbox/benchmark/theBenchmark.p',t41_filter_0) ).
thf(5467,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)],[770]) ).
thf(12291,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4613,9053]) ).
thf(12292,plain,
( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
!= ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v10_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12291]) ).
thf(12406,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk313 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12292]) ).
thf(12455,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12406]) ).
thf(446,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/sandbox/benchmark/theBenchmark.p',t46_filter_2) ).
thf(3791,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)],[446]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_partfun1) ).
thf(2700,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)],[273]) ).
thf(10147,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,4627]) ).
thf(10148,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10147]) ).
thf(10164,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) )
!= sk71 ),
inference(simp,[status(thm)],[10148]) ).
thf(792,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/sandbox/benchmark/theBenchmark.p',t43_filter_2) ).
thf(5555,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)],[792]) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',t32_funct_2) ).
thf(3202,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)],[348]) ).
thf(636,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/sandbox/benchmark/theBenchmark.p',t42_lattice4) ).
thf(4768,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)],[636]) ).
thf(2217,plain,
( ( sk95 @ v2_struct_0 )
& ( sk95 @ l2_struct_0 ) ),
inference(cnf,[status(esa)],[2216]) ).
thf(2219,plain,
sk95 @ v2_struct_0,
inference(cnfConj,[status(thm)],[2217]) ).
thf(30792,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v14_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,1026]) ).
thf(30793,plain,
( ( k1_xboole_0 @ v14_lattices )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[30792:[bind(A,$thf( sk1 ))]]) ).
thf(702,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/sandbox/benchmark/theBenchmark.p',redefinition_k11_filter_2) ).
thf(5154,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)],[702]) ).
thf(12279,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,8783]) ).
thf(12280,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12279]) ).
thf(12396,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk216 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12280]) ).
thf(1085,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)],[1083]) ).
thf(671,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(5001,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(532,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/sandbox/benchmark/theBenchmark.p',t51_lattice2) ).
thf(4241,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)],[532]) ).
thf(644,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/sandbox/benchmark/theBenchmark.p',d10_filter_0) ).
thf(4800,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)],[644]) ).
thf(412,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/sandbox/benchmark/theBenchmark.p',dt_g2_struct_0) ).
thf(3564,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)],[412]) ).
thf(8741,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,3326]) ).
thf(8742,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8741]) ).
thf(8757,plain,
sk218 != sk216,
inference(simp,[status(thm)],[8742]) ).
thf(928,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/sandbox/benchmark/theBenchmark.p',t80_filter_0) ).
thf(6159,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)],[928]) ).
thf(507,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/sandbox/benchmark/theBenchmark.p',t47_filter_2) ).
thf(4117,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)],[507]) ).
thf(14535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( A @ ( sk313 @ 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)],[14188,1081]) ).
thf(14536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( f1_s4_funct_2 @ ( A @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
!= ( C @ ( B @ r1_tarski ) ) )
| ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(simp,[status(thm)],[14535]) ).
thf(14537,plain,
! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14536:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f1_s4_funct_2 )),bind(D,$thf( D ))]]) ).
thf(14567,plain,
! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14537]) ).
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/sandbox/benchmark/theBenchmark.p',d2_funct_2) ).
thf(1738,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(320,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/sandbox/benchmark/theBenchmark.p',t33_partfun1) ).
thf(3041,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)],[320]) ).
thf(328,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/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).
thf(3095,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)],[328]) ).
thf(461,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/sandbox/benchmark/theBenchmark.p',t22_filter_2) ).
thf(3853,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)],[461]) ).
thf(992,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/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(6415,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)],[992]) ).
thf(498,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/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(4057,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)],[498]) ).
thf(30183,plain,
! [A: $i] :
( ( A != sk1 )
| ( k1_xboole_0 @ v10_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,1021]) ).
thf(30184,plain,
( ( k1_xboole_0 @ v10_lattices )
| ( sk1 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[30183:[bind(A,$thf( sk1 ))]]) ).
thf(3071,plain,
sk197 @ l3_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
thf(528,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(4217,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)],[528]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',t62_filter_2) ).
thf(2247,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)],[202]) ).
thf(734,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/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(5319,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)],[734]) ).
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/sandbox/benchmark/theBenchmark.p',t48_funct_2) ).
thf(1358,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(2948,plain,
sk187 @ l3_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(883,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ 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/sandbox/benchmark/theBenchmark.p',t25_lattice2) ).
thf(5949,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)],[883]) ).
thf(6697,plain,
( ( ( sk361 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,5153]) ).
thf(6698,plain,
( ( sk361 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6697]) ).
thf(6701,plain,
sk361 != sk71,
inference(simp,[status(thm)],[6698]) ).
thf(432,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/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).
thf(3697,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)],[432]) ).
thf(4959,plain,
sk344 @ l3_lattices,
inference(cnfConj,[status(thm)],[4958]) ).
thf(6631,plain,
( ( ( sk218 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,3326]) ).
thf(6632,plain,
( ( sk218 @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6631]) ).
thf(6633,plain,
sk218 != sk71,
inference(simp,[status(thm)],[6632]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(2558,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)],[249]) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',t67_partfun1) ).
thf(2113,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)],[181]) ).
thf(3408,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( C @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[3406]) ).
thf(3414,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
| ( A
!= ( C @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[3408]) ).
thf(3415,plain,
! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ k1_tarski @ r1_tarski ) ),
inference(simp,[status(thm)],[3414]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t4_filter_0) ).
thf(5736,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)],[832]) ).
thf(1141,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)],[1139]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',d19_binop_1) ).
thf(2426,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)],[229]) ).
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/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(1536,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(153,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(1981,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(397,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/sandbox/benchmark/theBenchmark.p',d7_lattices) ).
thf(3493,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)],[397]) ).
thf(1023,plain,
~ ( sk1 @ k6_lattices @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk2 @ ( sk1 @ k2_filter_2 ) @ ( sk1 @ u1_struct_0 @ r1_filter_2 ) ) ),
inference(cnfConj,[status(thm)],[1020]) ).
thf(949,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_lattice4) ).
thf(6262,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)],[949]) ).
thf(894,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
<=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_filter_0) ).
thf(5998,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)],[894]) ).
thf(781,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/sandbox/benchmark/theBenchmark.p',t84_lattice2) ).
thf(5504,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)],[781]) ).
thf(217,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(2357,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(2711,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)],[277]) ).
thf(766,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/sandbox/benchmark/theBenchmark.p',t83_filter_0) ).
thf(5453,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)],[766]) ).
thf(4932,plain,
sk341 @ l1_lattices,
inference(cnf,[status(esa)],[4931]) ).
thf(1140,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)],[1139]) ).
thf(623,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/sandbox/benchmark/theBenchmark.p',t6_filter_2) ).
thf(4695,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)],[623]) ).
thf(821,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/sandbox/benchmark/theBenchmark.p',t55_filter_2) ).
thf(5685,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)],[821]) ).
thf(503,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/sandbox/benchmark/theBenchmark.p',t46_lattice4) ).
thf(4093,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)],[503]) ).
thf(2949,plain,
sk187 @ v6_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(43945,plain,
! [B: $i,A: $i] :
( ( ( sk218 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3327,1230]) ).
thf(43946,plain,
! [B: $i,A: $i] :
( ( ( sk218 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[43945]) ).
thf(43947,plain,
! [A: $i] : ( A @ ( sk218 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[43946:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).
thf(538,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/sandbox/benchmark/theBenchmark.p',dt_k15_filter_2) ).
thf(4267,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)],[538]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(2030,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)],[164]) ).
thf(648,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/sandbox/benchmark/theBenchmark.p',t58_filter_0) ).
thf(4838,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)],[648]) ).
thf(944,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/sandbox/benchmark/theBenchmark.p',t14_lattice4) ).
thf(6245,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)],[944]) ).
thf(12287,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,7249]) ).
thf(12288,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12287]) ).
thf(12402,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12288]) ).
thf(1012,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/sandbox/benchmark/theBenchmark.p',d14_lattices) ).
thf(6511,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)],[1012]) ).
thf(929,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/sandbox/benchmark/theBenchmark.p',t39_filter_2) ).
thf(6161,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)],[929]) ).
thf(14446,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk313 @ 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)],[14431,1095]) ).
thf(14447,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f2_s4_funct_2 @ ( sk313 @ 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)],[14446]) ).
thf(14448,plain,
! [A: $i] : ( sk313 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[14447:[bind(A,$thf( sk313 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).
thf(14496,plain,
! [A: $i] : ( sk313 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[14448]) ).
thf(29416,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)],[1298,8150]) ).
thf(29417,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( B @ k1_funct_2 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[29416]) ).
thf(29418,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[29417:[bind(A,$thf( D @ ( D @ k1_funct_2 ) )),bind(B,$thf( D ))]]) ).
thf(32384,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[29418]) ).
thf(853,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(5841,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)],[853]) ).
thf(993,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/sandbox/benchmark/theBenchmark.p',t34_lattices) ).
thf(6420,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)],[993]) ).
thf(4392,plain,
sk299 @ l1_struct_0,
inference(cnf,[status(esa)],[4391]) ).
thf(879,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/sandbox/benchmark/theBenchmark.p',dt_k11_filter_2) ).
thf(5939,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)],[879]) ).
thf(4651,plain,
~ ( sk315 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[4645]) ).
thf(624,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/sandbox/benchmark/theBenchmark.p',t35_lattice4) ).
thf(4698,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)],[624]) ).
thf(637,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/sandbox/benchmark/theBenchmark.p',dt_k10_filter_0) ).
thf(4770,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)],[637]) ).
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/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(1553,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(987,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/sandbox/benchmark/theBenchmark.p',t60_filter_0) ).
thf(6390,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)],[987]) ).
thf(15169,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2268,9044]) ).
thf(15170,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15169]) ).
thf(15234,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk313 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[15170]) ).
thf(15255,plain,
( ( sk313 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[15234]) ).
thf(394,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/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(3478,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)],[394]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(2479,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)],[238]) ).
thf(995,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/sandbox/benchmark/theBenchmark.p',d7_filter_0) ).
thf(6425,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)],[995]) ).
thf(3067,plain,
sk196 @ v9_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(8163,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)],[3158,7004]) ).
thf(8164,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ v1_funct_1 )
!= ( A @ v1_funct_1 ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
inference(simp,[status(thm)],[8163]) ).
thf(8165,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[8164:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(15098,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[8165,2268]) ).
thf(15099,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15098]) ).
thf(784,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/sandbox/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(5536,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)],[784]) ).
thf(2960,plain,
sk188 @ v4_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
thf(1155,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)],[1154]) ).
thf(1157,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)],[1155]) ).
