Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LAT330+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n020.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 07:47:18 AM UTC 2026

% Result   : Theorem 171.27s 51.16s
% Output   : Refutation 177.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      : 1086
% Syntax   : Number of formulae    : 3515 ( 657 unt;   0 typ;  67 def)
%            Number of atoms       : 19530 (3242 equ;   0 cnn)
%            Maximal formula atoms :   58 (   5 avg)
%            Number of connectives : 65422 (5107   ~;2770   |;6940   &;45187   @)
%                                         ( 241 <=>;5177  =>;   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   : 8077 (  53   ^;7617   !; 340   ?;8077   :)
%                                         (   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(v13_lattices_decl,type,
    v13_lattices: $i > $o ).

thf(r1_filter_2_decl,type,
    r1_filter_2: $i > $i > $i > $o ).

thf(k18_filter_2_decl,type,
    k18_filter_2: $i > $i > $i ).

thf(k22_filter_2_decl,type,
    k22_filter_2: $i > $i > $i > $i ).

thf(k5_lattices_decl,type,
    k5_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(v14_lattices_decl,type,
    v14_lattices: $i > $o ).

thf(r1_realset1_decl,type,
    r1_realset1: $i > $i > $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(m1_lattice4_decl,type,
    m1_lattice4: $i > $i > $i > $o ).

thf(v2_lattice4_decl,type,
    v2_lattice4: $i > $i > $i > $o ).

thf(r2_lattice4_decl,type,
    r2_lattice4: $i > $i > $i > $o ).

thf(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(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(k6_domain_1_decl,type,
    k6_domain_1: $i > $i > $i ).

thf(k6_lattices_decl,type,
    k6_lattices: $i > $i ).

thf(a_2_1_lattice4_decl,type,
    a_2_1_lattice4: $i > $i > $i ).

thf(k3_lattice4_decl,type,
    k3_lattice4: $i > $i > $i ).

thf(a_2_1_domain_1_decl,type,
    a_2_1_domain_1: $i > $i > $i ).

thf(k3_lattice2_decl,type,
    k3_lattice2: $i > $i > $i > $i > $i ).

thf(k1_lattices_decl,type,
    k1_lattices: $i > $i > $i > $i ).

thf(r1_lattices_decl,type,
    r1_lattices: $i > $i > $i > $o ).

thf(k1_domain_1_decl,type,
    k1_domain_1: $i > $i > $i > $i > $i ).

thf(k12_filter_2_decl,type,
    k12_filter_2: $i > $i > $i ).

thf(k8_filter_2_decl,type,
    k8_filter_2: $i > $i > $i ).

thf(r3_lattices_decl,type,
    r3_lattices: $i > $i > $i > $o ).

thf(k10_filter_2_decl,type,
    k10_filter_2: $i > $i > $i ).

thf(k3_filter_0_decl,type,
    k3_filter_0: $i > $i > $i ).

thf(k4_filter_0_decl,type,
    k4_filter_0: $i > $i > $i > $i ).

thf(k13_filter_2_decl,type,
    k13_filter_2: $i > $i > $i ).

thf(k3_filter_2_decl,type,
    k3_filter_2: $i > $i > $i ).

thf(k7_filter_2_decl,type,
    k7_filter_2: $i > $i > $i ).

thf(k19_filter_2_decl,type,
    k19_filter_2: $i > $i > $i ).

thf(p1_s2_domain_1_decl,type,
    p1_s2_domain_1: $i > $i > $o ).

thf(k5_lattice4_decl,type,
    k5_lattice4: $i > $i ).

thf(k7_lattices_decl,type,
    k7_lattices: $i > $i > $i ).

thf(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(k1_lattice4_decl,type,
    k1_lattice4: $i > $i > $i ).

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(v3_lattice4_decl,type,
    v3_lattice4: $i > $i > $i > $o ).

thf(r1_lattice4_decl,type,
    r1_lattice4: $i > $i > $i > $o ).

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(k1_filter_0_decl,type,
    k1_filter_0: $i > $i ).

thf(v2_filter_0_decl,type,
    v2_filter_0: $i > $i > $o ).

thf(f1_s14_funct_2_decl,type,
    f1_s14_funct_2: $i ).

thf(f2_s14_funct_2_decl,type,
    f2_s14_funct_2: $i ).

thf(p1_s14_funct_2_decl,type,
    p1_s14_funct_2: $i > $i > $o ).

thf(a_3_0_filter_0_decl,type,
    a_3_0_filter_0: $i > $i > $i > $i ).

thf(f1_s12_funct_2_decl,type,
    f1_s12_funct_2: $i ).

thf(f3_s12_funct_2_decl,type,
    f3_s12_funct_2: $i > $i ).

thf(f2_s12_funct_2_decl,type,
    f2_s12_funct_2: $i ).

thf(f1_s13_funct_2_decl,type,
    f1_s13_funct_2: $i ).

thf(f3_s13_funct_2_decl,type,
    f3_s13_funct_2: $i > $i ).

thf(f2_s13_funct_2_decl,type,
    f2_s13_funct_2: $i ).

thf(a_3_1_domain_1_decl,type,
    a_3_1_domain_1: $i > $i > $i > $i ).

thf(k11_domain_1_decl,type,
    k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k13_domain_1_decl,type,
    k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k7_funcop_1_decl,type,
    k7_funcop_1: $i > $i > $i > $i > $i > $i ).

thf(k7_grcat_1_decl,type,
    k7_grcat_1: $i > $i ).

thf(k8_domain_1_decl,type,
    k8_domain_1: $i > $i > $i > $i > $i ).

thf(k11_filter_2_decl,type,
    k11_filter_2: $i > $i > $i ).

thf(k12_filter_0_decl,type,
    k12_filter_0: $i > $i > $i ).

thf(f1_s3_funct_2_decl,type,
    f1_s3_funct_2: $i ).

thf(f2_s3_funct_2_decl,type,
    f2_s3_funct_2: $i ).

thf(p1_s3_funct_2_decl,type,
    p1_s3_funct_2: $i > $i > $o ).

thf(a_3_7_domain_1_decl,type,
    a_3_7_domain_1: $i > $i > $i > $i ).

thf(a_4_1_domain_1_decl,type,
    a_4_1_domain_1: $i > $i > $i > $i > $i ).

thf(r1_filter_0_decl,type,
    r1_filter_0: $i > $i > $i > $i > $o ).

thf(v1_setwiseo_decl,type,
    v1_setwiseo: $i > $i > $o ).

thf(a_2_0_filter_0_decl,type,
    a_2_0_filter_0: $i > $i > $i ).

thf(a_3_1_filter_0_decl,type,
    a_3_1_filter_0: $i > $i > $i > $i ).

thf(k2_struct_0_decl,type,
    k2_struct_0: $i > $i > $i > $i ).

thf(k5_filter_2_decl,type,
    k5_filter_2: $i > $i > $i ).

thf(k6_filter_2_decl,type,
    k6_filter_2: $i > $i > $i ).

thf(k2_filter_2_decl,type,
    k2_filter_2: $i > $i > $i ).

thf(a_3_2_filter_2_decl,type,
    a_3_2_filter_2: $i > $i > $i > $i ).

thf(a_0_2_domain_1_decl,type,
    a_0_2_domain_1: $i ).

thf(f3_s9_domain_1_decl,type,
    f3_s9_domain_1: $i ).

thf(p1_s7_domain_1_decl,type,
    p1_s7_domain_1: $i > $o ).

thf(r1_filter_1_decl,type,
    r1_filter_1: $i > $i > $o ).

thf(f3_s11_funct_2_decl,type,
    f3_s11_funct_2: $i ).

thf(f4_s11_funct_2_decl,type,
    f4_s11_funct_2: $i ).

thf(f1_s11_funct_2_decl,type,
    f1_s11_funct_2: $i ).

thf(f2_s11_funct_2_decl,type,
    f2_s11_funct_2: $i ).

thf(f5_s11_funct_2_decl,type,
    f5_s11_funct_2: $i ).

thf(f6_s11_funct_2_decl,type,
    f6_s11_funct_2: $i ).

thf(f7_s11_funct_2_decl,type,
    f7_s11_funct_2: $i > $i ).

thf(k9_filter_2_decl,type,
    k9_filter_2: $i > $i > $i ).

thf(k1_struct_0_decl,type,
    k1_struct_0: $i > $i > $i ).

thf(r3_lattice4_decl,type,
    r3_lattice4: $i > $i > $i > $o ).

thf(k8_subset_1_decl,type,
    k8_subset_1: $i > $i ).

thf(a_0_1_domain_1_decl,type,
    a_0_1_domain_1: $i ).

thf(f2_s8_domain_1_decl,type,
    f2_s8_domain_1: $i ).

thf(k1_setwiseo_decl,type,
    k1_setwiseo: $i > $i ).

thf(a_2_0_filter_2_decl,type,
    a_2_0_filter_2: $i > $i > $i ).

thf(f1_s8_domain_1_decl,type,
    f1_s8_domain_1: $i ).

thf(f3_s8_domain_1_decl,type,
    f3_s8_domain_1: $i > $i ).

thf(p1_s8_domain_1_decl,type,
    p1_s8_domain_1: $i > $o ).

thf(k1_filter_2_decl,type,
    k1_filter_2: $i > $i ).

thf(f1_s9_domain_1_decl,type,
    f1_s9_domain_1: $i ).

thf(f2_s9_domain_1_decl,type,
    f2_s9_domain_1: $i ).

thf(f4_s9_domain_1_decl,type,
    f4_s9_domain_1: $i > $i > $i ).

thf(p1_s9_domain_1_decl,type,
    p1_s9_domain_1: $i > $i > $o ).

thf(f1_s4_subset_1_decl,type,
    f1_s4_subset_1: $i ).

thf(f2_s4_subset_1_decl,type,
    f2_s4_subset_1: $i ).

thf(p1_s4_subset_1_decl,type,
    p1_s4_subset_1: $i > $o ).

thf(f3_s4_subset_1_decl,type,
    f3_s4_subset_1: $i ).

thf(a_3_0_filter_2_decl,type,
    a_3_0_filter_2: $i > $i > $i > $i ).

thf(k23_filter_2_decl,type,
    k23_filter_2: $i > $i > $i ).

thf(a_3_1_filter_2_decl,type,
    a_3_1_filter_2: $i > $i > $i > $i ).

thf(sk1_decl,type,
    sk1: $i ).

thf(sk2_decl,type,
    sk2: $i ).

thf(sk3_decl,type,
    sk3: $i > $i > $i > $o ).

thf(sk4_decl,type,
    sk4: $i > $i > $i > $i ).

thf(sk5_decl,type,
    sk5: $i > $i > $i > $i > $i > $i ).

thf(sk6_decl,type,
    sk6: $i > $i > $i > $i ).

thf(sk7_decl,type,
    sk7: $i > $i > $i > $i ).

thf(sk8_decl,type,
    sk8: $i > $i > $i > $i ).

thf(sk9_decl,type,
    sk9: $i > $i > $i > $i ).

thf(sk10_decl,type,
    sk10: $i > $i > $i ).

thf(sk11_decl,type,
    sk11: $i > $i > $i ).

thf(sk12_decl,type,
    sk12: $i > $i > $i ).

thf(sk13_decl,type,
    sk13: $i > $i > $i ).

thf(sk14_decl,type,
    sk14: $i ).

thf(sk15_decl,type,
    sk15: $i > $i > $i ).

thf(sk18_decl,type,
    sk18: $i > $i ).

thf(sk19_decl,type,
    sk19: $i > $i ).

thf(sk25_decl,type,
    sk25: $i > $i > $i ).

thf(sk71_decl,type,
    sk71: $i ).

thf(sk80_decl,type,
    sk80: $i > $i ).

thf(sk81_decl,type,
    sk81: $i > $i > $i ).

thf(sk94_decl,type,
    sk94: $i ).

thf(sk95_decl,type,
    sk95: $i ).

thf(sk110_decl,type,
    sk110: $i > $i > $i ).

thf(sk111_decl,type,
    sk111: $i > $i > $i ).

thf(sk118_decl,type,
    sk118: $i ).

thf(sk138_decl,type,
    sk138: $i ).

thf(sk152_decl,type,
    sk152: $i ).

thf(sk157_decl,type,
    sk157: $i ).

thf(sk187_decl,type,
    sk187: $i ).

thf(sk188_decl,type,
    sk188: $i ).

thf(sk195_decl,type,
    sk195: $i > $i ).

thf(sk196_decl,type,
    sk196: $i ).

thf(sk197_decl,type,
    sk197: $i ).

thf(sk207_decl,type,
    sk207: $i ).

thf(sk216_decl,type,
    sk216: $i ).

thf(sk218_decl,type,
    sk218: $i ).

thf(sk234_decl,type,
    sk234: $i > $i > $i > $o ).

thf(sk235_decl,type,
    sk235: $i > $i > $i > $i ).

thf(sk236_decl,type,
    sk236: $i > $i > $i > $i ).

thf(sk249_decl,type,
    sk249: $i > $i ).

thf(sk276_decl,type,
    sk276: $i ).

thf(sk292_decl,type,
    sk292: $i ).

thf(sk296_decl,type,
    sk296: $i ).

thf(sk311_decl,type,
    sk311: $i ).

thf(sk313_decl,type,
    sk313: $i ).

thf(sk328_decl,type,
    sk328: $o ).

thf(sk329_decl,type,
    sk329: $i ).

thf(sk330_decl,type,
    sk330: $i ).

thf(sk336_decl,type,
    sk336: $o ).

thf(sk337_decl,type,
    sk337: $i ).

thf(sk338_decl,type,
    sk338: $i ).

thf(sk340_decl,type,
    sk340: $i ).

thf(sk343_decl,type,
    sk343: $i ).

thf(sk344_decl,type,
    sk344: $o ).

thf(sk345_decl,type,
    sk345: $i ).

thf(sk346_decl,type,
    sk346: $i ).

thf(sk349_decl,type,
    sk349: $i > $i ).

thf(sk355_decl,type,
    sk355: $i ).

thf(sk356_decl,type,
    sk356: $i ).

thf(sk359_decl,type,
    sk359: $i ).

thf(sk364_decl,type,
    sk364: $i > $i > $i ).

thf(sk365_decl,type,
    sk365: $i > $i > $i ).

thf(sk370_decl,type,
    sk370: $o ).

thf(sk371_decl,type,
    sk371: $i ).

thf(sk372_decl,type,
    sk372: $i ).

thf(sk384_decl,type,
    sk384: $i > $i ).

thf(sk404_decl,type,
    sk404: $i ).

thf(sk420_decl,type,
    sk420: $i ).

thf(sk445_decl,type,
    sk445: $o ).

thf(sk446_decl,type,
    sk446: $i ).

thf(sk447_decl,type,
    sk447: $i ).

thf(sk456_decl,type,
    sk456: $i ).

thf(sk469_decl,type,
    sk469: $i ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: $i] :
          ~ ( ( ( A @ l3_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ! [B: $i] :
                ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
               => ( ( A @ v13_lattices )
                 => ( B @ ( A @ k5_lattices @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k18_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 @ v13_lattices )
             => ( A @ ( sk1 @ k5_lattices @ ( sk1 @ k22_filter_2 ) ) @ ( A @ ( sk1 @ k18_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(sk249_def,definition,
    ( sk249
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ( B @ v1_xboole_0 )
          & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).

thf(sk276_def,definition,
    ( sk276
    = ( @+[A: $i] :
          ( ~ ( A @ v3_struct_0 )
          & ( A @ l1_struct_0 ) ) ) ) ).

thf(sk292_def,definition,
    ( sk292
    = ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).

thf(sk296_def,definition,
    ( sk296
    = ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).

thf(sk311_def,definition,
    ( sk311
    = ( @+[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(sk313_def,definition,
    ( sk313
    = ( @+[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(sk329_def,definition,
    ( sk329
    = ( @+[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(sk330_def,definition,
    ( sk330
    = ( @+[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(sk337_def,definition,
    ( sk337
    = ( @+[A: $i] :
          ~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
           => ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).

thf(sk338_def,definition,
    ( sk338
    = ( @+[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(sk340_def,definition,
    ( sk340
    = ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).

thf(sk343_def,definition,
    ( sk343
    = ( @+[A: $i] :
          ( ( A @ v3_lattices )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk345_def,definition,
    ( sk345
    = ( @+[A: $i] :
          ~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
           => ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).