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 ) )
=> ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
=> ( A @ v14_lattices ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_0) ).
thf(6068,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)],[909]) ).
thf(750,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/sandbox/benchmark/theBenchmark.p',t11_filter_0) ).
thf(5386,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)],[750]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',d1_realset1) ).
thf(2078,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)],[174]) ).
thf(4656,plain,
sk315 @ v7_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).
thf(2347,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)],[215]) ).
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/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(1412,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(2215,plain,
sk94 @ v3_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
thf(41410,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,40997]) ).
thf(41411,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41410]) ).
thf(41468,plain,
( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= k1_xboole_0 )
| ( ( sk1 @ u1_struct_0 )
!= sk14 ) ),
inference(simp,[status(thm)],[41411]) ).
thf(878,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/sandbox/benchmark/theBenchmark.p',t31_filter_2) ).
thf(5934,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)],[878]) ).
thf(2209,plain,
sk94 @ v9_lattices,
inference(cnfConj,[status(thm)],[2205]) ).
thf(4646,plain,
sk315 @ v4_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(872,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/sandbox/benchmark/theBenchmark.p',t3_filter_0) ).
thf(5907,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)],[872]) ).
thf(2743,plain,
sk157 @ v3_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(15133,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2268,8774]) ).
thf(15134,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ( k1_xboole_0 @ v14_lattices )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15133]) ).
thf(15253,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 @ v14_lattices ) ),
inference(simp,[status(thm)],[15134]) ).
thf(15277,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v14_lattices ) ),
inference(simp,[status(thm)],[15253]) ).
thf(505,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/sandbox/benchmark/theBenchmark.p',t44_lattice4) ).
thf(4102,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)],[505]) ).
thf(15156,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)],[2268,8768]) ).
thf(15157,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)],[15156]) ).
thf(15240,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)],[15157]) ).
thf(15262,plain,
( ( sk216 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[15240]) ).
thf(30364,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)],[1298,8149]) ).
thf(30365,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[30364]) ).
thf(30366,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[30365:[bind(A,$thf( C @ k1_zfmisc_1 )),bind(B,$thf( C ))]]) ).
thf(32645,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[30366]) ).
thf(3056,plain,
sk196 @ v7_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(776,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/sandbox/benchmark/theBenchmark.p',t53_lattices) ).
thf(5485,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)],[776]) ).
thf(15225,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)],[2268,7616]) ).
thf(15226,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)],[15225]) ).
thf(15245,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)],[15226]) ).
thf(15268,plain,
( ( sk138 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[15245]) ).
thf(8753,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,4039]) ).
thf(8754,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8753]) ).
thf(8761,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk216 ),
inference(simp,[status(thm)],[8754]) ).
thf(861,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/sandbox/benchmark/theBenchmark.p',dt_k2_struct_0) ).
thf(5860,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)],[861]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(1734,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(284,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/sandbox/benchmark/theBenchmark.p',d10_lattices) ).
thf(2792,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)],[284]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(5184,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)],[709]) ).
thf(21943,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)],[21901,1081]) ).
thf(21944,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)],[21943]) ).
thf(21945,plain,
! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[21944:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk207 @ k9_relat_1 ) )),bind(C,$thf( sk207 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(21994,plain,
! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[21945]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(1998,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)],[158]) ).
thf(602,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(4574,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)],[602]) ).
thf(3797,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk251 @ m1_subset_1 ) ),
inference(cnfConj,[status(thm)],[3796]) ).
thf(18726,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( k1_xboole_0 @ k1_tarski @ ( A @ sk251 @ m1_subset_1 ) ) ),
inference(paramod_ordered,[status(thm)],[1953,3797]) ).
thf(18727,plain,
k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ sk251 @ m1_subset_1 ),
inference(pattern_uni,[status(thm)],[18726:[bind(A,$thf( k1_xboole_0 ))]]) ).
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/sandbox/benchmark/theBenchmark.p',t16_binop_1) ).
thf(1476,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(12961,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ~ $true
| ( k1_xboole_0 @ v10_lattices ) ),
inference(paramod_ordered,[status(thm)],[2072,8014]) ).
thf(12962,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
!= ( k1_xboole_0 @ ( sk71 @ k2_relat_1 @ r1_tarski ) ) )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12961]) ).
thf(12992,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
| ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12962]) ).
thf(13004,plain,
( ( ( sk71 @ k2_relat_1 )
!= k1_xboole_0 )
| ( ( sk71 @ k1_relat_1 )
!= sk1 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ v10_lattices ) ),
inference(simp,[status(thm)],[12992]) ).
thf(12265,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,7613]) ).
thf(12266,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12265]) ).
thf(12370,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk71 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
| ( k1_xboole_0 @ l3_lattices ) ),
inference(simp,[status(thm)],[12266]) ).
thf(759,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/sandbox/benchmark/theBenchmark.p',t67_lattice2) ).
thf(5426,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)],[759]) ).
thf(550,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/sandbox/benchmark/theBenchmark.p',t69_filter_0) ).
thf(4338,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)],[550]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(3561,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)],[411]) ).
thf(838,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_0) ).
thf(5756,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)],[838]) ).
thf(9018,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,5226]) ).
thf(9019,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9018]) ).
thf(9028,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= sk295 ),
inference(simp,[status(thm)],[9019]) ).
thf(392,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/sandbox/benchmark/theBenchmark.p',t1_filter_2) ).
thf(3465,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)],[392]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',t12_binop_1) ).
thf(2591,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)],[253]) ).
thf(626,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/sandbox/benchmark/theBenchmark.p',t15_relset_1) ).
thf(4710,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)],[626]) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',d13_binop_1) ).
thf(2988,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)],[309]) ).
thf(967,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/sandbox/benchmark/theBenchmark.p',t54_filter_0) ).
thf(6322,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)],[967]) ).
thf(913,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/sandbox/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).
thf(6077,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)],[913]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
& ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(2273,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)],[205]) ).
thf(445,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/sandbox/benchmark/theBenchmark.p',t24_lattice4) ).
thf(3789,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)],[445]) ).
thf(433,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(3709,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(725,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/sandbox/benchmark/theBenchmark.p',dt_k12_filter_2) ).
thf(5272,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)],[725]) ).
thf(1097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) )
| ( ( D @ k1_relat_1 )
!= ( A @ k1_tarski ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) )
& ( ( 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)],[1096]) ).
thf(1099,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
| ~ ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) )
| ( ( D @ k1_relat_1 )
!= ( A @ k1_tarski ) )
| ~ ( D @ v1_funct_1 )
| ~ ( D @ v1_relat_1 ) ),
inference(cnfConj,[status(thm)],[1097]) ).
thf(1101,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)],[1099]) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(2823,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)],[287]) ).
thf(592,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(4542,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(646,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/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(4834,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)],[646]) ).
thf(685,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/sandbox/benchmark/theBenchmark.p',t30_filter_0) ).
thf(5087,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)],[685]) ).
thf(24732,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)],[2045,10164]) ).
thf(24733,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk71 ),
inference(pattern_uni,[status(thm)],[24732:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(24756,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
!= sk71 ),
inference(simp,[status(thm)],[24733]) ).
thf(2416,plain,
~ ( sk118 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2413]) ).
thf(444,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/sandbox/benchmark/theBenchmark.p',d17_lattice4) ).
thf(3780,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)],[444]) ).
thf(5592,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ v1_funct_2 ) ) )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5590]) ).
thf(5600,plain,
( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk402 @ v1_funct_2 ) ) )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5592]) ).
thf(536,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/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
thf(4261,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)],[536]) ).
thf(2944,plain,
sk187 @ v3_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(2956,plain,
sk188 @ v7_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
thf(705,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/sandbox/benchmark/theBenchmark.p',d1_lattice2) ).
thf(5162,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)],[705]) ).
thf(28116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k2_tarski ) )
!= ( D @ ( C @ k2_tarski ) ) )
| ( ( A @ k1_tarski )
!= ( B @ sk251 ) ) ),
inference(paramod_ordered,[status(thm)],[4553,13047]) ).
thf(28117,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski )
!= ( B @ sk251 ) ),
inference(pattern_uni,[status(thm)],[28116:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(690,axiom,
? [A: $i] : ( A @ l2_lattices ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(5109,plain,
? [A: $i] : ( A @ l2_lattices ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
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/sandbox/benchmark/theBenchmark.p',t123_funct_1) ).
thf(1308,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(789,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice4) ).
thf(5549,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)],[789]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(1661,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(694,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/sandbox/benchmark/theBenchmark.p',t27_lattices) ).
thf(5119,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)],[694]) ).
thf(500,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/sandbox/benchmark/theBenchmark.p',t17_relset_1) ).
thf(4074,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)],[500]) ).
thf(2739,plain,
sk157 @ v13_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',t29_partfun1) ).
thf(2917,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)],[298]) ).
thf(999,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/sandbox/benchmark/theBenchmark.p',t73_lattice2) ).
thf(6462,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)],[999]) ).
thf(608,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/sandbox/benchmark/theBenchmark.p',t59_filter_2) ).
thf(4619,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)],[608]) ).
thf(29262,plain,
! [A: $i] :
( ( A != sk157 )
| ( k1_xboole_0 @ v5_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,2744]) ).
thf(29263,plain,
( ( k1_xboole_0 @ v5_lattices )
| ( sk157 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29262:[bind(A,$thf( sk157 ))]]) ).
thf(3181,plain,
k6_nat_lat @ v4_lattices,
inference(cnfConj,[status(thm)],[3174]) ).
thf(2475,plain,
k13_nat_lat @ v5_lattices,
inference(cnfConj,[status(thm)],[2469]) ).
thf(650,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/sandbox/benchmark/theBenchmark.p',dt_k2_lattice2) ).
thf(4855,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)],[650]) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',t8_realset1) ).
thf(2786,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)],[283]) ).
thf(29634,plain,
! [A: $i] :
( ( A != sk315 )
| ( k1_xboole_0 @ v5_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,4654]) ).
thf(29635,plain,
( ( k1_xboole_0 @ v5_lattices )
| ( sk315 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29634:[bind(A,$thf( sk315 ))]]) ).