thf(sk346_def,definition,
    ( sk346
    = ( @+[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(sk355_def,definition,
    ( sk355
    = ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).

thf(sk356_def,definition,
    ( sk356
    = ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).

thf(sk359_def,definition,
    ( sk359
    = ( @+[A: $i] :
          ~ ( A @ v1_xboole_0 ) ) ) ).

thf(sk364_def,definition,
    ( sk364
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( A @ ( C @ r2_hidden ) )
           => ( C = B ) ) ) ) ).

thf(sk365_def,definition,
    ( sk365
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( C = B )
           => ( A @ ( C @ r2_hidden ) ) ) ) ) ).

thf(sk371_def,definition,
    ( sk371
    = ( @+[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(sk372_def,definition,
    ( sk372
    = ( @+[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(sk404_def,definition,
    ( sk404
    = ( @+[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(sk420_def,definition,
    ( sk420
    = ( @+[A: $i] :
          ( ~ ( A @ v3_struct_0 )
          & ( A @ l2_struct_0 ) ) ) ) ).

thf(sk446_def,definition,
    ( sk446
    = ( @+[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(sk447_def,definition,
    ( sk447
    = ( @+[A: $i] :
          ~ ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
           => ( ( ( A @ p1_s4_subset_1 )
               => ( f3_s4_subset_1 @ ( A @ r2_hidden ) ) )
              & ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
               => ( A @ p1_s4_subset_1 ) ) ) ) ) ) ).

thf(sk456_def,definition,
    ( sk456
    = ( @+[A: $i] :
          ( ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk469_def,definition,
    ( sk469
    = ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).

thf(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/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(2163,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(762,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) )
           => ( A @ ( B @ m2_lattice4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_filter_2) ).

thf(5422,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)],[762]) ).

thf(772,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ( ( B @ ( A @ k18_filter_2 ) )
                = ( A @ u1_struct_0 ) )
              & ~ ! [C: $i] :
                    ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                   => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                      = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_filter_2) ).

thf(5469,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)],[772]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).

thf(3883,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)],[465]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ( ( B @ v1_funct_1 )
            & ( B @ v1_relat_1 ) )
         => ! [C: $i] :
              ( ( ( C @ v1_funct_1 )
                & ( C @ v1_relat_1 ) )
             => ( ( ( ( C @ k1_relat_1 )
                    = A )
                  & ( ( B @ k1_relat_1 )
                    = A ) )
               => ( B = C ) ) ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).

thf(1290,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(1291,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)],[1290]) ).

thf(1295,plain,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1291]) ).

thf(1299,plain,
    ! [A: $i] :
      ( ( A @ sk19 @ v1_relat_1 )
      | ( A = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1295]) ).

thf(330,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(3116,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(3117,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)],[3116]) ).

thf(3118,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)],[3117]) ).

thf(3120,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3118]) ).

thf(3122,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3120]) ).

thf(3123,plain,
    k1_xboole_0 @ v1_xboole_0,
    inference(simp,[status(thm)],[3122]) ).

thf(710,axiom,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(5196,plain,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(5197,plain,
    ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[5196]) ).

thf(5198,plain,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[5197]) ).

thf(8136,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,5198]) ).

thf(8137,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8136]) ).

thf(8157,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[8137]) ).

thf(32854,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_tarski ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,8157]) ).

thf(32855,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_tarski ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[32854]) ).

thf(32856,plain,
    ! [A: $i] : ( A @ k1_tarski @ sk19 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[32855:[bind(A,$thf( C @ k1_tarski )),bind(B,$thf( C ))]]) ).

thf(32927,plain,
    ! [A: $i] : ( A @ k1_tarski @ sk19 @ v1_relat_1 ),
    inference(simp,[status(thm)],[32856]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ ( B @ v1_filter_0 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r2_hidden ) )
                <=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_0) ).

thf(4169,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)],[519]) ).

thf(882,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                        = ( D @ ( B @ ( A @ k3_lattices ) ) ) )
                      & ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                        = ( D @ ( B @ ( A @ k4_lattices ) ) ) ) )
                   => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattices) ).

thf(5950,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)],[882]) ).

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 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m3_lattice4 ) )
             => ( ( C
                  = ( B @ ( A @ k3_lattice4 ) ) )
              <=> ( ! [D: $i] :
                      ( ( A @ ( D @ m3_lattice4 ) )
                     => ( ( D @ ( B @ r1_tarski ) )
                       => ( D @ ( C @ r1_tarski ) ) ) )
                  & ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattice4) ).

thf(4290,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)],[542]) ).

thf(378,axiom,
    k1_xboole_0 @ v1_xboole_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(3397,plain,
    k1_xboole_0 @ v1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(130,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

thf(1840,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(934,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).

thf(6172,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)],[934]) ).

thf(246,axiom,
    ? [A: $i] :
      ( ( A @ v2_funct_1 )
      & ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(2542,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(2543,plain,
    ( ( sk138 @ v2_funct_1 )
    & ( sk138 @ v1_funct_1 )
    & ( sk138 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[2542]) ).

thf(2544,plain,
    sk138 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[2543]) ).

thf(904,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
      <=> ( A @ k1_lattice2 @ v14_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).

thf(6042,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)],[904]) ).

thf(126,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_subset_1 ) )
             => ( ( ( B @ ( D @ ( A @ r2_binop_1 ) ) )
                  & ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_binop_1) ).

thf(1818,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(109,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
      <=> ! [B: $i,C: $i] :
            ( ( ( ( B @ ( A @ k1_funct_1 ) )
                = ( C @ ( A @ k1_funct_1 ) ) )
              & ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
              & ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).

thf(1686,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(3,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ v1_relat_1 )
     => ( ( E
          = ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
       => ( ( ( E @ k2_relat_1 )
            = ( D @ ( B @ k2_tarski ) ) )
          & ( ( E @ k1_relat_1 )
            = ( C @ ( A @ k2_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relat_1) ).

thf(1029,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(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 ) )
      & ( ( ( 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)],[1029]) ).

thf(1032,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)],[1030]) ).

thf(1035,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)],[1032]) ).

thf(1036,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)],[1035]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_subset_1) ).

thf(2630,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(445,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( B @ v1_xboole_0 )
      & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(3785,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)],[445]) ).

thf(3786,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
      & ( A @ k1_zfmisc_1 @ ( A @ sk249 @ m1_subset_1 ) ) ),
    inference(cnf,[status(esa)],[3785]) ).

thf(3788,plain,
    ! [A: $i] : ( A @ sk249 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[3786]) ).

thf(369,axiom,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).

thf(3326,plain,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(3327,plain,
    ( ( sk218 @ v1_relat_1 )
    & ~ ( sk218 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[3326]) ).

thf(3328,plain,
    ~ ( sk218 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[3327]) ).

thf(13045,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk218 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,3328]) ).

thf(13046,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk218 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[13045]) ).

thf(13052,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != sk218 ),
    inference(simp,[status(thm)],[13046]) ).

thf(522,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v16_lattices )
          & ( A @ v15_lattices )
          & ( A @ v11_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v17_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).

thf(4188,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)],[522]) ).

thf(502,axiom,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(4091,plain,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(4092,plain,
    ( ~ ( sk276 @ v3_struct_0 )
    & ( sk276 @ l1_struct_0 ) ),
    inference(cnf,[status(esa)],[4091]) ).

thf(4094,plain,
    ~ ( sk276 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4092]) ).

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 @ v13_lattices )
           => ( B @ ( A @ k5_lattices @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k18_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_filter_2) ).

thf(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 @ v13_lattices )
             => ( B @ ( A @ k5_lattices @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k18_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(1021,plain,
    ~ ! [A: $i] :
        ( ( ( A @ l3_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ( ( A @ v13_lattices )
             => ( B @ ( A @ k5_lattices @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k18_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1022,plain,
    ( ~ ( sk2 @ ( sk1 @ k5_lattices @ ( sk1 @ k22_filter_2 ) ) @ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ u1_struct_0 @ r1_filter_2 ) ) )
    & ( sk1 @ v13_lattices )
    & ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
    & ( sk1 @ l3_lattices )
    & ( sk1 @ v10_lattices )
    & ~ ( sk1 @ v3_struct_0 ) ),
    inference(cnf,[status(esa)],[1021]) ).

thf(1024,plain,
    sk1 @ v10_lattices,
    inference(cnfConj,[status(thm)],[1022]) ).

thf(81,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
                          = ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_binop_1) ).

thf(1469,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(692,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ? [C: $i] :
            ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
            & ( A @ ( C @ m1_subset_1 ) ) )
       => ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ( ( C
                = ( B @ ( A @ k3_binop_1 ) ) )
            <=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_binop_1) ).

thf(5088,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)],[692]) ).

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/sandbox2/benchmark/theBenchmark.p',rc10_lattices) ).

thf(2733,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(2734,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)],[2733]) ).

thf(2744,plain,
    sk157 @ v14_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(745,axiom,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(5360,plain,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(5361,plain,
    ! [A: $i] : ( A @ ( A @ sk384 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[5360]) ).

thf(42,axiom,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( A @ ( B @ m1_subset_1 ) )
         => ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).

thf(1218,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(1219,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)],[1218]) ).

thf(1221,plain,
    ! [A: $i] :
      ( ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
      | ~ ( sk14 @ ( A @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[1219]) ).

thf(41006,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)],[5361,1221]) ).

thf(41007,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)],[41006]) ).

thf(41008,plain,
    ~ ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[41007:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ sk384 ))]]) ).

thf(41189,plain,
    ( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,41008]) ).

thf(41190,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41189]) ).

thf(41233,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != k1_xboole_0 ),
    inference(simp,[status(thm)],[41190]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_2) ).

thf(1190,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(600,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).

thf(4571,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)],[600]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v14_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) )
                       => ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_lattice2) ).

thf(4450,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)],[574]) ).

thf(858,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( A @ v14_lattices )
           => ( A @ k6_lattices @ ( B @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k2_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_2) ).

thf(5857,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)],[858]) ).

thf(180,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
    <=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

thf(2109,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(799,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k9_filter_2 ) )
        = ( B @ ( A @ k7_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_filter_2) ).

thf(5593,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)],[799]) ).

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/sandbox2/benchmark/theBenchmark.p',cc1_binop_1) ).

thf(2131,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(332,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).

thf(3127,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(3128,plain,
    ~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[3127]) ).

thf(3129,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[3128]) ).

thf(8140,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,3129]) ).

thf(8141,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8140]) ).

thf(8154,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[8141]) ).

thf(870,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ ( B @ v1_filter_0 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ ( C @ m1_filter_0 ) )
                 => ( ( C @ ( B @ r1_tarski ) )
                   => ( ( B = C )
                      | ( C
                        = ( A @ u1_struct_0 ) ) ) ) )
              & ( B
               != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_0) ).

thf(5896,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)],[870]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
              & ( A @ v14_lattices ) )
           => ( ( B
                = ( A @ u1_struct_0 ) )
              & ( A @ k17_filter_2 @ ( B @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_2) ).

thf(3798,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)],[449]) ).

thf(18,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).

thf(1104,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(1105,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(cnf,[status(esa)],[1104]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v6_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                  = ( B @ ( C @ ( A @ k2_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattices) ).

thf(4022,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)],[491]) ).

thf(426,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( B @ ( F @ m1_subset_1 ) )
                           => ( ( C @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
                       => ( ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_lattice2) ).

thf(3666,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)],[426]) ).

thf(629,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( ( ( D @ ( E @ r2_hidden ) )
                & ~ ( C @ ( E @ r2_hidden ) ) )
              | ( ~ ( D @ ( E @ r2_hidden ) )
                & ( C @ ( E @ r2_hidden ) ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).

thf(4729,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)],[629]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
        & ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).

thf(1233,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(1234,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)],[1233]) ).

thf(1237,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)],[1234]) ).

thf(735,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).

thf(5320,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(812,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m3_lattice4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_lattice4) ).

thf(5654,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)],[812]) ).

thf(964,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k20_filter_2 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k20_filter_2) ).

thf(6317,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)],[964]) ).

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/sandbox2/benchmark/theBenchmark.p',fc3_nat_lat) ).

thf(2470,plain,
    ( ( k13_nat_lat @ v10_lattices )
    & ( k13_nat_lat @ v9_lattices )
    & ( k13_nat_lat @ v8_lattices )
    & ( k13_nat_lat @ v7_lattices )
    & ( k13_nat_lat @ v6_lattices )
    & ( k13_nat_lat @ v5_lattices )
    & ( k13_nat_lat @ v4_lattices )
    & ( k13_nat_lat @ v3_lattices )
    & ~ ( k13_nat_lat @ v3_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(2471,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)],[2470]) ).

thf(2480,plain,
    k13_nat_lat @ v6_lattices,
    inference(cnfConj,[status(thm)],[2471]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).

thf(1081,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(1082,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(miniscope,[status(thm)],[1081]) ).

thf(1083,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ ( B @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[1082]) ).

thf(950,axiom,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_struct_0) ).

thf(6263,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)],[950]) ).

thf(150,axiom,
    ? [A: $i] :
      ( ( A @ v1_xboole_0 )
      & ( A @ v2_funct_1 )
      & ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).

thf(1972,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(1973,plain,
    ( ( sk71 @ v1_xboole_0 )
    & ( sk71 @ v2_funct_1 )
    & ( sk71 @ v1_funct_1 )
    & ( sk71 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1972]) ).

thf(1977,plain,
    sk71 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[1973]) ).

thf(1220,plain,
    ~ ( sk14 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1219]) ).

thf(6564,plain,
    ( ( ( sk71 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,1220]) ).

thf(6565,plain,
    ( ( sk71 @ v1_xboole_0 )
   != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6564]) ).

thf(6566,plain,
    sk71 != sk14,
    inference(simp,[status(thm)],[6565]) ).

thf(1014,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( C @ ( B @ a_2_0_filter_2 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( C @ ( D @ ( B @ r3_lattices ) ) )
            & ( A = D )
            & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_2) ).

thf(6527,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( ? [D: $i] :
              ( ( C @ ( D @ ( B @ r3_lattices ) ) )
              & ( A = D )
              & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
         => ( C @ ( B @ a_2_0_filter_2 ) @ ( A @ r2_hidden ) ) )
        & ( ( C @ ( B @ a_2_0_filter_2 ) @ ( A @ r2_hidden ) )
         => ? [D: $i] :
              ( ( C @ ( D @ ( B @ r3_lattices ) ) )
              & ( A = D )
              & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(148,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
         => ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
            & ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_realset1) ).

thf(1956,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(145,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
           => ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).

thf(1950,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(701,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k12_filter_0 ) )
        = ( B @ ( A @ k10_filter_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_filter_0) ).

thf(5131,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)],[701]) ).

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/sandbox2/benchmark/theBenchmark.p',t5_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 ) )
                 => ! [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(19,axiom,
    ( ( ( k1_xboole_0 @ k2_relat_1 )
      = k1_xboole_0 )
    & ( ( k1_xboole_0 @ k1_relat_1 )
      = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).

thf(1106,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(1107,plain,
    ( ( ( k1_xboole_0 @ k2_relat_1 )
      = k1_xboole_0 )
    & ( ( k1_xboole_0 @ k1_relat_1 )
      = k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1106]) ).

thf(1108,plain,
    ( ( k1_xboole_0 @ k1_relat_1 )
    = k1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1107]) ).

thf(1110,plain,
    ( ( k1_xboole_0 @ k1_relat_1 )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1108]) ).

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/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).

thf(3172,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(900,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k6_lattices @ ( A @ k3_lattices ) ) )
            = ( A @ k6_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattices) ).

thf(6022,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)],[900]) ).

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/sandbox2/benchmark/theBenchmark.p',rc9_lattices) ).

thf(2206,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(2207,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)],[2206]) ).

thf(2210,plain,
    sk94 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
          & ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
       => ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_partfun1) ).

thf(1053,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(1054,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)],[1053]) ).

thf(1055,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)],[1054]) ).

thf(1056,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)],[1055]) ).

thf(1026,plain,
    ~ ( sk1 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[1022]) ).

thf(6866,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)],[1056,1026]) ).

thf(6867,plain,
    ! [A: $i] :
      ( ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[6866:[bind(A,$thf( sk1 ))]]) ).

thf(7083,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)],[6867]) ).

thf(553,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
    <=> ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).

thf(4339,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)],[553]) ).

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/sandbox2/benchmark/theBenchmark.p',t49_funct_2) ).

thf(2395,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(400,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v14_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
               => ( ( C @ ( A @ ( B @ r2_lattice4 ) ) )
                  & ( A @ v14_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattice4) ).

thf(3509,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)],[400]) ).

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/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).

thf(3108,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(27,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
         => ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
            & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
            & ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_realset1) ).

thf(1140,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(1141,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)],[1140]) ).

thf(1142,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)],[1141]) ).

thf(613,axiom,
    ? [A: $i] :
      ( ( A @ v17_lattices )
      & ( A @ v16_lattices )
      & ( A @ v15_lattices )
      & ( A @ v14_lattices )
      & ( A @ v13_lattices )
      & ( A @ v11_lattices )
      & ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_lattices) ).

thf(4623,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)],[613]) ).

thf(899,axiom,
    ( ( k6_nat_lat @ l3_lattices )
    & ( k6_nat_lat @ v10_lattices )
    & ~ ( k6_nat_lat @ v3_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_nat_lat) ).

thf(6017,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)],[899]) ).

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/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).

thf(2120,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ! [C: $i] :
          ~ ( ~ ( B @ ( C @ r2_hidden ) )
            & ~ ( B @ ( C @ r2_tarski ) )
            & ( B @ ( C @ r1_tarski ) ) )
      & ! [C: $i] :
          ~ ( ! [D: $i] :
                ~ ( ! [E: $i] :
                      ( ( C @ ( E @ r1_tarski ) )
                     => ( D @ ( E @ r2_hidden ) ) )
                  & ( B @ ( D @ r2_hidden ) ) )
            & ( B @ ( C @ r2_hidden ) ) )
      & ! [C: $i,D: $i] :
          ( ( ( C @ ( D @ r1_tarski ) )
            & ( B @ ( C @ r2_hidden ) ) )
         => ( B @ ( D @ r2_hidden ) ) )
      & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(2121,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)],[2120]) ).

thf(2122,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)],[2121]) ).

thf(2126,plain,
    ! [A: $i] : ( A @ sk80 @ ( A @ r2_hidden ) ),
    inference(cnfConj,[status(thm)],[2122]) ).

thf(48,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
    <=> ( ( A != C )
        & ( B @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).

thf(1240,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(1241,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)],[1240]) ).

thf(1242,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)],[1241]) ).

thf(1244,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != C )
      | ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[1242]) ).

thf(1246,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
      | ( A != C ) ),
    inference(lifteq,[status(thm)],[1244]) ).

thf(1247,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ r2_hidden ) ),
    inference(simp,[status(thm)],[1246]) ).

thf(38314,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)],[2126,1247]) ).

thf(38315,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)],[38314]) ).

thf(38367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk80 )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[38315]) ).

thf(38388,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
     != ( B @ sk80 ) ),
    inference(simp,[status(thm)],[38367]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( ! [D: $i] :
              ( ( A @ ( D @ r2_hidden ) )
             => ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
          & ( ( C @ k1_relat_1 )
            = A ) )
       => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
          & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).

thf(1037,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(1038,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        | ~ ( B @ ( A @ ( C @ sk3 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( 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)],[1037]) ).

thf(1041,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)],[1038]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
         => ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).

thf(1200,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(767,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattices) ).

thf(5444,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)],[767]) ).

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/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).

thf(2077,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(907,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k5_lattices @ ( A @ k3_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattices) ).

thf(6057,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)],[907]) ).

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/sandbox2/benchmark/theBenchmark.p',fc1_nat_lat) ).

thf(3175,plain,
    ( ( k6_nat_lat @ v10_lattices )
    & ( k6_nat_lat @ v9_lattices )
    & ( k6_nat_lat @ v8_lattices )
    & ( k6_nat_lat @ v7_lattices )
    & ( k6_nat_lat @ v6_lattices )
    & ( k6_nat_lat @ v5_lattices )
    & ( k6_nat_lat @ v4_lattices )
    & ( k6_nat_lat @ v3_lattices )
    & ~ ( k6_nat_lat @ v3_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(3176,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)],[3175]) ).

thf(3185,plain,
    k6_nat_lat @ v6_lattices,
    inference(cnfConj,[status(thm)],[3176]) ).

thf(367,axiom,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_xboole_0 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(3314,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(3315,plain,
    ( ( sk216 @ v1_funct_1 )
    & ( sk216 @ v1_xboole_0 )
    & ( sk216 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[3314]) ).

thf(3317,plain,
    sk216 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[3315]) ).

thf(147,axiom,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).

thf(1954,plain,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(1955,plain,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[1954]) ).

thf(488,axiom,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(4004,plain,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(4005,plain,
    ~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[4004]) ).

thf(4006,plain,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[4005]) ).

thf(8146,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,4006]) ).

thf(8147,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8146]) ).

thf(8160,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[8147]) ).

thf(11634,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)],[1955,8160]) ).

thf(11635,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[11634:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(134,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( ( C @ k1_relat_1 )
          = k1_xboole_0 )
       => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
          & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).

thf(1882,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(167,axiom,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
      = ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).

thf(2045,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(2046,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
      = ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
    inference(cnf,[status(esa)],[2045]) ).

thf(2047,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
      = ( A @ k1_tarski @ k1_zfmisc_1 ) ),
    inference(lifteq,[status(thm)],[2046]) ).

thf(544,axiom,
    ? [A: $i] : ( A @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(4307,plain,
    ? [A: $i] : ( A @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(4308,plain,
    sk292 @ v1_xboole_0,
    inference(cnf,[status(esa)],[4307]) ).

thf(607,axiom,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).

thf(4604,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(4605,plain,
    ~ ? [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[4604]) ).

thf(4606,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[4605]) ).

thf(10159,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk292 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,4606]) ).

thf(10160,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[10159]) ).

thf(10170,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk292 ),
    inference(simp,[status(thm)],[10160]) ).

thf(26471,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 )
       != sk292 ) ),
    inference(paramod_ordered,[status(thm)],[2047,10170]) ).

thf(26472,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk292 ),
    inference(pattern_uni,[status(thm)],[26471:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(26525,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk292 ),
    inference(simp,[status(thm)],[26472]) ).

thf(2217,plain,
    sk94 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

thf(30157,plain,
    ! [A: $i] :
      ( ( A != sk94 )
      | ( k1_xboole_0 @ v3_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2217]) ).

thf(30158,plain,
    ( ( k1_xboole_0 @ v3_lattices )
    | ( sk94 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30157:[bind(A,$thf( sk94 ))]]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
                  = D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_binop_1) ).

thf(1068,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(546,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v3_filter_0 )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( B @ ( A @ k8_filter_0 ) @ v3_filter_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_filter_0) ).

thf(4311,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)],[546]) ).

thf(923,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v3_filter_0 )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r1_relat_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_filter_0) ).

thf(6106,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)],[923]) ).

thf(823,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ? [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
              & ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_2) ).

thf(5696,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)],[823]) ).

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/sandbox2/benchmark/theBenchmark.p',rc11_lattices) ).

thf(2941,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(2942,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)],[2941]) ).

thf(2953,plain,
    sk187 @ v15_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

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/sandbox2/benchmark/theBenchmark.p',t57_domain_1) ).

thf(2590,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(73,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ( ( A @ k1_relat_1 )
          = k1_xboole_0 )
      <=> ( ( A @ k2_relat_1 )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).

thf(1422,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(341,axiom,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).

thf(3168,plain,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(3169,plain,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[3168]) ).

thf(3171,plain,
    k1_xboole_0 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3169]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).

thf(1051,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(1052,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)],[1051]) ).

thf(8236,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)],[3171,1052]) ).

thf(8237,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)],[8236]) ).

thf(8238,plain,
    ! [A: $i] : ( k1_xboole_0 @ k1_relat_1 @ ( k1_xboole_0 @ k9_relat_1 ) @ ( A @ ( k1_xboole_0 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[8237:[bind(A,$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/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).

thf(3124,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(3125,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[3124]) ).

thf(3126,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[3125]) ).

thf(23504,plain,
    k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ),
    inference(rewrite,[status(thm)],[8238,3126]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
       => ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).

thf(1064,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(1065,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)],[1064]) ).

thf(349,axiom,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(3207,plain,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(3208,plain,
    ( ( sk207 @ v1_funct_1 )
    & ( sk207 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[3207]) ).

thf(3210,plain,
    sk207 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3208]) ).

thf(8518,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)],[3210,7083]) ).

thf(8519,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)],[8518]) ).

thf(8520,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)],[8519:[bind(A,$thf( sk207 ))]]) ).

thf(8602,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)],[1065,8520]) ).

thf(8603,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)],[8602]) ).

thf(8604,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)],[8603]) ).

thf(8613,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)],[8604]) ).

thf(3209,plain,
    sk207 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3208]) ).

thf(34404,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)],[8613,3209]) ).

thf(34405,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)],[34404]) ).

thf(34448,plain,
    ( ( ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ r1_tarski ) )
     != ( k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ) ) )
    | ( ( sk207 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23504,34405]) ).

thf(34449,plain,
    ( ( ( k1_xboole_0 @ ( sk207 @ k2_relat_1 @ r1_tarski ) )
     != ( k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ) ) )
    | ( ( sk207 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[34448]) ).

thf(34560,plain,
    ( ( k1_xboole_0 != k1_xboole_0 )
    | ( ( sk207 @ k2_relat_1 )
     != k1_xboole_0 )
    | ( ( sk207 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[34449]) ).

thf(34597,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)],[34560]) ).

thf(2947,plain,
    sk187 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(622,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
     => ( ( B @ ( A @ r1_tarski ) )
       => ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).

thf(4697,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)],[622]) ).

thf(478,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).

thf(3959,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(470,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k10_filter_2 ) )
        = ( B @ ( A @ k7_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_filter_2) ).

thf(3912,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)],[470]) ).

thf(1069,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)],[1068]) ).

thf(1070,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)],[1069]) ).

thf(1073,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)],[1070]) ).

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/sandbox2/benchmark/theBenchmark.p',t9_lattice2) ).

thf(2671,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(267,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ v1_relat_1 )
     => ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_realset1) ).

thf(2676,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(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/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).

thf(3012,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(39,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) )
        = ( A @ ( B @ k4_xboole_0 ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).

thf(1205,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(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/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).

thf(2282,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(815,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m2_filter_2 ) )
             => ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_2) ).

thf(5669,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)],[815]) ).

thf(551,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
        <=> ( B @ ( C @ r2_hidden ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

thf(4326,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)],[551]) ).

thf(724,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ r2_hidden ) )
               => ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).

thf(5265,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)],[724]) ).

thf(120,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
       => ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).

thf(1793,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(610,axiom,
    ! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(4614,plain,
    ! [A: $i] : ( A @ ( A @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(90,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_partfun1) ).

thf(1533,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(631,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m3_lattice4 ) )
         => ( A @ ( B @ m2_lattice4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lattice4) ).

thf(4747,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)],[631]) ).

thf(1002,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( B @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_2) ).

thf(6480,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)],[1002]) ).

thf(603,axiom,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
            = ( B @ f3_s4_funct_2 ) ) )
      & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
      & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
      & ( A @ v1_funct_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_funct_2) ).

thf(4588,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)],[603]) ).

thf(4589,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk311 @ ( 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 @ ( sk311 @ m2_relset_1 ) ) )
      & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ v1_funct_2 ) ) )
      & ( sk311 @ v1_funct_1 ) ),
    inference(cnf,[status(esa)],[4588]) ).

thf(4592,plain,
    f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ),
    inference(cnfConj,[status(thm)],[4589]) ).

thf(1012,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m2_filter_2 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) )
                = ( C @ ( B @ ( A @ a_3_1_filter_2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_2) ).

thf(6522,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)],[1012]) ).

thf(107,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( ( C @ k2_relat_1 )
            = B )
          & ( C @ v2_funct_1 ) )
       => ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
          & ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
          & ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).

thf(1671,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(4624,plain,
    ( ( sk313 @ v17_lattices )
    & ( sk313 @ v16_lattices )
    & ( sk313 @ v15_lattices )
    & ( sk313 @ v14_lattices )
    & ( sk313 @ v13_lattices )
    & ( sk313 @ v11_lattices )
    & ( sk313 @ v10_lattices )
    & ( sk313 @ v9_lattices )
    & ( sk313 @ v8_lattices )
    & ( sk313 @ v7_lattices )
    & ( sk313 @ v6_lattices )
    & ( sk313 @ v5_lattices )
    & ( sk313 @ v4_lattices )
    & ( sk313 @ v3_lattices )
    & ~ ( sk313 @ v3_struct_0 )
    & ( sk313 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4623]) ).

thf(4633,plain,
    sk313 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

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/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).

thf(3429,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(798,axiom,
    ( ( f3_s11_funct_2 != f4_s11_funct_2 )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
           => ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
                 != ( B @ f7_s11_funct_2 ) )
                & ( B != f4_s11_funct_2 )
                & ( B != f3_s11_funct_2 ) ) )
        & ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
          = f6_s11_funct_2 )
        & ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
          = f5_s11_funct_2 )
        & ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s11_funct_2) ).

thf(5579,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)],[798]) ).

thf(5580,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk404 @ ( 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 @ ( sk404 @ ( 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 @ ( sk404 @ ( 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 @ ( sk404 @ m2_relset_1 ) ) )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) )
      & ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ v1_funct_2 ) ) )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) )
      & ( ( sk404 @ v1_funct_1 )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) ) ),
    inference(cnf,[status(esa)],[5579]) ).

thf(5583,plain,
    ( ( ( f4_s11_funct_2 @ ( sk404 @ ( 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)],[5580]) ).

thf(5589,plain,
    ( ( ( f4_s11_funct_2 @ ( sk404 @ ( 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)],[5583]) ).

thf(490,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ l3_lattices )
        & ( B @ v17_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ! [C: $i] :
          ( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
            & ~ ( C @ v1_xboole_0 ) )
         => ( ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) )
          <=> ? [D: $i] :
                ( ? [E: $i] :
                    ( ( C @ ( E @ r2_hidden ) )
                    & ( C @ ( D @ r2_hidden ) )
                    & ( A
                      = ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
                    & ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
                & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice4) ).

thf(4011,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)],[490]) ).

thf(2740,plain,
    sk157 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(3316,plain,
    sk216 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3315]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).

thf(1137,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(1138,plain,
    ! [A: $i] :
      ( ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1137]) ).

thf(1139,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_relat_1 )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1138]) ).

thf(15630,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)],[3316,1139]) ).

thf(15631,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)],[15630]) ).

thf(15632,plain,
    ( ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) )
    = ( sk216 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15631:[bind(A,$thf( sk216 ))]]) ).

thf(103,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).

thf(1640,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(569,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                = ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).

thf(4435,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)],[569]) ).