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 ) )
=> ! [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/sandbox/benchmark/theBenchmark.p',t29_lattices) ).
thf(6305,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [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)],[962]) ).
thf(4649,plain,
sk315 @ v9_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(4962,plain,
! [A: $i] :
( ( ( ( A @ ( sk347 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( A @ f3_s13_funct_2 ) )
| ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
| ~ sk345 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk347 @ m2_relset_1 ) ) )
| ~ sk345 )
& ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk347 @ v1_funct_2 ) ) )
| ~ sk345 )
& ( ( sk347 @ v1_funct_1 )
| ~ sk345 )
& ( sk345
| ~ ( f2_s13_funct_2 @ ( sk346 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
& ( sk345
| ( f1_s13_funct_2 @ ( sk346 @ m1_subset_1 ) ) ) ),
inference(cnf,[status(esa)],[4961]) ).
thf(4964,plain,
( sk345
| ( f1_s13_funct_2 @ ( sk346 @ m1_subset_1 ) ) ),
inference(cnfConj,[status(thm)],[4962]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(2041,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)],[166]) ).
thf(29513,plain,
! [A: $i] :
( ( A != k13_nat_lat )
| ( k1_xboole_0 @ v9_lattices )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,2476]) ).
thf(29514,plain,
( ( k1_xboole_0 @ v9_lattices )
| ( k13_nat_lat @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29513:[bind(A,$thf( k13_nat_lat ))]]) ).
thf(518,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/sandbox/benchmark/theBenchmark.p',t158_funct_2) ).
thf(4175,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)],[518]) ).
thf(511,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/sandbox/benchmark/theBenchmark.p',t9_lattice4) ).
thf(4153,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)],[511]) ).
thf(527,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/sandbox/benchmark/theBenchmark.p',t59_domain_1) ).
thf(4214,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)],[527]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',t118_funct_2) ).
thf(2648,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)],[260]) ).
thf(416,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(3585,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)],[416]) ).
thf(841,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/sandbox/benchmark/theBenchmark.p',t46_filter_0) ).
thf(5781,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)],[841]) ).
thf(676,axiom,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(5023,plain,
! [A: $i] :
( ( A @ l3_lattices )
=> ( ( A @ l2_lattices )
& ( A @ l1_lattices ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(2330,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)],[213]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',rc1_nat_lat) ).
thf(2576,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)],[251]) ).
thf(578,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/sandbox/benchmark/theBenchmark.p',t51_filter_0) ).
thf(4478,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)],[578]) ).
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/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).
thf(1706,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(825,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ~ ( ! [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/sandbox/benchmark/theBenchmark.p',t60_filter_2) ).
thf(5699,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)],[825]) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(2680,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)],[269]) ).
thf(1210,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)],[1209]) ).
thf(1212,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)],[1210]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(2294,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)],[210]) ).
thf(5672,plain,
k6_nat_lat @ v13_lattices,
inference(cnfConj,[status(thm)],[5669]) ).
thf(938,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/sandbox/benchmark/theBenchmark.p',t30_filter_2) ).
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 ) )
=> ( ( ( 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)],[938]) ).
thf(1037,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)],[1036]) ).
thf(1044,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)],[1037]) ).
thf(1045,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)],[1044]) ).
thf(2421,plain,
sk118 @ v7_lattices,
inference(cnfConj,[status(thm)],[2413]) ).
thf(12324,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,8524]) ).
thf(12325,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12324]) ).
thf(12367,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk207 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12325]) ).
thf(486,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/sandbox/benchmark/theBenchmark.p',d6_lattices) ).
thf(3992,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)],[486]) ).
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/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).
thf(1512,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(620,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/sandbox/benchmark/theBenchmark.p',t40_filter_2) ).
thf(4687,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)],[620]) ).
thf(559,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/sandbox/benchmark/theBenchmark.p',t27_lattice4) ).
thf(4378,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)],[559]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(2719,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)],[278]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(3733,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)],[437]) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1370]) ).
thf(1379,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1373]) ).
thf(1380,plain,
! [A: $i] : ( A @ ( A @ ( k1_xboole_0 @ sk25 ) @ k2_relat_1 @ r1_tarski ) ),
inference(simp,[status(thm)],[1379]) ).
thf(753,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/sandbox/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(5398,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)],[753]) ).
thf(340,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(3164,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)],[340]) ).
thf(424,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/sandbox/benchmark/theBenchmark.p',t9_filter_2) ).
thf(3658,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)],[424]) ).
thf(2218,plain,
sk95 @ l2_struct_0,
inference(cnfConj,[status(thm)],[2217]) ).
thf(508,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/sandbox/benchmark/theBenchmark.p',t53_filter_2) ).
thf(4125,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)],[508]) ).
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/sandbox/benchmark/theBenchmark.p',t60_funct_2) ).
thf(1348,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(818,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/sandbox/benchmark/theBenchmark.p',t73_filter_0) ).
thf(5677,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)],[818]) ).
thf(907,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ ( A @ k1_filter_2 @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_2) ).
thf(6055,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)],[907]) ).
thf(674,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/sandbox/benchmark/theBenchmark.p',t121_funct_2) ).
thf(5009,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)],[674]) ).
thf(969,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/sandbox/benchmark/theBenchmark.p',d5_filter_2) ).
thf(6326,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)],[969]) ).
thf(43987,plain,
! [B: $i,A: $i] :
( ( ( sk361 @ sk18 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32119,1230]) ).
thf(43988,plain,
! [B: $i,A: $i] :
( ( ( sk361 @ sk18 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[43987]) ).
thf(43989,plain,
! [A: $i] : ( A @ ( sk361 @ sk18 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[43988:[bind(A,$thf( A )),bind(B,$thf( sk361 @ sk18 ))]]) ).
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/sandbox/benchmark/theBenchmark.p',t18_relat_1) ).
thf(1725,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(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/sandbox/benchmark/theBenchmark.p',t28_relat_1) ).
thf(1280,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(41074,plain,
( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,40850]) ).
thf(41075,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk295 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41074]) ).
thf(41079,plain,
( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk295 ),
inference(simp,[status(thm)],[41075]) ).
thf(801,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/sandbox/benchmark/theBenchmark.p',dt_k21_filter_2) ).
thf(5606,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)],[801]) ).
thf(13029,plain,
! [A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( sk361 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,5153]) ).
thf(13030,plain,
! [A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( sk361 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13029]) ).
thf(13043,plain,
! [A: $i] :
( ( A @ sk251 )
!= sk361 ),
inference(simp,[status(thm)],[13030]) ).
thf(363,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/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(3291,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)],[363]) ).
thf(723,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/sandbox/benchmark/theBenchmark.p',dt_k16_filter_2) ).
thf(5268,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)],[723]) ).
thf(29429,plain,
! [A: $i] :
( ( A != sk207 )
| ( k1_xboole_0 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,15263]) ).
thf(29430,plain,
! [A: $i] :
( ( A != sk207 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[29429]) ).
thf(29431,plain,
( ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
| ( sk207 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29430:[bind(A,$thf( sk207 ))]]) ).
thf(791,axiom,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s9_domain_1) ).
thf(5554,plain,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(2951,plain,
sk187 @ v15_lattices,
inference(cnfConj,[status(thm)],[2940]) ).
thf(587,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/sandbox/benchmark/theBenchmark.p',t164_funct_2) ).
thf(4523,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)],[587]) ).
thf(402,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/sandbox/benchmark/theBenchmark.p',t65_funct_2) ).
thf(3521,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)],[402]) ).
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/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(1876,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(2736,plain,
sk157 @ v8_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(2008,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)],[160]) ).
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/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).
thf(1248,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(1005,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_lattice4 ) )
= ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice4) ).
thf(6490,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v17_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k4_lattice4 ) )
= ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(783,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/sandbox/benchmark/theBenchmark.p',t13_filter_2) ).
thf(5527,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)],[783]) ).
thf(5596,plain,
( ( sk402 @ v1_funct_1 )
| ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
inference(cnfConj,[status(thm)],[5590]) ).
thf(5601,plain,
( ( sk402 @ v1_funct_1 )
| ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
inference(lifteq,[status(thm)],[5596]) ).
thf(581,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/sandbox/benchmark/theBenchmark.p',t44_funct_2) ).
thf(4491,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)],[581]) ).
thf(657,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(4885,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)],[657]) ).
thf(675,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).
thf(5014,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)],[675]) ).
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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(1480,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(605,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/sandbox/benchmark/theBenchmark.p',t57_filter_0) ).
thf(4597,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)],[605]) ).
thf(979,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/sandbox/benchmark/theBenchmark.p',fc1_filter_2) ).
thf(6366,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)],[979]) ).
thf(3062,plain,
sk196 @ v16_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(370,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/sandbox/benchmark/theBenchmark.p',t38_subset_1) ).
thf(3328,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)],[370]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',t16_funct_2) ).
thf(1989,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)],[156]) ).
thf(755,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_0) ).
thf(5404,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
= ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(923,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/sandbox/benchmark/theBenchmark.p',t47_filter_0) ).
thf(6114,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)],[923]) ).
thf(526,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/sandbox/benchmark/theBenchmark.p',t12_filter_2) ).
thf(4210,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)],[526]) ).
thf(576,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/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(4474,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)],[576]) ).
thf(41109,plain,
( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1975,40941]) ).
thf(41110,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( sk71 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[41109]) ).
thf(41158,plain,
( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
!= sk71 ),
inference(simp,[status(thm)],[41110]) ).
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 @ k1_lattice2 @ u1_struct_0 @ ( B @ ( A @ k5_filter_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).
thf(6273,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)],[953]) ).
thf(5110,plain,
sk358 @ l2_lattices,
inference(cnf,[status(esa)],[5109]) ).
thf(366,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/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(3309,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)],[366]) ).
thf(455,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/sandbox/benchmark/theBenchmark.p',t70_lattice2) ).
thf(3822,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)],[455]) ).
thf(990,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/sandbox/benchmark/theBenchmark.p',dt_k6_filter_2) ).
thf(6411,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)],[990]) ).
thf(43940,plain,
! [B: $i,A: $i] :
( ( ( sk218 @ sk18 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31616,1230]) ).
thf(43941,plain,
! [B: $i,A: $i] :
( ( ( sk218 @ sk18 @ v1_relat_1 )
!= ( B @ v1_relat_1 ) )
| ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(simp,[status(thm)],[43940]) ).
thf(43942,plain,
! [A: $i] : ( A @ ( sk218 @ sk18 @ k4_xboole_0 ) @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[43941:[bind(A,$thf( A )),bind(B,$thf( sk218 @ sk18 ))]]) ).
thf(932,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ 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/sandbox/benchmark/theBenchmark.p',t52_lattice2) ).
thf(6169,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)],[932]) ).
thf(704,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/sandbox/benchmark/theBenchmark.p',redefinition_k12_filter_0) ).
thf(5159,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)],[704]) ).
thf(7554,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2658,4039]) ).
thf(7555,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( sk152 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7554]) ).
thf(7557,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= sk152 ),
inference(simp,[status(thm)],[7555]) ).
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/sandbox/benchmark/theBenchmark.p',t17_binop_1) ).
thf(1816,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(612,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/sandbox/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(4631,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)],[612]) ).
thf(3177,plain,
k6_nat_lat @ v7_lattices,
inference(cnfConj,[status(thm)],[3174]) ).
thf(11626,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk216 ) ),
inference(paramod_ordered,[status(thm)],[1953,8761]) ).
thf(11627,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk216 ),
inference(pattern_uni,[status(thm)],[11626:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(688,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/sandbox/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(5105,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)],[688]) ).
thf(2746,plain,
sk157 @ v11_lattices,
inference(cnfConj,[status(thm)],[2732]) ).
thf(768,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] : ( A @ ( B @ m1_filter_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_2) ).
thf(5462,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)],[768]) ).
thf(460,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/sandbox/benchmark/theBenchmark.p',t75_lattice2) ).
thf(3850,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)],[460]) ).
thf(1168,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)],[1165]) ).
thf(1172,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)],[1168]) ).
thf(2417,plain,
sk118 @ v10_lattices,
inference(cnfConj,[status(thm)],[2413]) ).
thf(7509,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)],[1063,7252]) ).
thf(7510,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)],[7509]) ).
thf(7518,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)],[7510]) ).
thf(7535,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)],[7518]) ).
thf(8050,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)],[7535,2542]) ).
thf(8051,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)],[8050]) ).
thf(947,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(6258,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)],[947]) ).
thf(2961,plain,
sk188 @ v10_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
thf(1195,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)],[1192]) ).
thf(1197,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)],[1195]) ).
thf(29591,plain,
! [A: $i] :
( ( A != sk188 )
| ( k1_xboole_0 @ v3_filter_0 )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1298,2957]) ).
thf(29592,plain,
( ( k1_xboole_0 @ v3_filter_0 )
| ( sk188 @ sk18 @ v1_relat_1 ) ),
inference(pattern_uni,[status(thm)],[29591:[bind(A,$thf( sk188 ))]]) ).
thf(346,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/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(3196,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)],[346]) ).
thf(747,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_filter_0 )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ v14_lattices ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_filter_0) ).
thf(5378,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)],[747]) ).
thf(567,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/sandbox/benchmark/theBenchmark.p',t21_lattice4) ).
thf(4442,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)],[567]) ).
thf(493,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/sandbox/benchmark/theBenchmark.p',t28_subset_1) ).
thf(4034,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)],[493]) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(2619,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)],[257]) ).
thf(384,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/sandbox/benchmark/theBenchmark.p',t62_funct_2) ).
thf(3424,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)],[384]) ).
thf(660,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/sandbox/benchmark/theBenchmark.p',d3_lattice4) ).
thf(4912,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)],[660]) ).
thf(321,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/sandbox/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(3045,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)],[321]) ).
thf(5185,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)],[5184]) ).
thf(5186,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk367 ) @ r2_hidden ) )
| ( ( E @ ( F @ sk366 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk367 ) )
= E )
| ( ( E @ ( F @ sk366 ) )
!= E ) )
& ( ( F
= ( E @ k1_tarski ) )
| ~ ( F @ ( E @ ( F @ sk367 ) @ r2_hidden ) )
| ( F @ ( E @ ( F @ sk366 ) @ r2_hidden ) ) )
& ( ( F
= ( E @ k1_tarski ) )
| ( ( E @ ( F @ sk367 ) )
= E )
| ( F @ ( E @ ( F @ sk366 ) @ 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)],[5185]) ).
thf(5190,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[5186]) ).
thf(5199,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ r2_hidden ) )
| ( C != A )
| ( B
!= ( A @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[5190]) ).
thf(5200,plain,
! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[5199]) ).
thf(12326,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[4613,7130]) ).
thf(12327,plain,
( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ 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)],[12326]) ).
thf(12395,plain,
( ( f2_s4_funct_2 != k1_xboole_0 )
| ( sk1 != f1_s4_funct_2 )
| ( sk313 != sk71 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[12327]) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',d16_binop_1) ).
thf(3128,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)],[333]) ).
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/sandbox/benchmark/theBenchmark.p',d6_binop_1) ).
thf(1261,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(9008,plain,
( ( ( sk295 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4335,3326]) ).
thf(9009,plain,
( ( sk295 @ v1_xboole_0 )
!= ( sk218 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[9008]) ).
thf(9023,plain,
sk295 != sk218,
inference(simp,[status(thm)],[9009]) ).
thf(4659,plain,
sk315 @ v17_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(3886,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)],[463]) ).
thf(855,axiom,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1) ).
thf(5845,plain,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(976,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/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
thf(6351,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)],[976]) ).
thf(936,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/sandbox/benchmark/theBenchmark.p',t41_lattice4) ).
thf(6190,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)],[936]) ).
thf(375,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/sandbox/benchmark/theBenchmark.p',d18_binop_1) ).
thf(3362,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)],[375]) ).
thf(2966,plain,
sk188 @ l3_lattices,
inference(cnfConj,[status(thm)],[2955]) ).
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/sandbox/benchmark/theBenchmark.p',t13_relset_1) ).
thf(1268,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(3057,plain,
sk196 @ v5_lattices,
inference(cnfConj,[status(thm)],[3054]) ).
thf(970,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/sandbox/benchmark/theBenchmark.p',t32_lattice4) ).
thf(6329,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)],[970]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',t49_domain_1) ).
thf(2600,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)],[255]) ).
thf(1375,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1370]) ).
thf(1383,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk25 ) @ v1_funct_1 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1375]) ).
thf(1384,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_funct_1 ),
inference(simp,[status(thm)],[1383]) ).
thf(656,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/sandbox/benchmark/theBenchmark.p',d10_lattice4) ).
thf(4876,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)],[656]) ).
thf(8739,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3315,2437]) ).
thf(8740,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( sk216 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8739]) ).
thf(8758,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= sk216 ),
inference(simp,[status(thm)],[8740]) ).
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/sandbox/benchmark/theBenchmark.p',t64_funct_2) ).
thf(1976,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(453,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/sandbox/benchmark/theBenchmark.p',t4_relset_1) ).
thf(3817,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)],[453]) ).
thf(6227,plain,
( ( f2_s4_subset_1 = f3_s4_subset_1 )
| ( sk446 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk446 @ r2_hidden ) )
| sk444 ),
inference(cnfConj,[status(thm)],[6221]) ).
thf(6233,plain,
( ( sk446 @ p1_s4_subset_1 )
| ( f3_s4_subset_1 @ ( sk446 @ r2_hidden ) )
| sk444
| ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
inference(lifteq,[status(thm)],[6227]) ).
thf(915,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/sandbox/benchmark/theBenchmark.p',t89_filter_0) ).
thf(6082,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)],[915]) ).
thf(6348,plain,
sk454 @ v3_lattices,
inference(cnfConj,[status(thm)],[6345]) ).
thf(529,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/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(4229,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)],[529]) ).
thf(476,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/sandbox/benchmark/theBenchmark.p',d12_filter_0) ).
thf(3939,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)],[476]) ).
thf(867,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/sandbox/benchmark/theBenchmark.p',d11_filter_0) ).
thf(5891,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)],[867]) ).
thf(740,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/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(5354,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)],[740]) ).
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/sandbox/benchmark/theBenchmark.p',t55_partfun1) ).
thf(1880,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(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/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(1431,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(921,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/sandbox/benchmark/theBenchmark.p',t81_filter_0) ).
thf(6109,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)],[921]) ).
thf(490,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/sandbox/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(4019,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)],[490]) ).
thf(3076,plain,
sk197 @ v7_lattices,
inference(cnfConj,[status(thm)],[3070]) ).
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/sandbox/benchmark/theBenchmark.p',t6_lattice2) ).
thf(1902,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(583,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/sandbox/benchmark/theBenchmark.p',t44_filter_0) ).
thf(4501,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)],[583]) ).
thf(874,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/sandbox/benchmark/theBenchmark.p',t34_filter_2) ).
thf(5913,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)],[874]) ).
thf(795,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).
thf(5569,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)],[795]) ).
thf(911,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ 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/sandbox/benchmark/theBenchmark.p',t41_filter_2) ).
thf(6072,plain,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ u1_struct_0 @ 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)],[911]) ).
thf(9162,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ 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
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(paramod_ordered,[status(thm)],[1065,8777]) ).
thf(9163,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[9162]) ).
thf(9164,plain,
! [B: $i,A: $i] :
( ( ( B @ k2_relat_1 )
!= k1_xboole_0 )
| ( A != sk1 )
| ( B != sk216 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
| ~ ( B @ v1_relat_1 ) ),
inference(simp,[status(thm)],[9163]) ).
thf(9168,plain,
( ( ( sk216 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk216 @ k1_relat_1 @ r1_tarski ) )
| ~ ( sk216 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[9164]) ).
thf(40620,plain,
( ( ( sk216 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk216 @ k1_relat_1 @ r1_tarski ) )
| ~ $true ),
inference(rewrite,[status(thm)],[9168,3314]) ).
thf(40621,plain,
( ( ( sk216 @ k2_relat_1 )
!= k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
| ~ ( sk1 @ ( sk216 @ k1_relat_1 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[40620]) ).