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/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(2146,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(1027,plain,
    sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ),
    inference(cnfConj,[status(thm)],[1022]) ).

thf(41030,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)],[1027,1221]) ).

thf(41031,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)],[41030]) ).

thf(41129,plain,
    ! [A: $i] :
      ( ( ( sk1 @ u1_struct_0 )
       != sk14 )
      | ( sk2 != A )
      | ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41031]) ).

thf(41162,plain,
    ( ( ( sk1 @ u1_struct_0 )
     != sk14 )
    | ~ ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41129]) ).

thf(41620,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)],[1977,41162]) ).

thf(41621,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41620]) ).

thf(41626,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
     != sk71 )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41621]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_2) ).

thf(1078,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(697,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( B @ ( A @ r1_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).

thf(5120,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)],[697]) ).

thf(404,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( A @ ( C @ r2_hidden ) )
       => ( ( C @ ( D @ k1_funct_1 ) )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).

thf(3530,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( A @ ( C @ r2_hidden ) )
       => ( ( C @ ( D @ k1_funct_1 ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(8755,plain,
    ( ( ( sk216 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,1220]) ).

thf(8756,plain,
    ( ( sk216 @ v1_xboole_0 )
   != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8755]) ).

thf(8765,plain,
    sk216 != sk14,
    inference(simp,[status(thm)],[8756]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
       => ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).

thf(1066,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(1067,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)],[1066]) ).

thf(1975,plain,
    sk71 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[1973]) ).

thf(1028,plain,
    sk1 @ v13_lattices,
    inference(cnfConj,[status(thm)],[1022]) ).

thf(6848,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ v13_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)],[1056,1028]) ).

thf(6849,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[6848:[bind(A,$thf( sk1 ))]]) ).

thf(7074,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[6849]) ).

thf(7233,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1975,7074]) ).

thf(7234,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7233]) ).

thf(7235,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7234:[bind(A,$thf( sk71 ))]]) ).

thf(7650,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 @ v13_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)],[1067,7235]) ).

thf(7651,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 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7650]) ).

thf(7694,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7651]) ).

thf(7711,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7694]) ).

thf(1974,plain,
    sk71 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[1973]) ).

thf(11071,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 @ v13_lattices ) ),
    inference(rewrite,[status(thm)],[7711,1974]) ).

thf(11072,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[11071]) ).

thf(261,axiom,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

thf(2658,plain,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(2659,plain,
    ( ( sk152 @ v1_relat_1 )
    & ( sk152 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[2658]) ).

thf(2660,plain,
    sk152 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[2659]) ).

thf(7567,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,5198]) ).

thf(7568,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7567]) ).

thf(7573,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk152 ),
    inference(simp,[status(thm)],[7568]) ).

thf(59,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( C @ v2_funct_1 )
       => ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
          = ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).

thf(1310,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(646,axiom,
    ( ! [A: $i] :
        ( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
       => ? [B: $i] :
            ( ( B @ ( A @ p1_s14_funct_2 ) )
            & ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
           => ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
        & ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s14_funct_2) ).

thf(4836,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)],[646]) ).

thf(4837,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( sk330 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
        | ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
        | ~ sk328 )
      & ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk330 @ m2_relset_1 ) ) )
        | ~ sk328 )
      & ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk330 @ v1_funct_2 ) ) )
        | ~ sk328 )
      & ( ( sk330 @ v1_funct_1 )
        | ~ sk328 )
      & ( sk328
        | ~ ( A @ ( sk329 @ p1_s14_funct_2 ) )
        | ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
      & ( sk328
        | ( f1_s14_funct_2 @ ( sk329 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4836]) ).

thf(4839,plain,
    ( sk328
    | ( f1_s14_funct_2 @ ( sk329 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4837]) ).

thf(838,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k17_filter_2 )
        = ( A @ u1_struct_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_2) ).

thf(5755,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)],[838]) ).

thf(591,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

thf(4526,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(4527,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(cnf,[status(esa)],[4526]) ).

thf(4528,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[4527]) ).

thf(31,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
       => ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
          & ( ( C @ k1_relat_1 )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_funct_2) ).

thf(1161,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(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 ) )
      & ( ( ( 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)],[1161]) ).

thf(1164,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)],[1162]) ).

thf(1025,plain,
    sk1 @ l3_lattices,
    inference(cnfConj,[status(thm)],[1022]) ).

thf(6892,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)],[1056,1025]) ).

thf(6893,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[6892:[bind(A,$thf( sk1 ))]]) ).

thf(7096,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)],[6893]) ).

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/sandbox2/benchmark/theBenchmark.p',t9_domain_1) ).

thf(2448,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(917,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u1_lattices @ v3_binop_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice2) ).

thf(6089,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)],[917]) ).

thf(4638,plain,
    sk313 @ v15_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(989,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_filter_2 )
        = ( A @ k1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).

thf(6416,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)],[989]) ).

thf(444,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                    & ~ ( D @ v1_xboole_0 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
                        & ~ ( E @ v1_xboole_0 ) )
                     => ( ( ( E @ ( C @ r2_hidden ) )
                          & ( D @ ( B @ r2_hidden ) ) )
                       => ( ( E @ ( D @ ( A @ k20_filter_2 ) ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                          & ( E @ ( D @ ( A @ k20_filter_2 ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_2) ).

thf(3781,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)],[444]) ).

thf(571,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_domain_1) ).

thf(4440,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)],[571]) ).

thf(2476,plain,
    k13_nat_lat @ v7_lattices,
    inference(cnfConj,[status(thm)],[2471]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).

thf(1260,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(6789,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)],[1056,1024]) ).

thf(6790,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[6789:[bind(A,$thf( sk1 ))]]) ).

thf(7046,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)],[6790]) ).

thf(8554,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)],[3210,7046]) ).

thf(8555,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)],[8554]) ).

thf(8556,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)],[8555:[bind(A,$thf( sk207 ))]]) ).

thf(12316,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,8556]) ).

thf(12317,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12316]) ).

thf(12398,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk207 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12317]) ).

thf(140,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( B @ ( A @ k3_subset_1 ) )
        = ( B @ ( A @ k4_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).

thf(1919,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(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/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).

thf(3253,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(945,axiom,
    ( ( ! [A: $i] :
          ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
         => ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
          <=> ( A @ p1_s4_subset_1 ) ) )
      & ! [A: $i] :
          ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
         => ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
          <=> ( A @ p1_s4_subset_1 ) ) ) )
   => ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_subset_1) ).

thf(6225,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)],[945]) ).

thf(6226,plain,
    ( ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ ( f3_s4_subset_1 @ ( sk447 @ r2_hidden ) )
      | ~ ( sk447 @ p1_s4_subset_1 )
      | sk445 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( sk447 @ p1_s4_subset_1 )
      | ~ ( sk447 @ p1_s4_subset_1 )
      | sk445 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ ( f3_s4_subset_1 @ ( sk447 @ r2_hidden ) )
      | ( f3_s4_subset_1 @ ( sk447 @ r2_hidden ) )
      | sk445 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( sk447 @ p1_s4_subset_1 )
      | ( f3_s4_subset_1 @ ( sk447 @ r2_hidden ) )
      | sk445 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( f1_s4_subset_1 @ ( sk447 @ m1_subset_1 ) )
      | sk445 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk445
      | ~ ( f2_s4_subset_1 @ ( sk446 @ r2_hidden ) )
      | ~ ( sk446 @ p1_s4_subset_1 ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk445
      | ( sk446 @ p1_s4_subset_1 )
      | ~ ( sk446 @ p1_s4_subset_1 ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk445
      | ~ ( f2_s4_subset_1 @ ( sk446 @ r2_hidden ) )
      | ( f2_s4_subset_1 @ ( sk446 @ r2_hidden ) ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk445
      | ( sk446 @ p1_s4_subset_1 )
      | ( f2_s4_subset_1 @ ( sk446 @ r2_hidden ) ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk445
      | ( f1_s4_subset_1 @ ( sk446 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[6225]) ).

thf(6235,plain,
    ( ( f2_s4_subset_1 = f3_s4_subset_1 )
    | ( f1_s4_subset_1 @ ( sk447 @ m1_subset_1 ) )
    | sk445 ),
    inference(cnfConj,[status(thm)],[6226]) ).

thf(6241,plain,
    ( ( f1_s4_subset_1 @ ( sk447 @ m1_subset_1 ) )
    | sk445
    | ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
    inference(lifteq,[status(thm)],[6235]) ).

thf(7415,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)],[1975,7083]) ).

thf(7416,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)],[7415]) ).

thf(7417,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)],[7416:[bind(A,$thf( sk71 ))]]) ).

thf(12291,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,7417]) ).

thf(12292,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12291]) ).

thf(12421,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk71 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12292]) ).

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 ) )
         => ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_0) ).

thf(6117,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ! [E: $i] :
          ~ ( ! [F: $i] :
                ( ( A @ ( F @ m1_subset_1 ) )
               => ~ ( ( E
                      = ( F @ ( D @ k1_funct_1 ) ) )
                    & ( C @ ( F @ r2_hidden ) ) ) )
            & ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).

thf(1057,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(1058,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)],[1057]) ).

thf(1059,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)],[1058]) ).

thf(1062,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)],[1059]) ).

thf(1063,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)],[1062]) ).

thf(810,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v17_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
      <=> ( ( A @ k1_lattice2 @ l3_lattices )
          & ( A @ k1_lattice2 @ v17_lattices )
          & ( A @ k1_lattice2 @ v10_lattices )
          & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_2) ).

thf(5636,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)],[810]) ).

thf(43,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
                & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
                & ( D @ v1_funct_1 ) )
             => ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
                = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice2) ).

thf(1222,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(13039,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk14 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,1220]) ).

thf(13040,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[13039]) ).

thf(13056,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != sk14 ),
    inference(simp,[status(thm)],[13040]) ).

thf(759,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( B @ ( A @ k2_filter_0 ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                & ( B @ ( A @ k2_filter_0 ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                & ( B @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_0) ).

thf(5412,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)],[759]) ).

thf(905,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ! [E: $i] :
                      ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( C = F )
                              & ( B = E ) )
                           => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                            <=> ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_0) ).

thf(6046,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ 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)],[905]) ).

thf(2661,plain,
    sk152 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[2659]) ).

thf(6731,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)],[2661,1052]) ).

thf(6732,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)],[6731]) ).

thf(6733,plain,
    ! [A: $i] : ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6732:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).

thf(15611,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)],[2661,1139]) ).

thf(15612,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)],[15611]) ).

thf(15613,plain,
    ( ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) )
    = ( sk152 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15612:[bind(A,$thf( sk152 ))]]) ).

thf(21482,plain,
    ! [A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6733,15613]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).

thf(1095,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(37,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A @ ( B @ v3_binop_1 ) )
      <=> ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
              = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_binop_1) ).

thf(1193,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(1194,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)],[1193]) ).

thf(1196,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)],[1194]) ).

thf(2216,plain,
    sk94 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

thf(698,axiom,
    ? [A: $i] :
      ~ ( A @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(5123,plain,
    ? [A: $i] :
      ~ ( A @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

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/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).

thf(3088,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(874,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ( A @ v3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_filter_0 @ ( A @ k8_filter_0 ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_0) ).

thf(5921,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)],[874]) ).

thf(468,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(3898,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(608,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).

thf(4607,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(833,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v13_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
               => ( ( C @ ( A @ ( B @ r3_lattice4 ) ) )
                  & ( A @ v13_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice4) ).

thf(5740,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)],[833]) ).

thf(407,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).

thf(3545,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)],[407]) ).

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/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).

thf(2972,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(510,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) )
       => ( A @ v11_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice2) ).

thf(4142,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)],[510]) ).

thf(1243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ r2_hidden ) )
      | ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[1242]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
        & ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).

thf(1127,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(471,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).

thf(3915,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)],[471]) ).

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/sandbox2/benchmark/theBenchmark.p',t26_binop_1) ).

thf(2020,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(401,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( B @ ( A @ r2_filter_2 ) )
          <=> ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v1_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_2) ).

thf(3513,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v1_filter_0 ) )
             => ( B @ ( A @ r2_filter_2 ) ) )
            & ( ( B @ ( A @ r2_filter_2 ) )
             => ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v1_filter_0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(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/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).

thf(3308,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(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/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).

thf(2010,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(143,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
       => ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
          = ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).

thf(1935,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(829,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ ( B @ ( A @ k9_filter_2 ) @ m2_lattice4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_2) ).

thf(5723,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)],[829]) ).

thf(679,axiom,
    ? [A: $i] : ( A @ l2_struct_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).

thf(5055,plain,
    ? [A: $i] : ( A @ l2_struct_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(5056,plain,
    sk355 @ l2_struct_0,
    inference(cnf,[status(esa)],[5055]) ).

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/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).

thf(3140,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(492,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) )
          & ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) )
          & ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
          & ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
          & ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
          & ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_binop_1 ) ) )
       => ( A @ v10_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattice2) ).

thf(4030,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)],[492]) ).

thf(666,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r1_tarski ) )
                & ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice4) ).

thf(4963,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)],[666]) ).

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/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).

thf(2825,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(550,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_nat_lat ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ ( B @ ( A @ k24_filter_2 ) @ m2_nat_lat ) )
        & ( B @ ( A @ k24_filter_2 ) @ v3_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k24_filter_2) ).

thf(4322,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)],[550]) ).

thf(726,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v5_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( D @ ( C @ ( A @ r1_lattices ) ) )
                      & ( C @ ( B @ ( A @ r1_lattices ) ) ) )
                   => ( D @ ( B @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattices) ).

thf(5269,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)],[726]) ).

thf(836,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k7_lattices ) )
                = ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattices) ).

thf(5750,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)],[836]) ).

thf(137,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ! [D: $i] :
              ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
                & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
                & ( D @ v1_funct_1 ) )
             => ! [E: $i] :
                  ( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
                  & ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
                  & ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice2) ).

thf(1904,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(88,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).

thf(1518,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(609,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != D )
        & ( A != C )
        & ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).

thf(4610,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)],[609]) ).

thf(936,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
                = ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_0) ).

thf(6182,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)],[936]) ).

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/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).

thf(2405,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(44,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ! [C: $i] :
            ~ ( ! [D: $i] :
                  ~ ( ( C
                      = ( D @ ( B @ k1_funct_1 ) ) )
                    & ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
              & ( A @ ( C @ r2_hidden ) ) )
       => ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).

thf(1225,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(1226,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)],[1225]) ).

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 ) )
      & ( ( 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)],[1226]) ).

thf(1228,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)],[1227]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B
            = ( A @ k1_relat_1 ) )
        <=> ! [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
            <=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).

thf(1482,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(419,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k2_tarski ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ( ( D = B )
            | ( D = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

thf(3597,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)],[419]) ).

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)],[1974,1139]) ).

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(638,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( B @ ( D @ m1_subset_1 ) )
               => ( C @ ( D @ r2_hidden ) ) )
           => ( C @ ( B @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).

thf(4775,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)],[638]) ).

thf(587,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_struct_0 ) ) )
        <=> ( B @ ( C @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_struct_0) ).

thf(4511,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)],[587]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice2) ).

thf(5352,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)],[742]) ).

thf(739,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ m2_lattice4 ) )
        & ~ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k22_filter_2) ).

thf(5342,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)],[739]) ).

thf(8501,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)],[3209,1052]) ).

thf(8502,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)],[8501]) ).

thf(8503,plain,
    ! [A: $i] : ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[8502:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).

thf(15608,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)],[3209,1139]) ).

thf(15609,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)],[15608]) ).

thf(15610,plain,
    ( ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) )
    = ( sk207 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15609:[bind(A,$thf( sk207 ))]]) ).

thf(23573,plain,
    ! [A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[8503,15610]) ).

thf(297,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

thf(2916,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(555,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
                                = B ) ) )
                       => ( ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) )
                            = B )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_lattice2) ).

thf(4348,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)],[555]) ).

thf(431,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                <=> ( C @ ( D @ r2_hidden ) ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).

thf(3689,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)],[431]) ).

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/sandbox2/benchmark/theBenchmark.p',d7_lattices) ).

thf(3495,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(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/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).

thf(2708,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(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/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).

thf(2501,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(424,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i,E: $i] :
            ( ( A
              = ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
            & ( C @ ( E @ m1_subset_1 ) )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).

thf(3653,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)],[424]) ).

thf(7610,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)],[1975,7096]) ).

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 ) ) ) ),
    inference(simp,[status(thm)],[7610]) ).

thf(7612,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)],[7611:[bind(A,$thf( sk71 ))]]) ).

thf(12335,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,7612]) ).

thf(12336,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12335]) ).

thf(12407,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk71 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12336]) ).

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/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).

thf(2682,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(60,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i] :
          ( ( B
            = ( A @ k2_relat_1 ) )
        <=> ! [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
            <=> ? [D: $i] :
                  ( ( C
                    = ( D @ ( A @ k1_funct_1 ) ) )
                  & ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).

thf(1313,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(455,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k16_filter_2 ) )
        = ( B @ ( A @ k8_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k16_filter_2) ).

thf(3820,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)],[455]) ).

thf(4637,plain,
    ~ ( sk313 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4624]) ).

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/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).

thf(3204,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(883,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_lattice4 ) )
            = ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattice4) ).

thf(5953,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)],[883]) ).