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/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(1917,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(988,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v10_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_filter_2 )
= ( A @ k1_filter_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).
thf(6404,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)],[988]) ).
thf(2470,plain,
k13_nat_lat @ v10_lattices,
inference(cnfConj,[status(thm)],[2469]) ).
thf(632,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/sandbox/benchmark/theBenchmark.p',d4_lattices) ).
thf(4734,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)],[632]) ).
thf(38312,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)],[1875,38307]) ).
thf(38313,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk13 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[38312:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(959,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/sandbox/benchmark/theBenchmark.p',t28_lattice4) ).
thf(6297,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)],[959]) ).
thf(4655,plain,
sk315 @ v6_lattices,
inference(cnfConj,[status(thm)],[4645]) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',t31_relat_1) ).
thf(2672,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)],[266]) ).
thf(33128,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)],[31616,1137]) ).
thf(33129,plain,
! [A: $i] :
( ( ( sk218 @ sk18 @ v1_relat_1 )
!= ( A @ v1_relat_1 ) )
| ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(simp,[status(thm)],[33128]) ).
thf(33130,plain,
( ( sk218 @ sk18 @ k1_relat_1 @ ( sk218 @ sk18 @ k9_relat_1 ) )
= ( sk218 @ sk18 @ k2_relat_1 ) ),
inference(pattern_uni,[status(thm)],[33129:[bind(A,$thf( sk218 @ sk18 ))]]) ).
thf(352,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/sandbox/benchmark/theBenchmark.p',t10_realset1) ).
thf(3227,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)],[352]) ).
thf(625,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/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(4702,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)],[625]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(2321,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)],[211]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(4642,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)],[615]) ).
thf(786,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/sandbox/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(5542,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)],[786]) ).
thf(19379,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)],[19342,1081]) ).
thf(19380,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)],[19379]) ).
thf(19381,plain,
! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[19380:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk152 @ k9_relat_1 ) )),bind(C,$thf( sk152 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).
thf(19427,plain,
! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
inference(simp,[status(thm)],[19381]) ).
thf(732,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/sandbox/benchmark/theBenchmark.p',d2_lattices) ).
thf(5307,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)],[732]) ).
thf(420,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/sandbox/benchmark/theBenchmark.p',d13_lattices) ).
thf(3626,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)],[420]) ).
thf(629,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ( A @ v3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ k1_lattice2 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattice2) ).
thf(4723,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)],[629]) ).
thf(811,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v15_lattices )
<=> ( ( A @ v14_lattices )
& ( A @ v13_lattices ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_lattices) ).
thf(5649,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)],[811]) ).
thf(2206,plain,
~ ( sk94 @ v3_struct_0 ),
inference(cnfConj,[status(thm)],[2205]) ).
thf(844,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/sandbox/benchmark/theBenchmark.p',t48_lattices) ).
thf(5789,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)],[844]) ).
thf(29651,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)],[1298,8146]) ).
thf(29652,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ k4_tarski ) ) )
| ( A @ sk18 @ v1_relat_1 ) ),
inference(simp,[status(thm)],[29651]) ).
thf(29653,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk18 @ v1_relat_1 ),
inference(pattern_uni,[status(thm)],[29652:[bind(A,$thf( E @ ( D @ k4_tarski ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(32438,plain,
! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk18 @ v1_relat_1 ),
inference(simp,[status(thm)],[29653]) ).
thf(926,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/sandbox/benchmark/theBenchmark.p',fc2_filter_2) ).
thf(6145,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)],[926]) ).
thf(11630,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= sk152 ) ),
inference(paramod_ordered,[status(thm)],[1953,7557]) ).
thf(11631,plain,
( ( k1_xboole_0 @ k1_tarski )
!= sk152 ),
inference(pattern_uni,[status(thm)],[11630:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',t26_binop_1) ).
thf(2018,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)],[161]) ).
thf(513,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/sandbox/benchmark/theBenchmark.p',t37_lattice2) ).
thf(4161,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)],[513]) ).
thf(721,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/sandbox/benchmark/theBenchmark.p',t20_filter_0) ).
thf(5261,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)],[721]) ).
thf(594,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/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(4547,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)],[594]) ).
thf(633,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/sandbox/benchmark/theBenchmark.p',t31_filter_0) ).
thf(4742,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)],[633]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(2238,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)],[201]) ).
thf(814,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/sandbox/benchmark/theBenchmark.p',t52_filter_2) ).
thf(5664,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)],[814]) ).
thf(522,axiom,
! [A: $i] :
( ( ( A @ l3_lattices )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k1_lattice2 @ v3_lattices )
& ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
thf(4189,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)],[522]) ).
thf(15207,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2268,9047]) ).
thf(15208,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
!= ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15207]) ).
thf(15249,plain,
! [B: $i,A: $i] :
( ( B != k1_xboole_0 )
| ( A != sk1 )
| ( sk313 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15208]) ).
thf(15273,plain,
( ( sk313 != k1_xboole_0 )
| ~ ( k1_xboole_0 @ v3_struct_0 )
| ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
inference(simp,[status(thm)],[15249]) ).
thf(347,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/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(3200,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)],[347]) ).
thf(950,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/sandbox/benchmark/theBenchmark.p',d13_filter_2) ).
thf(6265,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)],[950]) ).
thf(13035,plain,
! [A: $i] :
( ( ( A @ sk251 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,1218]) ).
thf(13036,plain,
! [A: $i] :
( ( A @ sk251 @ v1_xboole_0 )
!= ( sk14 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[13035]) ).
thf(13048,plain,
! [A: $i] :
( ( A @ sk251 )
!= sk14 ),
inference(simp,[status(thm)],[13036]) ).
thf(435,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/sandbox/benchmark/theBenchmark.p',dt_k13_filter_2) ).
thf(3721,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)],[435]) ).
thf(1069,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)],[1067]) ).
thf(919,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/sandbox/benchmark/theBenchmark.p',redefinition_k24_filter_2) ).
thf(6094,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)],[919]) ).
thf(873,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/sandbox/benchmark/theBenchmark.p',dt_k18_filter_2) ).
thf(5911,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)],[873]) ).
thf(318,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/sandbox/benchmark/theBenchmark.p',t159_funct_2) ).
thf(3035,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)],[318]) ).
thf(59390,plain,
$false,
inference(e,[status(thm)],[2163,5385,3053,6530,3399,3798,3434,4166,1586,1501,2452,4447,3962,1718,24747,5469,6387,3883,5116,6167,1024,2744,41159,1190,2336,3008,1454,2072,3661,2412,2876,1237,4183,2921,5390,6285,5654,6317,2499,5205,6074,2544,12383,1179,5733,8755,6014,5582,1950,6374,2280,1110,3317,4391,2947,5173,5224,1142,5265,6017,2363,1200,5444,4931,12458,6057,42662,3990,4037,4376,3072,41081,2210,6177,2104,5718,13007,2231,6495,3905,14117,2381,15267,5069,2908,3549,1808,2659,2953,5297,12371,3912,1073,5625,4960,1728,6338,5982,3012,1205,3402,1533,5691,1793,4623,6031,21834,5614,1437,14431,1173,4532,6295,5589,8150,4647,11014,3175,1164,2141,4564,3017,5967,1078,1426,6505,3429,5565,1137,7431,3135,4011,15263,7556,4870,2740,29420,6089,2933,4650,5713,2476,5674,3253,2459,1342,3121,5005,1640,7068,13640,9801,1063,1954,1354,2146,4980,1222,2360,29392,6046,1095,1914,3502,1391,5921,5301,5874,1228,2957,3335,1196,22379,6236,4792,2216,4343,5227,6466,5740,3545,2972,4142,2046,1127,6268,2548,22461,5745,9027,1046,4665,14188,2136,5750,29572,6291,1518,2531,6182,15605,4775,4511,4249,5342,1887,4637,1709,1298,8515,2708,6506,4778,8146,2745,2703,1055,4238,3263,4439,3976,2603,4866,6242,3644,2735,12943,3275,6034,13429,19342,3342,2269,3061,6423,29512,2501,4654,3617,4334,3125,1826,12394,6315,4349,10174,1191,6332,27308,3803,2466,1059,1132,15264,2691,31616,6049,41475,5214,5802,4265,5077,1545,2420,3374,5868,5256,6455,2403,3638,1514,4194,5127,13045,5622,4928,4317,3084,3312,5851,4551,7047,5829,3014,5727,3835,3180,13044,5091,4471,3602,1875,3268,4008,5792,4595,5974,31458,3524,3934,5027,15261,5856,3527,3093,3152,2178,5787,15105,2222,2950,5957,6002,38951,38307,28522,4903,1811,38478,3075,5597,4857,2996,1109,14495,6523,3453,6534,5680,6300,21510,1828,3973,1151,21427,2540,2034,4871,4115,8759,6438,28674,2073,1183,12379,1051,6204,2964,4660,15360,1351,2286,41155,1201,41076,3184,5929,2058,2437,3537,1928,6648,4055,3068,7613,15271,8774,12430,1215,5643,3421,5384,3712,5370,7004,3808,1072,1119,2424,6347,2371,5321,5846,5897,6702,12411,4040,3756,4536,6021,3327,1433,5489,2965,5629,1104,3559,4628,9024,1975,5695,9026,2954,31249,3582,5157,6482,2364,2118,13049,3795,4199,5875,2204,31456,4407,2473,13019,5411,3984,3169,3265,1153,5697,1338,5142,18645,7019,32254,5487,1783,10165,4076,2737,1311,15258,5862,2083,4031,2660,28130,4172,7999,1636,6464,3037,1163,2409,3827,2733,1021,2277,16205,4661,32237,1223,4712,4466,1091,8783,1255,5794,8756,5579,6528,4609,4989,1174,5366,3752,3069,3233,3371,4449,4493,5085,2150,3816,1619,2986,5396,15563,2414,4836,6509,3207,7565,3682,4021,3339,1238,4044,5843,2958,3191,1920,1457,3535,2211,21409,1910,3445,3166,6303,1032,3980,5492,1365,2628,40997,2477,3090,22284,2663,29633,3314,3065,15103,14643,1178,2872,1951,6292,4553,3894,1819,1624,33233,32119,4187,5341,5551,3144,1159,1079,1027,2327,2213,2547,1128,29340,2741,4461,4732,5330,3799,4544,2631,3078,8149,12945,1118,3968,5854,1936,12414,8530,1089,3909,6413,5904,1234,1983,6324,4957,2157,1143,5145,2100,3413,1270,13006,3122,2946,5270,2801,6335,1953,5673,7249,1121,4486,6459,1064,5502,1970,2694,4693,21332,1096,5428,8014,4233,8768,5362,1540,1138,5978,2268,3205,24754,3060,3176,6218,1397,29729,5031,4860,6271,5941,4653,1082,3326,5818,3922,3000,3179,4983,29249,5181,4772,15265,11625,5107,1182,7846,2868,4389,7998,2419,1075,5743,8008,4421,4315,3010,5464,4750,43978,5253,5337,32297,14189,5547,18016,3032,1791,4648,15270,1214,5662,13046,12454,6501,15275,3671,2085,3723,10163,44049,2666,1644,6275,2472,4180,1039,12408,6097,5374,1974,1050,3819,2006,2813,5823,3920,3083,6349,5947,4846,29694,3486,12410,4508,1382,2598,3059,5380,29394,1231,4970,5134,1131,1799,9053,3937,5766,6346,5683,3692,2697,3064,5603,4259,1979,3074,4689,1627,4361,3476,5544,1202,4625,4765,38935,16997,3841,4572,5170,39182,3903,5747,5310,5153,41156,1814,1086,4644,4288,24743,4195,4567,15101,4081,41474,2208,2043,3587,3183,3173,4476,9044,3306,1846,1054,5434,38323,6260,6070,6647,2963,1035,2368,1071,6378,1187,4906,2440,5209,2089,1026,3508,1895,2189,6038,1996,5872,4308,2423,7133,5666,2677,5359,1219,4657,4562,6052,3158,2144,6192,6368,2936,1135,5524,16694,1146,2292,6026,8760,1680,1698,1959,4116,1103,4613,41077,3890,33027,4874,6084,5230,3079,29348,2941,38496,4393,5608,6469,3888,2734,4269,5647,3686,5758,4365,2524,3396,5400,5598,5241,1154,4000,6493,2859,11615,2981,5121,1388,5612,3900,1226,4505,2959,4662,5456,4341,2727,2970,19086,5474,3504,4283,3255,6312,22377,1125,2393,3086,9025,3736,3081,3266,2674,8777,42050,5876,5984,5097,6344,38187,3590,3604,4381,6407,5239,41473,3404,4612,27431,1124,43983,2220,4096,5471,5086,10215,1092,1090,2161,4251,4526,1503,5039,1669,8152,3077,4796,6357,38476,6532,3695,2738,4149,3208,5282,6091,1058,4060,2706,3641,6123,6248,1258,8524,5784,2474,6372,3568,1638,3355,5432,3170,29510,1194,43904,2538,2415,5848,2669,1122,5870,4790,1282,2478,3251,7130,3155,2214,5244,3551,2422,4305,1117,6147,44090,1048,6112,5303,5827,9047,1933,5901,3106,2116,5610,2943,13005,5407,2945,4616,1043,2856,29582,3138,3182,3066,2896,15577,3160,6216,1175,5816,2025,3055,2267,5439,2446,32471,1838,2542,4635,5114,6165,5035,3747,13050,2742,31541,4445,2129,15259,5730,5894,41157,4569,5994,3073,1630,7566,3572,4897,1162,4452,6319,6080,3298,4652,4296,44058,3483,3971,1344,1022,4726,6553,12381,4684,1061,1952,2911,4554,6376,29390,2350,1245,5482,3806,6504,15566,2535,2207,6029,40941,8007,2075,2418,4933,6255,4832,5340,1198,4720,24757,2439,2962,2365,5931,2725,5372,5442,2212,1213,3759,3838,1066,1445,2369,3674,3241,5976,4918,2022,7434,4954,2967,2390,5299,29415,6180,3512,3178,39078,1102,6485,1694,1973,4481,4158,2069,29523,1076,4331,1948,1034,2952,4458,1467,2471,1420,4529,2124,1134,1081,3455,3278,4168,1049,21901,2914,1583,5538,5587,1304,1873,3427,6540,2107,1203,1208,15276,12368,3395,2503,1684,1145,4113,4355,12377,4336,5003,9022,5716,29269,5125,5478,3214,2588,5944,3462,5980,1368,3209,6384,4658,2942,3988,6362,6120,1516,3315,15269,41471,1025,5602,35654,33336,5111,3082,13047,2407,4961,3058,5079,1531,40850,1230,2160,4593,2888,2569,4346,3063,1038,15598,5276,1235,5560,3769,4164,2656,3080,2747,5955,1987,5420,31460,5467,12455,3114,3791,1188,10162,2700,10164,5555,3202,3026,4768,2219,30793,5154,12396,3127,1085,8148,5001,4241,2545,4800,3564,15411,8757,6159,1130,4117,14567,1738,1218,3041,3095,3853,2468,1220,6415,4057,30184,2939,3071,8151,4217,2247,5319,1358,2948,5949,6701,3697,4959,6633,2558,2113,3415,5736,1141,3124,2426,1536,1981,3493,1023,6262,4611,2543,5998,11054,5504,2357,1972,2711,5453,4932,1140,5226,4695,5685,4093,41082,2949,43947,4267,2030,11617,4838,6245,12402,6511,6161,14496,32384,5841,3288,6420,6220,4392,2435,5939,4651,4698,4770,1553,6390,1108,15255,3478,2479,6425,2045,3092,3067,1180,15099,5536,2960,1157,6068,5386,2078,4656,2347,1412,2215,41468,5934,1216,2209,4646,5907,2743,15277,4102,15262,35470,32645,3056,5485,15268,8761,5860,2071,2658,1734,2792,5184,21994,1998,4574,3797,18727,1476,13004,1062,12370,5426,4338,3561,5756,9028,3465,2591,4710,2988,6322,6077,2273,3789,3709,5272,37989,1101,15088,2823,4542,4834,5087,24756,2416,3780,5600,4261,2944,5828,2956,5162,28117,5109,1308,5549,1661,5119,4074,2739,2917,6462,4619,29263,3181,2475,4855,2786,29635,3324,6305,4649,4964,2041,29514,4175,4153,4214,2648,3585,5781,5023,2330,2576,4478,1706,5699,2680,1212,2294,5672,6198,1045,2421,12367,3992,1512,4687,4378,2719,3733,7883,1380,5398,3164,3658,2218,4125,15572,4039,1348,5677,6055,5009,6326,43989,1725,1280,41079,5606,13043,3291,5268,1229,29431,5554,2951,4523,3521,1876,2736,2008,1248,6490,5527,5601,4491,4885,5014,1480,4597,5247,6366,3062,3328,1989,5404,6114,4210,4474,6287,41158,6273,5110,3309,3822,6411,43942,6169,5159,7557,8521,1816,4631,3177,11627,5105,2746,5462,3850,1172,2417,8051,6258,2961,1288,1197,29592,3196,5378,4442,4034,4193,2619,3424,4912,1065,3045,5200,12395,3128,1261,9023,1019,4659,3886,5845,1093,6351,1236,6190,2159,3362,2731,2966,1268,9038,5151,5668,3057,6329,2600,1384,4876,8758,1976,7616,3817,6233,6082,6348,4229,3939,2539,5891,5354,8147,3740,1880,1431,6109,4019,3076,1902,7252,4501,5913,4627,5569,6072,40621,1917,6404,2470,4734,4335,38313,6297,4655,2672,33130,3227,4702,2321,4642,5542,19427,5307,3626,4723,5649,2206,27438,5789,32438,1184,6145,11631,2018,4161,5261,4547,4742,2438,2238,3316,5664,4189,15273,3200,6265,10161,13048,3721,1069,6094,5911,3035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT329+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n019.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 20:56:34 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.64/1.76 % [INFO] Parsing done (773ms).
% 3.64/1.78 % [INFO] Running in sequential loop mode.
% 4.93/2.18 % [INFO] eprover registered as external prover.
% 4.93/2.19 % [INFO] Scanning for conjecture ...
% 6.23/2.54 % [INFO] Found a conjecture (or negated_conjecture) and 3001 axioms. Running axiom selection ...
% 9.11/3.39 % [INFO] Axiom selection finished. Selected 1016 axioms (removed 1985 axioms).
% 12.25/4.21 % [INFO] Problem is first-order (TPTP FOF).
% 12.25/4.28 % [INFO] Type checking passed.
% 12.25/4.29 % [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 ...
% 189.01/70.56 % External prover 'e' found a proof!
% 189.01/70.56 % [INFO] Killing All external provers ...