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 ) )
     => ( B @ ( B @ ( A @ r3_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).

thf(4539,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)],[594]) ).

thf(2735,plain,
    sk157 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

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/sandbox2/benchmark/theBenchmark.p',t15_binop_1) ).

thf(1985,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(566,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ! [C: $i] :
                ( ( A @ ( C @ m2_filter_2 ) )
               => ( B @ ( C @ m2_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_filter_2) ).

thf(4422,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)],[566]) ).

thf(1019,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( D @ ( A @ k6_filter_2 ) @ ( E @ ( A @ k6_filter_2 ) @ ( A @ r3_lattices ) ) )
                         => ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
                        & ( ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) )
                         => ( D @ ( A @ k6_filter_2 ) @ ( E @ ( A @ k6_filter_2 ) @ ( A @ r3_lattices ) ) ) )
                        & ( ( B @ ( A @ k5_filter_2 ) @ ( C @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ r3_lattices ) ) )
                         => ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                        & ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                         => ( B @ ( A @ k5_filter_2 ) @ ( C @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_2) ).

thf(6547,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)],[1019]) ).

thf(8148,plain,
    ( ( ( sk218 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,3328]) ).

thf(8149,plain,
    ( ( sk218 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8148]) ).

thf(8156,plain,
    sk218 != k1_xboole_0,
    inference(simp,[status(thm)],[8149]) ).

thf(31656,plain,
    ! [A: $i] :
      ( ( A != sk218 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,8156]) ).

thf(31657,plain,
    ! [A: $i] :
      ( ( A != sk218 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[31656]) ).

thf(31658,plain,
    sk218 @ sk19 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[31657:[bind(A,$thf( sk218 ))]]) ).

thf(34226,plain,
    ! [A: $i] :
      ( ( ( sk218 @ sk19 @ 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)],[31658,1139]) ).

thf(34227,plain,
    ! [A: $i] :
      ( ( ( sk218 @ sk19 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[34226]) ).

thf(34228,plain,
    ( ( sk218 @ sk19 @ k1_relat_1 @ ( sk218 @ sk19 @ k9_relat_1 ) )
    = ( sk218 @ sk19 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[34227:[bind(A,$thf( sk218 @ sk19 ))]]) ).

thf(203,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).

thf(2269,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(530,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).

thf(4224,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)],[530]) ).

thf(230,axiom,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

thf(2437,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(2438,plain,
    ~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[2437]) ).

thf(2439,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[2438]) ).

thf(8138,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,2439]) ).

thf(8139,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8138]) ).

thf(8158,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[8139]) ).

thf(30318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k4_tarski ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,8158]) ).

thf(30319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k4_tarski ) ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[30318]) ).

thf(30320,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk19 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[30319:[bind(A,$thf( E @ ( D @ k4_tarski ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).

thf(33226,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk19 @ v1_relat_1 ),
    inference(simp,[status(thm)],[30320]) ).

thf(3318,plain,
    sk216 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3315]) ).

thf(8804,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3318,7074]) ).

thf(8805,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8804]) ).

thf(8806,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8805:[bind(A,$thf( sk216 ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',rc12_lattices) ).

thf(3055,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(3056,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)],[3055]) ).

thf(3061,plain,
    ~ ( sk196 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[3056]) ).

thf(991,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( B @ ( A @ k6_filter_2 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_2) ).

thf(6423,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)],[991]) ).

thf(1007,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( B @ ( A @ k4_lattice4 ) )
            = ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice4) ).

thf(6506,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)],[1007]) ).

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/sandbox2/benchmark/theBenchmark.p',redefinition_k21_filter_2) ).

thf(3485,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(2270,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    inference(cnf,[status(esa)],[2269]) ).

thf(8527,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)],[3210,7096]) ).

thf(8528,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)],[8527]) ).

thf(8529,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)],[8528:[bind(A,$thf( sk207 ))]]) ).

thf(15291,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)],[2270,8529]) ).

thf(15292,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)],[15291]) ).

thf(15348,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)],[15292]) ).

thf(15394,plain,
    ( ( sk207 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15348]) ).

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/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).

thf(3280,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(439,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_2 ) )
         => ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_2) ).

thf(3744,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)],[439]) ).

thf(892,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( B @ ( A @ k4_lattice4 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice4) ).

thf(5989,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)],[892]) ).

thf(731,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
                <=> ! [D: $i] :
                      ( ( A @ ( D @ m1_subset_1 ) )
                     => ! [E: $i] :
                          ( ( A @ ( E @ m1_subset_1 ) )
                         => ! [F: $i] :
                              ( ( A @ ( F @ m1_subset_1 ) )
                             => ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                                = ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_binop_1) ).

thf(5289,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)],[731]) ).

thf(827,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ~ ( ! [D: $i] :
                      ( ( A @ ( D @ m2_filter_2 ) )
                     => ~ ( ( ( ( D @ ( C @ r2_hidden ) )
                              & ~ ( D @ ( B @ r2_hidden ) ) )
                            | ( ~ ( D @ ( C @ r2_hidden ) )
                              & ( D @ ( B @ r2_hidden ) ) ) )
                          & ( D @ ( A @ r2_filter_2 ) ) ) )
                  & ( B != C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_2) ).

thf(5706,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)],[827]) ).

thf(7481,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 @ v13_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)],[1065,7235]) ).

thf(7482,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 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7481]) ).

thf(7523,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7482]) ).

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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7523]) ).

thf(8021,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 @ v13_lattices ) ),
    inference(rewrite,[status(thm)],[7532,1974]) ).

thf(8022,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[8021]) ).

thf(171,axiom,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

thf(2073,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(2074,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    inference(cnf,[status(esa)],[2073]) ).

thf(2545,plain,
    sk138 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[2543]) ).

thf(7418,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)],[2545,7083]) ).

thf(7419,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)],[7418]) ).

thf(7420,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)],[7419:[bind(A,$thf( sk138 ))]]) ).

thf(7599,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)],[1065,7420]) ).

thf(7600,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)],[7599]) ).

thf(7601,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)],[7600]) ).

thf(7603,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)],[7601]) ).

thf(10181,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)],[7603,2544]) ).

thf(10182,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)],[10181]) ).

thf(12983,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)],[2074,10182]) ).

thf(12984,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)],[12983]) ).

thf(13010,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)],[12984]) ).

thf(13025,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)],[13010]) ).

thf(450,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( B @ ( A @ k8_filter_0 ) @ u1_lattices )
              = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
            & ( ( B @ ( A @ k8_filter_0 ) @ u2_lattices )
              = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
            & ( ( B @ ( A @ k8_filter_0 ) @ u1_struct_0 )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_filter_0) ).

thf(3803,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)],[450]) ).

thf(30012,plain,
    ! [A: $i] :
      ( ( A != k13_nat_lat )
      | ( k1_xboole_0 @ v7_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2476]) ).

thf(30013,plain,
    ( ( k1_xboole_0 @ v7_lattices )
    | ( k13_nat_lat @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30012:[bind(A,$thf( k13_nat_lat ))]]) ).

thf(24,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
     => ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
        & ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).

thf(1130,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(1131,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)],[1130]) ).

thf(1132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
    inference(cnfConj,[status(thm)],[1131]) ).

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/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).

thf(3043,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(852,axiom,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).

thf(5836,plain,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(6641,plain,
    ( ( ( sk218 @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,3328]) ).

thf(6642,plain,
    ( ( sk218 @ v1_xboole_0 )
   != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6641]) ).

thf(6643,plain,
    sk218 != sk71,
    inference(simp,[status(thm)],[6642]) ).

thf(2745,plain,
    sk157 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

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/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).

thf(2571,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(434,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ ( B @ ( A @ k13_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_filter_2) ).

thf(3713,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)],[434]) ).

thf(948,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v16_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ? [C: $i] :
                ( ( B @ ( C @ ( A @ r2_lattices ) ) )
                & ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_lattices) ).

thf(6253,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)],[948]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
    <=> ! [B: $i] :
          ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

thf(3028,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(3029,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)],[3028]) ).

thf(3030,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)],[3029]) ).

thf(3031,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ r2_hidden ) )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3030]) ).

thf(3033,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ r2_hidden ) )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3031]) ).

thf(3034,plain,
    ! [A: $i] :
      ~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[3033]) ).

thf(15184,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk80 @ ( A @ r2_hidden ) )
       != ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2126,3034]) ).

thf(15185,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk80 @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[15184]) ).

thf(15192,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk80 )
       != k1_xboole_0 )
      | ( A != B ) ),
    inference(simp,[status(thm)],[15185]) ).

thf(15198,plain,
    ! [A: $i] :
      ( ( A @ sk80 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[15192]) ).

thf(32686,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk80 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,15198]) ).

thf(32687,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk80 ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[32686]) ).

thf(32688,plain,
    ! [A: $i] : ( A @ sk80 @ sk19 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[32687:[bind(A,$thf( C @ sk80 )),bind(B,$thf( C ))]]) ).

thf(33329,plain,
    ! [A: $i] : ( A @ sk80 @ sk19 @ v1_relat_1 ),
    inference(simp,[status(thm)],[32688]) ).

thf(804,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v8_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) )
                  = C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).

thf(5604,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)],[804]) ).

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/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).

thf(2373,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(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/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).

thf(3014,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(3180,plain,
    k6_nat_lat @ v8_lattices,
    inference(cnfConj,[status(thm)],[3176]) ).

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/sandbox2/benchmark/theBenchmark.p',t14_binop_1) ).

thf(2533,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(834,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
       => ( A @ k6_lattices @ ( A @ k18_filter_2 ) @ ( A @ k17_filter_2 @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_2) ).

thf(5744,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)],[834]) ).

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/sandbox2/benchmark/theBenchmark.p',rc1_lattice2) ).

thf(2414,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(2415,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)],[2414]) ).

thf(2420,plain,
    sk118 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(141,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
      <=> ( ( B
            = ( A @ ( C @ k1_funct_1 ) ) )
          & ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).

thf(1922,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(5585,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ m2_relset_1 ) ) )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5580]) ).

thf(5588,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ m2_relset_1 ) ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5585]) ).

thf(1133,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
    inference(cnfConj,[status(thm)],[1131]) ).

thf(14801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ 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)],[5588,1133]) ).

thf(14802,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ 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)],[14801]) ).

thf(14803,plain,
    ( ( f2_s11_funct_2 @ ( sk404 @ k2_relat_1 @ r1_tarski ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[14802:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk404 ))]]) ).

thf(16641,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( sk404 @ 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)],[14803,1083]) ).

thf(16642,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( sk404 @ 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)],[16641]) ).

thf(16643,plain,
    ! [A: $i] :
      ( ( f2_s11_funct_2 @ ( A @ ( sk404 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[16642:[bind(A,$thf( sk404 @ k2_relat_1 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( C ))]]) ).

thf(16721,plain,
    ! [A: $i] :
      ( ( f2_s11_funct_2 @ ( A @ ( sk404 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[16643]) ).

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/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).

thf(2713,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(402,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
                & ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_0) ).

thf(3517,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
                & ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(486,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( A @ ( E @ r2_hidden ) )
        & ( E @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).

thf(3998,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)],[486]) ).

thf(338,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
      & ( k1_xboole_0 @ v1_funct_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).

thf(3157,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(3158,plain,
    ( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
    & ( k1_xboole_0 @ v1_funct_1 ) ),
    inference(miniscope,[status(thm)],[3157]) ).

thf(3159,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
      & ( k1_xboole_0 @ v1_funct_1 ) ),
    inference(cnf,[status(esa)],[3158]) ).

thf(3160,plain,
    k1_xboole_0 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3159]) ).

thf(8162,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)],[3160,7083]) ).

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 ) ) ) ),
    inference(simp,[status(thm)],[8162]) ).

thf(8164,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)],[8163:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15213,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8164,2270]) ).

thf(15214,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15213]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
                            = ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
                          & ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
                            = ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_binop_1) ).

thf(1084,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(1085,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)],[1084]) ).

thf(1087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ m1_subset_1 ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
      | ~ ( B @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1085]) ).

thf(86,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
       => ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).

thf(1514,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(2631,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
    inference(cnf,[status(esa)],[2630]) ).

thf(2632,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) )
      = ( A @ k1_subset_1 ) ),
    inference(lifteq,[status(thm)],[2631]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).

thf(2547,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(2548,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(cnf,[status(esa)],[2547]) ).

thf(2549,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(lifteq,[status(thm)],[2548]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).

thf(3092,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(3093,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[3092]) ).

thf(3094,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[3093]) ).

thf(38795,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k3_subset_1 ) )
      = k1_xboole_0 ),
    inference(rewrite,[status(thm)],[2632,2549,3094]) ).

thf(986,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k6_lattices @ ( A @ k7_lattices ) )
        = ( A @ k5_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice4) ).

thf(6396,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)],[986]) ).

thf(711,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k4_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattices) ).

thf(5199,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)],[711]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ! [C: $i] :
          ( ( ( C @ v1_funct_1 )
            & ( C @ v1_relat_1 ) )
         => ( ( ( ( C @ k2_relat_1 )
                = ( A @ k1_tarski ) )
              & ( ( B @ k2_relat_1 )
                = ( A @ k1_tarski ) )
              & ( ( B @ k1_relat_1 )
                = ( C @ k1_relat_1 ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).

thf(1145,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(1146,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)],[1145]) ).

thf(1147,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)],[1146]) ).

thf(557,axiom,
    ? [A: $i] : ( A @ l1_struct_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(4358,plain,
    ? [A: $i] : ( A @ l1_struct_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

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/sandbox2/benchmark/theBenchmark.p',cc5_lattice2) ).

thf(3216,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(977,axiom,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).

thf(6363,plain,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(6364,plain,
    ( ( sk456 @ v3_lattices )
    & ~ ( sk456 @ v3_struct_0 )
    & ( sk456 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[6363]) ).

thf(6365,plain,
    sk456 @ l3_lattices,
    inference(cnfConj,[status(thm)],[6364]) ).

thf(10161,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,4606]) ).

thf(10162,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[10161]) ).

thf(10173,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[10162]) ).

thf(26497,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)],[2047,10173]) ).

thf(26498,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[26497:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(26517,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[26498]) ).

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/sandbox2/benchmark/theBenchmark.p',rc2_lattice2) ).

thf(3071,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(3072,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)],[3071]) ).

thf(3084,plain,
    sk197 @ v3_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(835,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
                          & ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                       => ( ( C @ ( E @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
                          & ( E @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_0) ).

thf(5746,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)],[835]) ).

thf(476,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != D )
        & ( A != C )
        & ( ( B @ ( A @ k2_tarski ) )
          = ( D @ ( C @ k2_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).

thf(3951,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)],[476]) ).

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/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).

thf(2024,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(920,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattice4) ).

thf(6098,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)],[920]) ).

thf(4632,plain,
    sk313 @ v13_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(458,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m2_filter_2 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
                          & ( B @ ( C @ r2_hidden ) ) )
                       => ( B @ ( D @ r2_hidden ) ) ) ) )
              & ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( ( B @ ( D @ r2_hidden ) )
                          & ( B @ ( C @ r2_hidden ) ) )
                       => ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_2) ).

thf(3835,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)],[458]) ).

thf(5837,plain,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[5836]) ).

thf(41073,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)],[5837,1221]) ).

thf(41074,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)],[41073]) ).

thf(41075,plain,
    ~ ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[41074:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ k8_subset_1 ))]]) ).

thf(41265,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)],[3123,41075]) ).

thf(41266,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41265]) ).

thf(41310,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != k1_xboole_0 ),
    inference(simp,[status(thm)],[41266]) ).

thf(42917,plain,
    ! [A: $i] :
      ( ( A
       != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,41310]) ).

thf(42918,plain,
    ! [A: $i] :
      ( ( A
       != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[42917]) ).

thf(42919,plain,
    sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ sk19 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[42918:[bind(A,$thf( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ))]]) ).

thf(9029,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk292 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,4006]) ).

thf(9030,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9029]) ).

thf(9039,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk292 ),
    inference(simp,[status(thm)],[9030]) ).

thf(586,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( A @ r1_tarski ) )
       => ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
          & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).

thf(4507,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)],[586]) ).

thf(132,axiom,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).

thf(1875,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(901,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k3_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_2) ).

thf(6025,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)],[901]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v3_filter_0 )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B @ ( A @ k10_filter_0 ) @ k3_relat_1 )
              = ( A @ u1_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_filter_0) ).

thf(4771,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)],[637]) ).

thf(688,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( B @ ( C @ ( A @ r1_lattices ) ) )
                  & ( C @ ( B @ ( A @ r1_lattices ) ) ) )
               => ( B = C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).

thf(5077,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)],[688]) ).

thf(45,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).

thf(1231,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(1232,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ ( B @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1231]) ).

thf(667,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
     => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_2) ).

thf(4967,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)],[667]) ).

thf(358,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).

thf(3268,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(41250,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,41075]) ).

thf(41251,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41250]) ).

thf(41309,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) ),
    inference(simp,[status(thm)],[41251]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ k1_lattice2 )
        = ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_filter_2) ).

thf(4595,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)],[604]) ).

thf(843,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v16_lattices )
              & ( A @ v11_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C
                    = ( B @ ( A @ k7_lattices ) ) )
                <=> ( B @ ( C @ ( A @ r2_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattices) ).

thf(5792,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)],[843]) ).