% 189.01/70.56 % Time passed: 70025ms (effective reasoning time: 68774ms)
% 189.01/70.56 % 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)>
% 189.01/70.57 % Axioms used in derivation (1016): t31_lattice2, d14_filter_2, t7_filter_0, dt_k4_filter_2, t1_filter_2, t45_lattice4, t2_filter_0, t21_zfmisc_1, t11_filter_2, t13_relset_1, dt_k7_filter_0, rc1_lattice2, d1_lattices, t119_funct_2, t158_relat_1, t17_lattice4, dt_k9_filter_2, t50_lattice4, redefinition_m2_relset_1, fraenkel_a_1_0_domain_1, t51_partfun1, t24_filter_0, t10_lattice2, d13_filter_0, t38_filter_2, fraenkel_a_3_2_domain_1, cc5_lattice2, t31_filter_0, t37_lattice2, t78_filter_0, t43_lattice2, dt_m1_lattice4, fc1_zfmisc_1, t35_subset_1, t135_zfmisc_1, t25_relset_1, t30_relat_1, d4_funct_1, t20_lattice4, t39_lattices, t76_lattice2, d10_lattices, t20_zfmisc_1, d1_tarski, dt_k2_lattice2, d20_binop_1, t66_funct_2, t62_filter_0, t66_partfun1, dt_k1_filter_2, t80_filter_0, t53_subset_1, t44_filter_2, d6_filter_0, d5_relat_1, t109_xboole_1, redefinition_k16_filter_2, t25_lattice2, d10_binop_1, t10_filter_2, t36_lattice4, t19_filter_2, t34_filter_2, t29_filter_0, fc2_filter_0, t81_filter_0, t24_lattice4, d13_lattices, cc3_lattice2, d14_binop_1, dt_k9_domain_1, d6_lattice2, t7_subset_1, t30_lattice2, t32_funct_2, d11_binop_1, t2_realset1, t3_xboole_1, d4_lattice4, t3_realset1, d3_subset_1, fc1_xboole_0, rc12_lattices, dt_k7_domain_1, t34_xboole_1, t29_lattice2, t59_filter_2, d1_lattice2, t56_partfun1, t63_filter_2, t59_partfun1, s12_funct_2, t43_lattices, s3_funct_2, t28_filter_2, t42_filter_0, cc6_lattices, t57_lattice2, t33_lattice2, t16_funct_2, d16_lattices, t113_zfmisc_1, t67_lattice2, t7_lattice2, t48_domain_1, t111_zfmisc_1, dt_k2_subset_1, t8_subset_1, t80_lattice2, t9_filter_2, existence_l1_lattices, t32_lattice4, d5_tarski, t15_funct_1, dt_k11_domain_1, t26_lattices, fc4_relat_1, t19_lattices, t4_ordinal1, t1_subset, dt_k1_lattice4, t147_relat_1, t10_partfun1, t47_lattice2, d5_xboole_0, t4_lattice4, t9_lattice2, fc4_subset_1, t12_filter_2, t168_funct_2, t10_relset_1, dt_k15_filter_2, fc3_relat_1, d8_funct_1, t69_filter_0, t57_filter_2, t144_relat_1, t57_domain_1, existence_l3_lattices, dt_k6_nat_lat, t39_filter_2, t53_lattices, dt_k3_funct_2, dt_k5_lattices, t7_funct_2, t87_filter_0, fc4_lattice2, t42_zfmisc_1, t21_lattice2, t14_binop_1, dt_k1_subset_1, t19_relat_1, dt_k16_filter_2, t28_binop_1, dt_k13_domain_1, fc1_lattice2, dt_g2_struct_0, t72_lattice2, t117_zfmisc_1, t32_relat_1, dt_k4_subset_1, t83_filter_0, t35_lattice4, t55_filter_2, t23_filter_0, redefinition_k12_filter_2, t16_lattice4, abstractness_v2_struct_0, t46_lattice4, dt_m2_nat_lat, d7_binop_1, existence_m3_lattice4, existence_m1_struct_0, dt_k3_lattice4, t35_zfmisc_1, t18_filter_0, rc2_struct_0, dt_k1_lattice2, t65_partfun1, t44_funct_2, fraenkel_a_2_0_lattice4, t117_funct_1, d10_filter_0, cc4_lattice2, dt_k1_struct_0, t26_lattice4, cc2_lattice2, t85_filter_0, dt_m1_realset1, t110_zfmisc_1, t103_zfmisc_1, dt_k19_filter_2, dt_u2_struct_0, t63_partfun1, t15_relset_1, t14_filter_0, fraenkel_a_2_0_filter_0, rc2_partfun1, t18_relat_1, fc1_filter_0, t48_filter_0, d9_lattice4, t49_funct_2, t41_lattice2, t64_filter_2, t50_funct_2, t70_zfmisc_1, t69_zfmisc_1, cc4_lattices, redefinition_k11_filter_0, fc2_filter_2, rc3_funct_1, fraenkel_a_3_3_domain_1, l70_filter_2, dt_k5_filter_0, dt_k3_filter_0, d1_struct_0, t27_zfmisc_1, t37_xboole_1, t41_zfmisc_1, fc2_lattice2, dt_m2_relset_1, cc1_relat_1, dt_k7_funct_2, dt_k5_filter_2, t59_lattice2, t70_partfun1, fc3_lattice2, t26_filter_0, t56_relat_1, t83_lattice2, t17_funct_1, t21_filter_2, t43_filter_2, redefinition_k2_funct_2, t2_funct_1, t36_subset_1, t29_partfun1, t33_lattice4, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, t32_filter_0, commutativity_k7_domain_1, t46_lattice2, fraenkel_a_2_0_domain_1, d2_tarski, dt_k2_binop_1, involutiveness_k3_subset_1, rc1_funct_1, t53_filter_0, d5_lattices, t17_binop_1, t25_funct_2, t31_relat_1, t15_binop_1, dt_m2_realset1, redefinition_k13_filter_2, redefinition_k6_filter_0, dt_k1_filter_0, dt_k6_filter_2, t115_zfmisc_1, t66_lattice2, t62_funct_1, t65_funct_2, t19_funct_1, dt_m2_lattice4, t41_filter_2, d11_filter_0, t26_filter_2, t31_lattices, s13_funct_2, fraenkel_a_2_2_domain_1, t129_zfmisc_1, d4_subset_1, t2_binop_1, d6_binop_1, dt_m1_filter_2, t27_lattices, t64_funct_2, reflexivity_r3_lattices, t20_filter_2, d1_xboole_0, d9_lattices, t56_filter_0, fraenkel_a_3_0_filter_0, t130_zfmisc_1, t3_filter_2, t175_partfun1, t15_relat_1, t48_funct_2, fraenkel_a_3_7_domain_1, d16_lattice4, t70_filter_0, t72_filter_0, t48_filter_2, t46_filter_0, t40_lattice2, t64_relat_1, t138_zfmisc_1, t25_subset_1, t37_filter_0, rc11_lattices, rc3_lattices, t52_filter_0, t108_zfmisc_1, t165_funct_2, t57_filter_0, dt_l1_lattices, dt_k12_filter_2, dt_k4_lattice4, t45_filter_2, t60_partfun1, existence_m1_realset1, dt_k11_filter_2, t31_partfun1, dt_k7_lattices, t3_funct_2, rc2_subset_1, existence_l2_lattices, l59_filter_2, t27_relset_1, t52_domain_1, t118_zfmisc_1, t55_partfun1, s4_subset_1, t8_funct_2, t118_funct_2, t29_lattice4, t76_nat_lat, t14_relset_1, t39_lattice4, t16_relset_1, t38_lattice4, d13_relat_1, t28_lattice2, t164_funct_2, d15_lattice4, fc2_funct_2, t6_boole, t12_funct_1, dt_k6_subset_1, t10_relat_1, d1_relat_1, t59_filter_0, t1_xboole_1, t26_relset_1, t64_partfun1, t47_lattice4, d5_filter_2, existence_l2_struct_0, t32_lattices, t19_filter_0, t44_lattice4, t49_filter_0, t5_subset, t17_filter_2, redefinition_k12_filter_0, t29_relat_1, d14_lattice4, cc6_lattice2, t50_filter_2, t77_funct_2, t59_domain_1, t34_filter_0, d4_filter_2, t5_lattice4, t54_filter_2, t22_lattices, t32_partfun1, d6_tarski, t4_relat_1, t26_binop_1, t28_subset_1, d12_lattices, d17_lattice4, fc3_subset_1, t128_zfmisc_1, t39_partfun1, t75_zfmisc_1, redefinition_k4_filter_2, t8_lattice4, rc1_filter_0, d2_realset1, t51_filter_2, fc2_subset_1, t45_funct_2, d9_filter_2, t25_zfmisc_1, d4_relat_1, d7_lattices, t6_lattice2, t23_binop_1, t150_relat_1, existence_m1_relset_1, t1_zfmisc_1, dt_m2_filter_2, t47_filter_2, t50_lattices, fc4_filter_2, s8_domain_1, dt_l3_lattices, t48_lattice2, t30_filter_2, d16_nat_lat, t79_zfmisc_1, t12_lattice2, t5_funct_2, dt_k8_funct_2, d12_lattice4, t16_filter_2, t167_funct_2, dt_m1_struct_0, t17_lattices, t11_funct_2, t65_filter_2, t40_funct_2, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t24_binop_1, t27_lattice4, t75_lattice2, t4_filter_0, t89_filter_0, dt_l2_lattices, redefinition_k7_domain_1, t40_filter_0, d3_filter_2, d12_filter_2, t72_partfun1, t8_funct_1, t2_tarski, t16_funct_1, t28_zfmisc_1, t72_zfmisc_1, t82_funct_2, dt_k4_filter_0, t33_xboole_1, s9_domain_1, t84_lattice2, t47_lattices, d7_filter_2, d20_lattices, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t38_filter_0, d3_lattices, t23_zfmisc_1, t34_lattice4, cc5_lattices, t4_subset, t38_subset_1, d18_lattices, t169_funct_2, t44_lattices, dt_k2_funct_1, cc1_funct_2, t39_subset_1, d8_filter_0, t56_lattice2, t52_subset_1, t60_filter_0, t5_ordinal1, rc13_lattices, t4_boole, t71_lattice2, d2_funct_2, t22_lattice2, t8_filter_2, t70_lattice2, dt_k8_domain_1, dt_k17_filter_2, fc3_filter_2, t15_lattice4, t74_zfmisc_1, t32_xboole_1, t61_filter_2, dt_k8_filter_0, t14_funct_1, t5_filter_2, t9_zfmisc_1, d7_filter_0, existence_m2_realset1, existence_m3_realset1, t56_subset_1, dt_k1_domain_1, t17_funct_2, t85_lattice2, redefinition_k14_filter_2, t75_filter_0, t13_lattice2, fc1_realset1, t25_filter_2, t132_funct_2, t45_lattices, t49_lattice4, t51_funct_2, d12_binop_1, t21_lattices, t12_zfmisc_1, d2_lattice4, t38_lattice2, t139_zfmisc_1, t16_lattice2, cc1_funct_1, t4_funct_2, redefinition_k1_filter_2, d10_lattice4, s11_funct_2, d3_relat_2, s2_domain_1, rc3_struct_0, t3_ordinal1, t9_domain_1, d6_filter_2, t25_lattices, t7_boole, dt_k14_filter_2, dt_k5_lattice4, t11_binop_1, t55_filter_0, t143_relat_1, d2_subset_1, t27_lattice2, commutativity_k4_lattices, redefinition_k9_filter_2, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, rc2_lattice2, commutativity_k2_struct_0, t7_filter_2, t23_filter_2, dt_k6_domain_1, t157_funct_1, t31_lattice4, fc5_lattice2, d17_lattices, dt_k2_partfun1, rc2_funct_1, t158_funct_2, dt_k9_filter_0, t90_filter_0, redefinition_k15_filter_2, t4_subset_1, redefinition_k1_domain_1, rc1_funct_2, l48_filter_2, t26_zfmisc_1, t6_filter_2, t69_partfun1, t7_ordinal1, dt_k10_filter_2, t9_funct_2, t31_funct_2, rc1_subset_1, t48_lattice4, t68_filter_0, fc6_lattice2, t8_lattice2, t18_lattices, cc1_lattices, t5_filter_0, t64_zfmisc_1, fc5_relat_1, dt_k3_lattice2, t30_filter_0, t40_lattice4, t13_filter_2, redefinition_r3_lattices, t40_lattices, t4_filter_2, t113_funct_2, t71_partfun1, d21_lattices, t41_lattices, t159_funct_2, t116_zfmisc_1, d4_lattices, existence_m1_filter_0, t2_lattice2, redefinition_m1_filter_2, dt_k2_struct_0, t49_lattices, t14_funct_2, t27_binop_1, t48_lattices, dt_k2_lattice4, t9_filter_0, t65_funct_1, t40_filter_2, fc1_nat_lat, fraenkel_a_3_1_domain_1, t60_funct_2, t7_lattice4, t36_filter_2, cc2_funct_1, t5_realset1, s4_funct_2, t41_lattice4, rc9_lattices, dt_k7_filter_2, d2_zfmisc_1, cc1_filter_0, t169_partfun1, fraenkel_a_2_1_lattice4, t26_lattice2, dt_k24_filter_2, t17_lattice2, t18_funct_1, d3_lattice2, t4_relset_1, t10_filter_0, t31_subset_1, t3_subset, cc1_relset_1, fc1_filter_2, t25_binop_1, d2_binop_1, d6_lattice4, t30_lattice4, s1_domain_1, t12_filter_0, t124_funct_1, t50_lattice2, t55_subset_1, t79_funct_2, dt_u1_lattices, fraenkel_a_2_1_domain_1, d13_filter_2, existence_m1_subset_1, t22_lattice4, existence_m1_filter_2, commutativity_k2_tarski, t3_relat_1, t22_filter_0, t24_relat_1, t8_relset_1, t106_zfmisc_1, t125_zfmisc_1, t73_filter_0, t11_relset_1, t155_relat_1, t27_filter_2, t15_subset_1, t44_filter_0, t118_funct_1, d9_binop_1, t19_lattice2, t146_relat_1, t35_xboole_1, t49_domain_1, d17_binop_1, dt_k2_filter_0, dt_k2_funct_2, d2_filter_0, rc1_nat_lat, t5_lattice2, free_g2_struct_0, dt_k20_filter_2, t17_relset_1, cc3_lattices, d5_subset_1, t99_partfun1, t107_zfmisc_1, t9_realset1, t121_funct_2, t114_zfmisc_1, dt_k23_filter_2, t58_partfun1, d1_zfmisc_1, t27_filter_0, t15_filter_2, t11_lattice4, rc2_relat_1, t36_lattice2, existence_m2_relset_1, d4_binop_1, t64_filter_0, t38_zfmisc_1, t75_nat_lat, t9_lattice4, t69_enumset1, t82_lattice2, t22_zfmisc_1, t14_filter_2, d1_filter_0, redefinition_k7_filter_0, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, t62_lattice2, t39_filter_0, t74_lattice2, t11_filter_0, t29_filter_2, existence_m2_lattice4, t23_lattice4, d4_lattice2, t116_funct_2, fraenkel_a_3_6_domain_1, t168_partfun1, s14_funct_2, t51_filter_0, t14_lattice4, t37_lattice4, redefinition_k2_binop_1, t74_filter_0, t60_nat_lat, t61_lattice2, t6_funct_2, redefinition_k24_filter_2, t32_filter_2, t58_filter_2, t44_lattice2, t41_subset_1, fc3_nat_lat, d3_lattice4, t157_relat_1, cc3_finsub_1, t56_filter_2, t65_lattice2, t42_filter_2, t51_subset_1, t21_subset_1, existence_m1_lattice4, d5_filter_0, d10_filter_2, t36_zfmisc_1, d4_filter_0, reflexivity_r1_filter_2, t45_lattice2, t8_realset1, dt_m3_lattice4, d3_tarski, cc6_funct_2, redefinition_k1_struct_0, t25_lattice4, d8_realset1, rc1_relat_1, t54_funct_1, t24_filter_2, t40_subset_1, t17_subset_1, t6_relset_1, d1_relset_1, redefinition_k11_filter_2, fc1_struct_0, t52_lattice2, t18_binop_1, redefinition_k3_lattices, t78_lattice2, t37_filter_2, fraenkel_a_3_1_filter_0, t39_zfmisc_1, d1_realset1, d15_lattices, t131_funct_2, dt_k22_filter_2, t119_zfmisc_1, dt_k4_lattices, t60_relat_1, rc1_lattice4, t77_lattice2, fraenkel_a_3_4_domain_1, t24_lattice2, t19_lattice4, reflexivity_r1_tarski, t9_funct_1, t6_zfmisc_1, t18_funct_2, dt_l2_struct_0, t52_lattices, t1_realset1, t2_xboole_1, t35_lattice2, t57_partfun1, t9_mcart_1, t34_funct_2, t67_filter_0, t52_filter_2, symmetry_r1_filter_2, t27_finsub_1, redefinition_m1_struct_0, t18_filter_2, t10_subset_1, t41_filter_0, existence_m2_nat_lat, d12_funct_1, d2_lattices, t9_relset_1, dt_g3_lattices, fc6_relat_1, d15_binop_1, rc6_lattices, free_g3_lattices, t77_filter_0, cc7_lattices, d14_lattices, dt_k10_filter_0, t54_lattice2, t21_lattice4, t36_xboole_1, dt_k8_subset_1, dt_k3_filter_2, t58_filter_0, redefinition_k2_filter_2, d4_xboole_0, t47_filter_0, t39_lattice2, d7_lattice4, d8_filter_2, t20_relat_1, dt_k1_lattices, t73_zfmisc_1, t69_lattice2, dt_k12_domain_1, t53_filter_2, t18_lattice4, d5_binop_1, t54_subset_1, t123_funct_1, t29_lattices, t88_filter_0, d1_relat_2, t82_filter_0, t33_filter_2, redefinition_k2_struct_0, t54_filter_0, t15_filter_0, dt_k2_filter_2, t68_zfmisc_1, t12_funct_2, d16_binop_1, t20_filter_0, t28_finsub_1, t32_lattice2, d8_binop_1, abstractness_v3_lattices, t26_finsub_1, t51_lattice2, t136_zfmisc_1, t8_boole, rc1_xboole_0, t24_partfun1, redefinition_k8_funct_2, t35_filter_2, t34_zfmisc_1, t80_zfmisc_1, t5_relat_1, t24_zfmisc_1, t55_lattice2, t120_funct_2, t59_funct_2, fc7_relat_1, t60_funct_1, t46_filter_2, t23_finsub_1, t30_finsub_1, dt_k21_filter_2, t134_zfmisc_1, fc8_relat_1, t10_realset1, dt_k3_binop_1, rc5_struct_0, t23_relat_1, t10_zfmisc_1, t2_subset, redefinition_k21_filter_2, d9_filter_0, t38_funct_2, t33_partfun1, t34_finsub_1, d3_relat_1, t85_funct_2, t37_zfmisc_1, t49_filter_2, t65_relat_1, t21_relat_1, dt_k6_filter_0, t156_relat_1, t109_zfmisc_1, fraenkel_a_2_3_domain_1, t60_domain_1, t152_relat_1, dt_k6_lattices, t25_partfun1, dt_m1_filter_0, d18_binop_1, redefinition_k10_filter_2, t115_funct_2, d6_lattices, t9_tarski, t51_lattices, commutativity_k3_lattices, t149_relat_1, fc2_realset1, d13_lattice4, t32_finsub_1, t48_subset_1, d1_lattice4, d8_lattices, t28_relat_1, d1_funct_1, d1_filter_2, t81_lattice2, t34_lattices, d12_filter_0, t42_lattice4, t50_subset_1, t65_filter_0, d10_xboole_0, d2_lattice2, d11_filter_2, t34_lattice2, dt_k2_lattices, d19_lattices, t67_partfun1, t3_boole, fc1_lattice4, dt_u2_lattices, d8_relat_2, t25_relat_1, dt_k8_filter_2, t13_binop_1, t53_lattice2, existence_l1_struct_0, t45_filter_0, t49_subset_1, t7_tarski, rc1_partfun1, t71_filter_0, redefinition_r1_filter_2, t28_lattice4, t79_lattice2, d5_funct_1, t6_ordinal1, dt_k18_filter_2, redefinition_k6_subset_1, rc10_lattices, t12_relset_1, cc1_lattice2, cc5_funct_2, t60_lattice2, t50_filter_0, t43_lattice4, t58_lattice2, t22_filter_2, d3_filter_0, d1_binop_1, rc2_xboole_0, fraenkel_a_3_5_domain_1, s7_domain_1, t62_filter_2, dt_m3_realset1, dt_k13_nat_lat, t30_zfmisc_1, rc4_struct_0, dt_k10_domain_1, t49_lattice2, fraenkel_a_0_1_domain_1, t66_filter_0, t16_binop_1, t31_filter_2, t6_filter_0, redefinition_k3_filter_2, d13_binop_1, idempotence_k4_subset_1, t40_zfmisc_1, d11_lattices, t63_filter_0, t63_lattice2, t174_partfun1, t55_funct_2, t18_lattice2, t112_zfmisc_1, t73_lattice2, existence_m2_filter_2, d3_binop_1, t60_filter_2, t6_lattice4, t14_lattice2, dt_k13_filter_2, t13_filter_0, d2_relat_1, dt_k3_lattices, t68_lattice2, d19_binop_1, cc2_lattices, redefinition_k4_lattices, t61_funct_2, fc3_lattices, dt_k3_subset_1, fraenkel_a_0_2_domain_1, fc1_funct_2, cc1_binop_1, t6_relat_1, t172_partfun1, t33_subset_1, t30_partfun1, t65_zfmisc_1, t63_subset_1, t112_partfun1, t38_xboole_1, fraenkel_a_4_1_domain_1, t23_lattices, t3_filter_0, t10_lattice4, antisymmetry_r2_hidden, d5_lattice4, d8_lattice4, t64_lattice2, t22_subset_1, redefinition_k6_domain_1
% 189.01/70.57 % No. of inferences in proof: 3429
% 189.01/70.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 70025 ms resp. 68774 ms w/o parsing
% 195.00/71.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 195.00/71.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------