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/sandbox2/benchmark/theBenchmark.p',d8_realset1) ).

thf(3431,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(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/sandbox2/benchmark/theBenchmark.p',t118_funct_2) ).

thf(2650,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(938,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v9_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
                  = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattices) ).

thf(6187,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)],[938]) ).

thf(642,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ? [F: $i] :
                            ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
                            & ( D @ ( F @ r2_hidden ) )
                            & ( C @ ( F @ m1_subset_1 ) ) )
                       => ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice2) ).

thf(4815,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)],[642]) ).

thf(819,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v14_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_filter_0) ).

thf(5682,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)],[819]) ).

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/sandbox2/benchmark/theBenchmark.p',t5_relat_1) ).

thf(2222,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(563,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) )
       => ( A @ v11_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice2) ).

thf(4411,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)],[563]) ).

thf(2950,plain,
    sk187 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(670,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ! [C: $i] :
          ~ ( ~ ( B @ ( C @ r2_hidden ) )
            & ~ ( B @ ( C @ r2_tarski ) )
            & ( B @ ( C @ r1_tarski ) ) )
      & ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
         => ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
      & ! [C: $i,D: $i] :
          ( ( ( C @ ( D @ r1_tarski ) )
            & ( B @ ( C @ r2_hidden ) ) )
         => ( B @ ( D @ r2_hidden ) ) )
      & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).

thf(4985,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)],[670]) ).

thf(4986,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)],[4985]) ).

thf(4987,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)],[4986]) ).

thf(4988,plain,
    ! [A: $i] : ( A @ sk349 @ ( A @ r2_hidden ) ),
    inference(cnfConj,[status(thm)],[4987]) ).

thf(869,axiom,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l2_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).

thf(5892,plain,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l2_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

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/sandbox2/benchmark/theBenchmark.p',d10_lattices) ).

thf(2794,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(15298,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)],[2270,7420]) ).

thf(15299,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)],[15298]) ).

thf(15351,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)],[15299]) ).

thf(15398,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15351]) ).

thf(466,axiom,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( ( A @ v2_struct_0 )
       => ( A
          = ( A @ u2_struct_0 @ ( A @ u1_struct_0 @ g2_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v2_struct_0) ).

thf(3887,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)],[466]) ).

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/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).

thf(2027,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(782,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k3_lattice4 ) @ m3_lattice4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice4) ).

thf(5526,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)],[782]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
                = ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_domain_1) ).

thf(4173,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)],[520]) ).

thf(7558,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,4006]) ).

thf(7559,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7558]) ).

thf(7564,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk152 ),
    inference(simp,[status(thm)],[7559]) ).

thf(3075,plain,
    sk197 @ v8_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(1040,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)],[1038]) ).

thf(6653,plain,
    ( ( ( sk152 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,1220]) ).

thf(6654,plain,
    ( ( sk152 @ v1_xboole_0 )
   != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6653]) ).

thf(6657,plain,
    sk152 != sk14,
    inference(simp,[status(thm)],[6654]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
         => ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
              & ( C @ v1_funct_1 ) )
           => ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
              & ( B @ ( A @ ( C @ v1_partfun1 ) ) )
              & ~ ( C @ v1_xboole_0 )
              & ( C @ v1_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).

thf(1632,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(487,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
        = ( A @ k2_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_subset_1) ).

thf(4001,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)],[487]) ).

thf(990,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
               => ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( C @ r2_hidden ) )
                  & ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( B @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_2) ).

thf(6419,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)],[990]) ).

thf(108,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).

thf(1682,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(25,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
        = ( C @ ( B @ k4_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).

thf(1134,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(1135,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)],[1134]) ).

thf(1136,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)],[1135]) ).

thf(128,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
           => ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_partfun1) ).

thf(1828,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(7236,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2545,7074]) ).

thf(7237,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7236]) ).

thf(7238,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7237:[bind(A,$thf( sk138 ))]]) ).

thf(7498,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 @ v13_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)],[1065,7238]) ).

thf(7499,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 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7498]) ).

thf(7520,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7499]) ).

thf(7528,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7520]) ).

thf(7858,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 @ v13_lattices ) ),
    inference(rewrite,[status(thm)],[7528,2544]) ).

thf(7859,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7858]) ).

thf(12969,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk138 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true
      | ( k1_xboole_0 @ v13_lattices ) ),
    inference(paramod_ordered,[status(thm)],[2074,7859]) ).

thf(12970,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk138 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk138 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12969]) ).

thf(12998,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( sk138 @ k2_relat_1 )
       != k1_xboole_0 )
      | ( ( sk138 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12970]) ).

thf(13013,plain,
    ( ( ( sk138 @ k2_relat_1 )
     != k1_xboole_0 )
    | ( ( sk138 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12998]) ).

thf(151,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( B != k1_xboole_0 )
       => ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).

thf(1978,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(3598,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)],[3597]) ).

thf(3599,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)],[3598]) ).

thf(3603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != A )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(cnfConj,[status(thm)],[3599]) ).

thf(3612,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != A )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(lifteq,[status(thm)],[3603]) ).

thf(3613,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[3612]) ).

thf(27207,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)],[3613,3034]) ).

thf(27208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[27207]) ).

thf(27221,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) )
       != k1_xboole_0 )
      | ( A != C ) ),
    inference(simp,[status(thm)],[27208]) ).

thf(27233,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[27221]) ).

thf(788,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_lattice4 ) )
         => ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r1_tarski ) )
                 => ( B @ ( C @ ( A @ k1_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice4) ).

thf(5541,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)],[788]) ).

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 ) )
         => ( ( B @ ( A @ k18_filter_2 ) )
            = ( B @ ( A @ a_2_0_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).

thf(5914,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)],[872]) ).

thf(706,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ k1_tarski ) )
    <=> ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

thf(5156,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)],[706]) ).

thf(906,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k13_filter_2 ) )
        = ( B @ ( A @ k7_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k13_filter_2) ).

thf(6054,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)],[906]) ).

thf(29907,plain,
    ! [A: $i] :
      ( ( A != sk94 )
      | ( k1_xboole_0 @ v5_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2210]) ).

thf(29908,plain,
    ( ( k1_xboole_0 @ v5_lattices )
    | ( sk94 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29907:[bind(A,$thf( sk94 ))]]) ).

thf(811,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                      & ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_0) ).

thf(5650,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)],[811]) ).

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/sandbox2/benchmark/theBenchmark.p',fc4_lattice2) ).

thf(3357,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(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 @ 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)],[1067,7420]) ).

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 @ 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)],[7674]) ).

thf(7697,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)],[7675]) ).

thf(7714,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)],[7697]) ).

thf(28368,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)],[7714,2544]) ).

thf(28369,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)],[28368]) ).

thf(245,axiom,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).

thf(2540,plain,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(890,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
                     => ( ( D @ ( C @ ( A @ r3_lattices ) ) )
                       => ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice4) ).

thf(5985,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)],[890]) ).

thf(362,axiom,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_subset_1) ).

thf(3290,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(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/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).

thf(3300,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(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/sandbox2/benchmark/theBenchmark.p',rc1_filter_0) ).

thf(2956,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(2957,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)],[2956]) ).

thf(2964,plain,
    sk188 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

thf(484,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_domain_1) ).

thf(3986,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)],[484]) ).

thf(438,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(3732,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)],[438]) ).

thf(3733,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)],[3732]) ).

thf(3734,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)],[3733]) ).

thf(3735,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ( A != B ) ),
    inference(cnfConj,[status(thm)],[3734]) ).

thf(3738,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ( A != B ) ),
    inference(lifteq,[status(thm)],[3735]) ).

thf(3739,plain,
    ! [A: $i] : ( A @ ( A @ r1_tarski ) ),
    inference(simp,[status(thm)],[3738]) ).

thf(753,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
                = ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_0) ).

thf(5384,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)],[753]) ).

thf(585,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k1_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattices) ).

thf(4504,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)],[585]) ).

thf(9031,plain,
    ( ( ( sk292 @ v1_xboole_0 )
     != ( sk218 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,3328]) ).

thf(9032,plain,
    ( ( sk292 @ v1_xboole_0 )
   != ( sk218 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9031]) ).

thf(9035,plain,
    sk292 != sk218,
    inference(simp,[status(thm)],[9032]) ).

thf(644,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v5_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
                      = ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattices) ).

thf(4825,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)],[644]) ).

thf(75,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).

thf(1433,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(4628,plain,
    sk313 @ v16_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

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/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).

thf(3406,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(633,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
                    = ( D @ ( C @ ( B @ u1_lattices @ ( B @ u1_struct_0 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice2) ).

thf(4751,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)],[633]) ).

thf(7128,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)],[2545,7046]) ).

thf(7129,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)],[7128]) ).

thf(7130,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)],[7129:[bind(A,$thf( sk138 ))]]) ).

thf(15282,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2270,7130]) ).

thf(15283,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15282]) ).

thf(15360,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15283]) ).

thf(15365,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15360]) ).

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/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).

thf(2367,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(3068,plain,
    sk196 @ v10_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(532,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_filter_2) ).

thf(4230,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)],[532]) ).

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/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).

thf(2861,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(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
      <=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
          = ( C @ k1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_partfun1) ).

thf(1210,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(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 ) )
      & ( ( ( 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)],[1210]) ).

thf(1213,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)],[1211]) ).

thf(1215,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)],[1213]) ).

thf(78,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
    <=> ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).

thf(1447,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(694,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
        <=> ( A @ k1_lattice2 @ ( B @ m1_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_filter_2) ).

thf(5101,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)],[694]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( ( B @ k1_relat_1 )
          = k1_xboole_0 )
       => ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
          & ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
          & ( B @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).

thf(1112,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(1113,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)],[1112]) ).

thf(1115,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)],[1113]) ).

thf(1119,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)],[1115]) ).

thf(943,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r3_relat_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_filter_0) ).

thf(6221,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)],[943]) ).

thf(2424,plain,
    sk118 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(2368,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)],[2367]) ).

thf(2371,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_funct_1 ),
    inference(cnfConj,[status(thm)],[2368]) ).

thf(5124,plain,
    ~ ! [A: $i] : ( A @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[5123]) ).

thf(5125,plain,
    ~ ( sk359 @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[5124]) ).

thf(8142,plain,
    ( ( ( sk359 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,5125]) ).

thf(8143,plain,
    ( ( sk359 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8142]) ).

thf(8159,plain,
    sk359 != k1_xboole_0,
    inference(simp,[status(thm)],[8143]) ).

thf(31011,plain,
    ! [A: $i] :
      ( ( A != sk359 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,8159]) ).

thf(31012,plain,
    ! [A: $i] :
      ( ( A != sk359 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[31011]) ).

thf(31013,plain,
    sk359 @ sk19 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[31012:[bind(A,$thf( sk359 ))]]) ).

thf(44259,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk359 @ sk19 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[31013,1232]) ).

thf(44260,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk359 @ sk19 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[44259]) ).

thf(44261,plain,
    ! [A: $i] : ( A @ ( sk359 @ sk19 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44260:[bind(A,$thf( A )),bind(B,$thf( sk359 @ sk19 ))]]) ).

thf(1005,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) )
       => ( ( A @ k6_lattices )
          = ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice2) ).

thf(6498,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)],[1005]) ).

thf(5321,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    inference(cnf,[status(esa)],[5320]) ).

thf(477,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v16_lattices )
            & ( B @ v15_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ! [F: $i] :
                            ( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                           => ( ( ( D @ ( C @ ( A @ r2_lattices ) ) )
                                & ( D = F )
                                & ( C = E ) )
                             => ( F @ ( E @ ( B @ r2_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_2) ).

thf(3955,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)],[477]) ).

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/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).

thf(3243,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(2965,plain,
    ~ ( sk188 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2957]) ).

thf(808,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
                     => ( ( B @ ( A @ ( E @ v1_lattice4 ) ) )
                       => ( ( D @ ( C @ ( A @ r3_lattices ) ) )
                        <=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice4) ).

thf(5629,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)],[808]) ).

thf(589,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
        = ( C @ ( B @ ( A @ k1_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).

thf(4519,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)],[589]) ).

thf(8198,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)],[3160,7046]) ).

thf(8199,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)],[8198]) ).

thf(8200,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)],[8199:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15209,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8200,2270]) ).

thf(15210,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15209]) ).

thf(624,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ k7_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_0) ).

thf(4707,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)],[624]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( E @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_lattice2) ).

thf(3870,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( E @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(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/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).

thf(3211,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(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/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).

thf(2392,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(922,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_nat_lat ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k24_filter_2 ) )
        = ( B @ k1_lattice2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k24_filter_2) ).

thf(6103,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)],[922]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ v1_relat_1 )
         => ( ( B @ ( A @ r1_tarski ) )
           => ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
              & ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).

thf(1696,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(3184,plain,
    k6_nat_lat @ v9_lattices,
    inference(cnfConj,[status(thm)],[3176]) ).

thf(580,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
       => ! [B: $i] :
            ( ( A @ ( B @ m2_filter_2 ) )
           => ~ ( ! [C: $i] :
                    ( ( A @ ( C @ m2_filter_2 ) )
                   => ~ ( ( C @ ( A @ r2_filter_2 ) )
                        & ( C @ ( B @ r1_tarski ) ) ) )
                & ( B
                 != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_2) ).

thf(4475,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)],[580]) ).

thf(38316,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)],[4988,1247]) ).

thf(38317,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)],[38316]) ).

thf(38371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk349 )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[38317]) ).

thf(38392,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
     != ( B @ sk349 ) ),
    inference(simp,[status(thm)],[38371]) ).

thf(7125,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)],[1975,7046]) ).

thf(7126,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)],[7125]) ).

thf(7127,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)],[7126:[bind(A,$thf( sk71 ))]]) ).

thf(12333,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,7127]) ).

thf(12334,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12333]) ).

thf(12375,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk71 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12334]) ).

thf(581,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m1_filter_0 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_0) ).

thf(4483,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)],[581]) ).

thf(2954,plain,
    sk187 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(1072,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)],[1069]) ).

thf(1074,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)],[1072]) ).

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/sandbox2/benchmark/theBenchmark.p',cc7_lattices) ).

thf(3097,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(1003,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k7_lattices ) )
            = ( B @ ( A @ k7_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l70_filter_2) ).

thf(6482,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)],[1003]) ).

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/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).

thf(3257,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(3258,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)],[3257]) ).

thf(3259,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)],[3258]) ).

thf(3261,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3259]) ).

thf(3264,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3261]) ).

thf(3265,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[3264]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
        & ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relat_1) ).

thf(1306,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(685,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k3_lattices ) ) )
                = ( B @ ( C @ ( A @ k7_grcat_1 @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funcop_1 ) ) ) ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattice4) ).

thf(5070,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)],[685]) ).

thf(112,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( ( B @ k1_relat_1 )
          = ( A @ k1_tarski ) )
       => ( ( B @ k2_relat_1 )
          = ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).

thf(1708,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(658,axiom,
    ? [A: $i] : ( A @ l1_lattices ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).

thf(4910,plain,
    ? [A: $i] : ( A @ l1_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

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/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).

thf(2000,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(732,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
      <=> ? [B: $i] :
            ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                    = B )
                  & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                    = B ) ) )
            & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattices) ).

thf(5298,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)],[732]) ).

thf(4590,plain,
    sk311 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[4589]) ).

thf(9046,plain,
    ! [A: $i] :
      ( ( ( sk311 @ 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)],[4590,7083]) ).

thf(9047,plain,
    ! [A: $i] :
      ( ( ( sk311 @ 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)],[9046]) ).

thf(9048,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[9047:[bind(A,$thf( sk311 ))]]) ).

thf(650,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( B @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).

thf(4853,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)],[650]) ).

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/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).

thf(3229,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(14728,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ 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)],[5588,1132]) ).

thf(14729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ 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)],[14728]) ).

thf(14730,plain,
    ( ( f1_s11_funct_2 @ ( sk404 @ k1_relat_1 @ r1_tarski ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[14729:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk404 ))]]) ).

thf(9088,plain,
    ! [A: $i] :
      ( ( ( sk311 @ 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)],[4590,7046]) ).

thf(9089,plain,
    ! [A: $i] :
      ( ( ( sk311 @ 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)],[9088]) ).

thf(9090,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[9089:[bind(A,$thf( sk311 ))]]) ).

thf(15247,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2270,9090]) ).

thf(15248,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15247]) ).

thf(15355,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk311 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15248]) ).

thf(15402,plain,
    ( ( sk311 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15355]) ).

thf(757,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
      <=> ( A @ k1_lattice2 @ v13_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_lattice2) ).

thf(5406,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)],[757]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v14_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( A @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_0) ).

thf(3591,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)],[417]) ).

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/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).

thf(2910,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(4629,plain,
    sk313 @ v10_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(2473,plain,
    k13_nat_lat @ v3_lattices,
    inference(cnfConj,[status(thm)],[2471]) ).

thf(7652,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)],[1067,7417]) ).

thf(7653,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)],[7652]) ).

thf(7691,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)],[7653]) ).

thf(7707,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)],[7691]) ).

thf(10227,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)],[7707,1974]) ).

thf(10228,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)],[10227]) ).

thf(12979,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)],[2074,10228]) ).

thf(12980,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)],[12979]) ).

thf(13002,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)],[12980]) ).

thf(13017,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)],[13002]) ).

thf(1197,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)],[1194]) ).

thf(1199,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)],[1197]) ).

thf(27193,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)],[2047,3613]) ).

thf(27194,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
    inference(pattern_uni,[status(thm)],[27193:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(27238,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
    inference(simp,[status(thm)],[27194]) ).

thf(38345,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)],[27238,1247]) ).

thf(38346,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)],[38345]) ).

thf(38369,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)],[38346]) ).

thf(38390,plain,
    ! [B: $i,A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != ( k1_xboole_0 @ k1_tarski @ ( B @ k4_xboole_0 ) ) ),
    inference(simp,[status(thm)],[38369]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
                            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
                            & ( F @ v1_funct_1 ) )
                         => ( ( ( F
                                = ( B @ ( D @ k1_realset1 ) ) )
                              & ( E
                                = ( B @ ( C @ k1_realset1 ) ) ) )
                           => ( ( ( D @ ( C @ ( A @ r5_binop_1 ) ) )
                               => ( F @ ( E @ ( B @ r5_binop_1 ) ) ) )
                              & ( ( D @ ( C @ ( A @ r4_binop_1 ) ) )
                               => ( F @ ( E @ ( B @ r4_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_2) ).

thf(1148,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(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 ) )
      & ( ( 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)],[1148]) ).

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 ) ) )
      | ( 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)],[1149]) ).

thf(1152,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)],[1150]) ).

thf(1153,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)],[1152]) ).

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/sandbox2/benchmark/theBenchmark.p',t13_binop_1) ).

thf(3186,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(7667,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 @ v13_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)],[1067,7238]) ).

thf(7668,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 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7667]) ).

thf(7693,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7668]) ).

thf(7709,plain,
    ( ( ( sk138 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
    | ~ ( sk138 @ v1_relat_1 )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7693]) ).

thf(11031,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 @ v13_lattices ) ),
    inference(rewrite,[status(thm)],[7709,2544]) ).

thf(11032,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[11031]) ).

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/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(2118,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(703,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
                          = ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
                       => ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) )
                          = ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_lattice2) ).

thf(5142,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)],[703]) ).

thf(947,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_lattice4 ) )
            = ( A @ k7_grcat_1 @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_setwiseo ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_lattice4) ).

thf(6250,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)],[947]) ).

thf(13033,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,2439]) ).

thf(13034,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[13033]) ).

thf(13051,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( C @ ( B @ k4_tarski ) ) ),
    inference(simp,[status(thm)],[13034]) ).

thf(984,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ u1_struct_0 @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_filter_2) ).

thf(6388,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)],[984]) ).

thf(13043,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,4006]) ).

thf(13044,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[13043]) ).

thf(13049,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( B @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[13044]) ).

thf(30262,plain,
    ! [A: $i] :
      ( ( A != sk456 )
      | ( k1_xboole_0 @ l3_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,6365]) ).

thf(30263,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ( sk456 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30262:[bind(A,$thf( sk456 ))]]) ).

thf(2737,plain,
    ~ ( sk157 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2734]) ).

thf(860,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k1_lattice4 ) )
        = ( A @ k5_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattice4) ).

thf(5862,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)],[860]) ).

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/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).

thf(2296,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(117,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).

thf(1736,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(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/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).

thf(2621,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(9027,plain,
    ( ( ( sk292 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,1220]) ).

thf(9028,plain,
    ( ( sk292 @ v1_xboole_0 )
   != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9027]) ).

thf(9041,plain,
    sk292 != sk14,
    inference(simp,[status(thm)],[9028]) ).

thf(3269,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[3268]) ).

thf(18112,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
    inference(rewrite,[status(thm)],[3269,2549]) ).

thf(737,axiom,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
        & ( A @ u2_lattices @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).

thf(5334,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)],[737]) ).

thf(1043,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)],[1038]) ).

thf(1046,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)],[1043]) ).

thf(1047,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)],[1046]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i] :
          ( ( ( B @ v1_funct_1 )
            & ( B @ v1_relat_1 ) )
         => ( ( ! [C: $i] :
                  ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
                 => ( ( C @ ( A @ k1_funct_1 ) )
                    = ( C @ ( B @ k1_funct_1 ) ) ) )
              & ( ( A @ k1_relat_1 )
                = ( B @ k1_relat_1 ) ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).

thf(1730,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(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/sandbox2/benchmark/theBenchmark.p',t159_funct_2) ).

thf(3037,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(678,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v17_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                       => ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
                  & ( C @ ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_0) ).

thf(5049,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)],[678]) ).

thf(69,axiom,
    ! [A: $i,B: $i] :
      ~ ( ! [C: $i] :
            ( ( ( C @ v1_funct_1 )
              & ( C @ v1_relat_1 ) )
           => ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
                & ( B
                  = ( C @ k1_relat_1 ) ) ) )
        & ~ ( ( B != k1_xboole_0 )
            & ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).

thf(1370,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(1371,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)],[1370]) ).

thf(1372,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)],[1371]) ).

thf(1375,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1372]) ).

thf(1386,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1375]) ).

thf(1387,plain,
    ! [A: $i] : ( A @ ( A @ ( k1_xboole_0 @ sk25 ) @ k2_relat_1 @ r1_tarski ) ),
    inference(simp,[status(thm)],[1386]) ).

thf(971,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k23_filter_2 ) @ m2_nat_lat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k23_filter_2) ).

thf(6343,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)],[971]) ).

thf(2541,plain,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[2540]) ).

thf(673,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).

thf(5002,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)],[673]) ).

thf(41576,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,41162]) ).

thf(41577,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41576]) ).

thf(41625,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
     != sk292 )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41577]) ).

thf(884,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( A @ k6_lattices @ ( B @ ( A @ r3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattices) ).

thf(5956,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)],[884]) ).

thf(15231,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2270,8806]) ).

thf(15232,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15231]) ).

thf(15359,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[15232]) ).

thf(15407,plain,
    ( ( sk216 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[15359]) ).

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/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).

thf(3154,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(47,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( ( C @ v2_funct_1 )
          & ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
          & ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
       => ( B @ ( A @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).

thf(1238,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(9019,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk292 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,5198]) ).

thf(9020,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9019]) ).

thf(9036,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk292 ),
    inference(simp,[status(thm)],[9020]) ).

thf(231,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relat_1) ).

thf(2440,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(2441,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
    inference(cnf,[status(esa)],[2440]) ).

thf(30230,plain,
    ! [A: $i] :
      ( ( A != sk157 )
      | ( k1_xboole_0 @ v3_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2745]) ).

thf(30231,plain,
    ( ( k1_xboole_0 @ v3_lattices )
    | ( sk157 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30230:[bind(A,$thf( sk157 ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',t25_subset_1) ).

thf(2705,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(9085,plain,
    ! [A: $i] :
      ( ( ( sk311 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4590,7074]) ).

thf(9086,plain,
    ! [A: $i] :
      ( ( ( sk311 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9085]) ).

thf(9087,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[9086:[bind(A,$thf( sk311 ))]]) ).

thf(12359,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,9087]) ).

thf(12360,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12359]) ).

thf(12372,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk311 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12360]) ).

thf(12437,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12372]) ).

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/sandbox2/benchmark/theBenchmark.p',t27_lattice2) ).

thf(2409,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(831,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( B @ ( A @ k3_filter_0 ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_0) ).

thf(5734,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)],[831]) ).

thf(1091,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)],[1085]) ).

thf(913,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k1_lattice4 ) )
            = ( A @ k7_grcat_1 @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_setwiseo ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_lattice4) ).

thf(6079,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)],[913]) ).

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/sandbox2/benchmark/theBenchmark.p',d19_binop_1) ).

thf(2428,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(249,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
    <=> ( ( A
          = ( B @ k1_tarski ) )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).

thf(2560,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(967,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k15_filter_2 ) )
        = ( B @ ( A @ k7_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).

thf(6328,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)],[967]) ).

thf(10155,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,4606]) ).

thf(10156,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[10155]) ).

thf(10171,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk216 ),
    inference(simp,[status(thm)],[10156]) ).

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/sandbox2/benchmark/theBenchmark.p',t62_filter_2) ).

thf(2249,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(946,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ( ( B @ ( A @ k2_filter_0 ) )
                = ( A @ u1_struct_0 ) )
              & ~ ! [C: $i] :
                    ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                   => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                      = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_0) ).

thf(6247,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)],[946]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).

thf(1121,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(1122,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(cnf,[status(esa)],[1121]) ).

thf(1123,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(lifteq,[status(thm)],[1122]) ).

thf(676,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( A @ ( G @ m1_subset_1 ) )
        & ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_domain_1) ).

thf(5044,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)],[676]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i] :
          ( ( ( B @ v1_funct_1 )
            & ( B @ v1_relat_1 ) )
         => ( ( ! [C: $i,D: $i] :
                  ( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
                    & ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
                 => ( ( ( C @ ( A @ k1_funct_1 ) )
                      = D )
                  <=> ( ( D @ ( B @ k1_funct_1 ) )
                      = C ) ) )
              & ( ( A @ k2_relat_1 )
                = ( B @ k1_relat_1 ) )
              & ( ( A @ k1_relat_1 )
                = ( B @ k2_relat_1 ) )
              & ( A @ v2_funct_1 ) )
           => ( B
              = ( A @ k2_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).

thf(1166,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(1167,plain,
    ! [B: $i,A: $i] :
      ( ( ( B
          = ( A @ k2_funct_1 ) )
        | ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
         != ( A @ ( B @ sk11 ) ) )
        | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
         != ( A @ ( B @ sk10 ) ) )
        | ( ( A @ k2_relat_1 )
         != ( B @ k1_relat_1 ) )
        | ( ( A @ k1_relat_1 )
         != ( B @ k2_relat_1 ) )
        | ~ ( A @ v2_funct_1 )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) )
      & ( ( 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)],[1166]) ).

thf(1168,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)],[1167]) ).

thf(1174,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)],[1168]) ).

thf(1206,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != ( A @ ( B @ k4_xboole_0 ) ) ) ),
    inference(cnf,[status(esa)],[1205]) ).

thf(1207,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != ( A @ ( B @ k4_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[1206]) ).

thf(1208,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[1207]) ).

thf(1209,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
      = A ),
    inference(cnf,[status(esa)],[1208]) ).

thf(38609,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
      = A ),
    inference(lifteq,[status(thm)],[1209]) ).

thf(14121,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,1132]) ).

thf(14122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14121]) ).

thf(14123,plain,
    f1_s4_funct_2 @ ( sk311 @ k1_relat_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[14122:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk311 ))]]) ).

thf(14138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk311 @ k1_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[14123,1083]) ).

thf(14139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk311 @ k1_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14138]) ).

thf(14140,plain,
    ! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk311 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14139:[bind(A,$thf( sk311 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14199,plain,
    ! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk311 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14140]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
          & ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
       => ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).

thf(1216,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(1217,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)],[1216]) ).

thf(304,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).

thf(2969,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(747,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                  = C ) )
           => ( B
              = ( A @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice2) ).

thf(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 ) )
               => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                  = C ) )
           => ( B
              = ( A @ k6_lattices ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(3069,plain,
    sk196 @ v9_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

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/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).

thf(2032,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(453,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ v3_lattices )
       => ( A
          = ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).

thf(3814,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)],[453]) ).

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/sandbox2/benchmark/theBenchmark.p',t120_funct_2) ).

thf(2890,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(1008,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( B @ ( A @ k2_lattice4 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice4) ).

thf(6509,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)],[1008]) ).

thf(7562,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,4006]) ).

thf(7563,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7562]) ).

thf(7565,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk71 ),
    inference(simp,[status(thm)],[7563]) ).

thf(875,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k2_lattice4 ) )
        = ( A @ k6_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattice4) ).

thf(5924,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)],[875]) ).

thf(41174,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,41008]) ).

thf(41175,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41174]) ).

thf(41234,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) ),
    inference(simp,[status(thm)],[41175]) ).

thf(340,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).

thf(3166,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(778,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_lattice4) ).

thf(5492,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)],[778]) ).

thf(771,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v6_group_1 )
      <=> ( A @ k1_lattice2 @ v6_group_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_lattice2) ).

thf(5465,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)],[771]) ).

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 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
               => ( ( C @ ( B @ ( A @ k22_filter_2 ) ) )
                  = ( C @ ( B @ ( A @ a_3_2_filter_2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_filter_2) ).

thf(5534,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)],[785]) ).

thf(11628,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk292 ) ),
    inference(paramod_ordered,[status(thm)],[1955,9039]) ).

thf(11629,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk292 ),
    inference(pattern_uni,[status(thm)],[11628:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(30344,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( B @ ( C @ k2_tarski ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,27233]) ).

thf(30345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( B @ ( C @ k2_tarski ) ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[30344]) ).

thf(30346,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk19 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[30345:[bind(A,$thf( E @ ( D @ k2_tarski ) )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).

thf(33233,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk19 @ v1_relat_1 ),
    inference(simp,[status(thm)],[30346]) ).

thf(30,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
       => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
          & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_funct_2) ).

thf(1156,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(1157,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)],[1156]) ).

thf(1159,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)],[1157]) ).

thf(13035,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,3129]) ).

thf(13036,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[13035]) ).

thf(13055,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( B @ ( B @ k1_funct_2 ) ) ),
    inference(simp,[status(thm)],[13036]) ).

thf(2741,plain,
    sk157 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(1378,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk25 ) @ v1_relat_1 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1372]) ).

thf(1391,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk25 ) @ v1_relat_1 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1378]) ).

thf(1392,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_relat_1 ),
    inference(simp,[status(thm)],[1391]) ).

thf(118,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k1_funct_2 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ? [E: $i] :
              ( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
              & ( ( E @ k1_relat_1 )
                = A )
              & ( D = E )
              & ( E @ v1_funct_1 )
              & ( E @ v1_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_2) ).

thf(1740,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(2958,plain,
    sk188 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

thf(475,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k14_filter_2 ) )
        = ( B @ ( A @ k8_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).

thf(3948,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)],[475]) ).

thf(144,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v3_filter_0 )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v12_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_filter_0) ).

thf(1938,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(755,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( D @ ( C @ ( B @ r3_lattices ) ) )
            & ( A = D )
            & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).

thf(5391,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)],[755]) ).

thf(865,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i,D: $i] :
          ( ( ( B @ ( A @ g2_struct_0 ) )
            = ( D @ ( C @ g2_struct_0 ) ) )
         => ( ( B = D )
            & ( A = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_struct_0) ).

thf(5879,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)],[865]) ).

thf(825,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_0) ).

thf(5702,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)],[825]) ).

thf(994,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) )
                    = ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattices) ).

thf(6432,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)],[994]) ).

thf(889,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v11_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
               => ( A @ v11_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattice4) ).

thf(5983,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)],[889]) ).

thf(648,axiom,
    k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_nat_lat) ).

thf(4849,plain,
    k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(523,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
         => ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_realset1) ).

thf(4192,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)],[523]) ).

thf(602,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ k2_lattice4 ) @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) )
                = ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice4) ).

thf(4585,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)],[602]) ).

thf(2477,plain,
    k13_nat_lat @ v5_lattices,
    inference(cnfConj,[status(thm)],[2471]) ).

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/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).

thf(3198,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(993,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v15_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).

thf(6427,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)],[993]) ).

thf(30137,plain,
    ! [A: $i] :
      ( ( A != sk157 )
      | ( k1_xboole_0 @ v7_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2735]) ).

thf(30138,plain,
    ( ( k1_xboole_0 @ v7_lattices )
    | ( sk157 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30137:[bind(A,$thf( sk157 ))]]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
       => ! [B: $i] :
            ( ( ( B @ v1_funct_1 )
              & ( B @ v1_relat_1 ) )
           => ( ( B
                = ( A @ k2_funct_1 ) )
            <=> ( ! [C: $i,D: $i] :
                    ( ( ( ( C
                          = ( D @ ( A @ k1_funct_1 ) ) )
                        & ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
                     => ( ( D
                          = ( C @ ( B @ k1_funct_1 ) ) )
                        & ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
                    & ( ( ( D
                          = ( C @ ( B @ k1_funct_1 ) ) )
                        & ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
                     => ( ( C
                          = ( D @ ( A @ k1_funct_1 ) ) )
                        & ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
                & ( ( B @ k1_relat_1 )
                  = ( A @ k2_relat_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).

thf(1555,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(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/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).

thf(2332,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(29929,plain,
    ! [A: $i] :
      ( ( A != sk187 )
      | ( k1_xboole_0 @ v15_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2953]) ).

thf(29930,plain,
    ( ( k1_xboole_0 @ v15_lattices )
    | ( sk187 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29929:[bind(A,$thf( sk187 ))]]) ).

thf(671,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( A @ ( B @ v1_filter_2 ) )
          <=> ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ v2_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_2) ).

thf(4994,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)],[671]) ).

thf(635,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( ( D @ ( E @ r2_hidden ) )
              | ( C @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).

thf(4757,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)],[635]) ).

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/sandbox2/benchmark/theBenchmark.p',t172_partfun1) ).

thf(3137,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(3065,plain,
    sk196 @ v6_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(707,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m2_filter_2 ) )
             => ( ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( C @ r1_tarski ) )
                & ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_2) ).

thf(5177,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)],[707]) ).

thf(822,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_lattice2 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( C @ ( A @ k6_filter_2 ) @ ( A @ k7_lattices ) )
                  = ( C @ ( A @ k1_lattice2 @ k7_lattices ) ) )
                & ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k7_lattices ) )
                  = ( B @ ( A @ k7_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_2) ).

thf(5690,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)],[822]) ).

thf(41304,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,41075]) ).

thf(41305,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41304]) ).

thf(41306,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk71 ),
    inference(simp,[status(thm)],[41305]) ).

thf(1171,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)],[1167]) ).

thf(1178,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)],[1171]) ).

thf(3329,plain,
    sk218 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3327]) ).

thf(8845,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)],[3329,1052]) ).

thf(8846,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)],[8845]) ).

thf(8847,plain,
    ! [A: $i] : ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[8846:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).

thf(15614,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)],[3329,1139]) ).

thf(15615,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)],[15614]) ).

thf(15616,plain,
    ( ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) )
    = ( sk218 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15615:[bind(A,$thf( sk218 ))]]) ).

thf(25750,plain,
    ! [A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[8847,15616]) ).

thf(25752,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)],[25750,1083]) ).

thf(25753,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)],[25752]) ).

thf(25754,plain,
    ! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[25753:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk218 @ k9_relat_1 ) )),bind(C,$thf( sk218 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(25844,plain,
    ! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[25754]) ).

thf(958,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v17_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v17_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
              & ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_filter_0) ).

thf(6292,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)],[958]) ).

thf(463,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( A != B )
        & ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(3877,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( A != B )
        & ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(794,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k3_filter_2 ) )
        = ( B @ ( A @ k3_filter_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).

thf(5566,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)],[794]) ).

thf(908,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k1_filter_2 @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_2) ).

thf(6060,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)],[908]) ).

thf(2213,plain,
    sk94 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

thf(15304,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)],[2270,7612]) ).

thf(15305,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)],[15304]) ).

thf(15363,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)],[15305]) ).

thf(15368,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15363]) ).

thf(988,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ~ ( ! [D: $i] :
                      ( ( A @ ( D @ m1_filter_0 ) )
                     => ~ ( ( ( ( D @ ( C @ r2_hidden ) )
                              & ~ ( D @ ( B @ r2_hidden ) ) )
                            | ( ~ ( D @ ( C @ r2_hidden ) )
                              & ( D @ ( B @ r2_hidden ) ) ) )
                          & ( A @ ( D @ v1_filter_0 ) ) ) )
                  & ( B != C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_0) ).

thf(6402,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)],[988]) ).

thf(44054,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)],[2544,1232]) ).

thf(44055,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)],[44054]) ).

thf(44056,plain,
    ! [A: $i] : ( A @ ( sk138 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44055:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).

thf(2211,plain,
    sk94 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

thf(952,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice4) ).

thf(6267,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)],[952]) ).

thf(501,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) )
              <=> ? [D: $i] :
                    ( ? [E: $i] :
                        ( ( B @ ( E @ r2_hidden ) )
                        & ( B @ ( D @ r2_hidden ) )
                        & ( C
                          = ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
                        & ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice4) ).

thf(4080,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)],[501]) ).

thf(894,axiom,
    ! [A: $i] :
      ( ( a_0_1_domain_1 @ ( A @ r2_hidden ) )
    <=> ? [B: $i] :
          ( ( B @ p1_s8_domain_1 )
          & ( A
            = ( B @ f3_s8_domain_1 ) )
          & ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).

thf(5993,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)],[894]) ).

thf(548,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).

thf(4316,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(683,axiom,
    ? [A: $i] : ( A @ l2_lattices ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).

thf(5065,plain,
    ? [A: $i] : ( A @ l2_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(5066,plain,
    sk356 @ l2_lattices,
    inference(cnf,[status(esa)],[5065]) ).

thf(8144,plain,
    ( ( ( sk14 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3123,1220]) ).

thf(8145,plain,
    ( ( sk14 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8144]) ).

thf(8155,plain,
    sk14 != k1_xboole_0,
    inference(simp,[status(thm)],[8145]) ).

thf(10167,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,4606]) ).

thf(10168,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[10167]) ).

thf(10172,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk71 ),
    inference(simp,[status(thm)],[10168]) ).

thf(26485,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)],[2047,10172]) ).

thf(26486,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk71 ),
    inference(pattern_uni,[status(thm)],[26485:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(26531,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk71 ),
    inference(simp,[status(thm)],[26486]) ).

thf(969,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice2) ).

thf(6339,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)],[969]) ).

thf(153,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).

thf(1983,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(12329,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,7420]) ).

thf(12330,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12329]) ).

thf(12382,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk138 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12330]) ).

thf(939,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ u1_struct_0 @ m3_lattice4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice4) ).

thf(6195,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)],[939]) ).

thf(1109,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1107]) ).

thf(1111,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1109]) ).

thf(30180,plain,
    ! [A: $i] :
      ( ( A != sk207 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,15394]) ).

thf(30181,plain,
    ! [A: $i] :
      ( ( A != sk207 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[30180]) ).

thf(30182,plain,
    ( ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ( sk207 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30181:[bind(A,$thf( sk207 ))]]) ).

thf(4636,plain,
    sk313 @ v11_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(133,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( C @ k2_relat_1 @ ( B @ r2_hidden ) )
          & ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).

thf(1878,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(3078,plain,
    sk197 @ v3_filter_0,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(911,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u2_lattices @ v3_binop_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattice2) ).

thf(6075,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)],[911]) ).

thf(67,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_2) ).

thf(1360,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(64,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
        & ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_2) ).

thf(1350,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(856,axiom,
    f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1) ).

thf(5854,plain,
    f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(12271,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,7235]) ).

thf(12272,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12271]) ).

thf(12422,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk71 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12272]) ).

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/sandbox2/benchmark/theBenchmark.p',t1_filter_2) ).

thf(3467,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(807,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k6_lattices )
        = ( A @ k1_lattice2 @ k5_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_lattice2) ).

thf(5626,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)],[807]) ).

thf(1143,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)],[1141]) ).

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/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).

thf(2115,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(704,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i,C: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
            & ~ ( C @ v1_xboole_0 ) )
         => ! [D: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                & ~ ( D @ v1_xboole_0 ) )
             => ~ ( ! [E: $i] :
                      ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ~ ( ( D @ ( F @ r2_hidden ) )
                              & ( C @ ( E @ r2_hidden ) )
                              & ( B
                                = ( F @ ( E @ ( A @ k4_lattices ) ) ) ) ) ) )
                  & ( D @ ( C @ ( A @ k5_filter_0 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_0) ).

thf(5145,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)],[704]) ).

thf(921,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( A @ v13_lattices )
           => ( B @ ( A @ k5_lattices @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_filter_2) ).

thf(6101,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)],[921]) ).

thf(53,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
     => ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
       => ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).

thf(1270,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(2946,plain,
    sk187 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

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/sandbox2/benchmark/theBenchmark.p',d13_binop_1) ).

thf(2990,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(720,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ v11_lattices )
           => ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_0) ).

thf(5238,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)],[720]) ).

thf(146,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).

thf(1952,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(1953,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    inference(cnf,[status(esa)],[1952]) ).

thf(817,axiom,
    ( ( k6_nat_lat @ l3_lattices )
    & ( k6_nat_lat @ v13_lattices )
    & ( k6_nat_lat @ v10_lattices )
    & ~ ( k6_nat_lat @ v3_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_nat_lat) ).

thf(5673,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)],[817]) ).

thf(674,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m1_filter_0 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
                          & ( B @ ( C @ r2_hidden ) ) )
                       => ( B @ ( D @ r2_hidden ) ) ) ) )
              & ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( ( B @ ( D @ r2_hidden ) )
                          & ( B @ ( C @ r2_hidden ) ) )
                       => ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_filter_0) ).

thf(5006,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)],[674]) ).

thf(217,axiom,
    ! [A: $i] :
      ( ( A @ v1_finset_1 )
     => ( ( A @ k5_finsub_1 )
        = ( A @ k1_zfmisc_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).

thf(2359,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(30831,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,1027]) ).

thf(30832,plain,
    ( ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
    | ( sk1 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30831:[bind(A,$thf( sk1 ))]]) ).

thf(647,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( B @ r1_tarski ) )
       => ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
          & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).

thf(4845,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)],[647]) ).

thf(8013,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,3129]) ).

thf(8014,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8013]) ).

thf(8016,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk71 ),
    inference(simp,[status(thm)],[8014]) ).

thf(8753,plain,
    ( ( ( sk359 @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,5125]) ).

thf(8754,plain,
    ( ( sk359 @ v1_xboole_0 )
   != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8753]) ).

thf(8768,plain,
    sk359 != sk216,
    inference(simp,[status(thm)],[8754]) ).

thf(433,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
                <=> ! [D: $i] :
                      ( ( A @ ( D @ m1_subset_1 ) )
                     => ! [E: $i] :
                          ( ( A @ ( E @ m1_subset_1 ) )
                         => ! [F: $i] :
                              ( ( A @ ( F @ m1_subset_1 ) )
                             => ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                                = ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_binop_1) ).

thf(3704,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)],[433]) ).

thf(746,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ? [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
              & ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_0) ).

thf(5362,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)],[746]) ).

thf(479,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(3963,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ~ ( A @ ( B @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

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/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).

thf(2858,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(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/sandbox2/benchmark/theBenchmark.p',t13_lattice2) ).

thf(2537,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(868,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) )
                = ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice4) ).

thf(5889,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)],[868]) ).

thf(503,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i,C: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
            & ~ ( C @ v1_xboole_0 ) )
         => ! [D: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                & ~ ( D @ v1_xboole_0 ) )
             => ~ ( ! [E: $i] :
                      ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ~ ( ( D @ ( F @ r2_hidden ) )
                              & ( C @ ( E @ r2_hidden ) )
                              & ( B
                                = ( F @ ( E @ ( A @ k3_lattices ) ) ) ) ) ) )
                  & ( D @ ( C @ ( A @ k20_filter_2 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_2) ).

thf(4095,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)],[503]) ).

thf(848,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattice2) ).

thf(5811,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)],[848]) ).

thf(928,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
                      = ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
                      = ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattices) ).

thf(6128,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)],[928]) ).

thf(718,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
                          = ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
                       => ( ( ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) )
                            = ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice2) ).

thf(5233,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)],[718]) ).

thf(3060,plain,
    sk196 @ l3_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(643,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ ( B @ v2_filter_0 ) )
              & ( B
               != ( A @ k1_filter_0 ) ) )
          <=> ( A @ ( B @ v1_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_0) ).

thf(4817,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)],[643]) ).

thf(30117,plain,
    ! [A: $i] :
      ( ( A != sk355 )
      | ( k1_xboole_0 @ l2_struct_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,5056]) ).

thf(30118,plain,
    ( ( k1_xboole_0 @ l2_struct_0 )
    | ( sk355 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30117:[bind(A,$thf( sk355 ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).

thf(3311,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(687,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
        & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice2) ).

thf(5075,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)],[687]) ).

thf(708,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v14_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_lattice2) ).

thf(5181,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)],[708]) ).

thf(689,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v7_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
                   => ( D @ ( C @ ( A @ k2_lattices ) ) @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattices) ).

thf(5080,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)],[689]) ).

thf(806,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
              <=> ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
                  = ( A @ k5_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_0) ).

thf(5620,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)],[806]) ).

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/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).

thf(3010,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(123,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).

thf(1810,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(495,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
     => ( ( ( D @ ( C @ r1_tarski ) )
          & ( B @ ( A @ r1_tarski ) ) )
       => ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).

thf(4049,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)],[495]) ).

thf(879,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k3_filter_0 ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_0) ).

thf(5941,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)],[879]) ).

thf(44216,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)],[3329,1232]) ).

thf(44217,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)],[44216]) ).

thf(44218,plain,
    ! [A: $i] : ( A @ ( sk218 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44217:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).

thf(2323,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(3179,plain,
    k6_nat_lat @ v7_lattices,
    inference(cnfConj,[status(thm)],[3176]) ).

thf(695,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
              & ( A @ v14_lattices ) )
           => ( ( ( B @ ( A @ k19_filter_2 ) )
                = ( A @ u1_struct_0 ) )
              & ( A @ k17_filter_2 @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_2) ).

thf(5107,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)],[695]) ).

thf(29961,plain,
    ! [A: $i] :
      ( ( A != sk313 )
      | ( k1_xboole_0 @ l3_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,4633]) ).

thf(29962,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ( sk313 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29961:[bind(A,$thf( sk313 ))]]) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( C @ v2_funct_1 )
       => ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
          & ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).

thf(1182,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(628,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v4_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                  = ( B @ ( C @ ( A @ k1_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattices) ).

thf(4721,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)],[628]) ).

thf(518,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).

thf(4167,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(567,axiom,
    ! [A: $i] :
      ( ( A @ l1_lattices )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
        & ( A @ u1_lattices @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).

thf(4425,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)],[567]) ).

thf(437,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
        & ( E @ v1_funct_1 ) )
     => ( ( ( D @ ( B @ r1_tarski ) )
          & ( C @ ( A @ r1_tarski ) ) )
       => ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
          & ( E @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).

thf(3728,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)],[437]) ).

thf(960,axiom,
    ( ( k13_nat_lat @ l3_lattices )
    & ( k13_nat_lat @ v10_lattices )
    & ~ ( k13_nat_lat @ v3_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_nat_lat) ).

thf(6304,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)],[960]) ).

thf(2419,plain,
    sk118 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ~ ( ( ( A @ ( B @ k9_relat_1 ) )
            = k1_xboole_0 )
          & ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
          & ( A != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).

thf(1075,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(596,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).

thf(4545,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)],[596]) ).

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/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).

thf(2080,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(661,axiom,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).

thf(4936,plain,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ( A @ l3_lattices ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(4937,plain,
    ( ( sk343 @ v3_lattices )
    & ( sk343 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4936]) ).

thf(4938,plain,
    sk343 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4937]) ).

thf(72,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).

thf(1414,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(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/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).

thf(2240,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(561,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( A @ r1_tarski ) )
       => ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
          = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).

thf(4406,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)],[561]) ).

thf(791,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( D @ r2_hidden ) )
                    <=> ( ( C @ ( D @ ( A @ r3_lattices ) ) )
                        & ( D @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_filter_2) ).

thf(5547,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)],[791]) ).

thf(630,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ k1_lattice2 )
        = ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice2) ).

thf(4744,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)],[630]) ).

thf(111,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A @ ( B @ v1_binop_1 ) )
      <=> ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
                  = ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_binop_1) ).

thf(1700,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(931,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_filter_0) ).

thf(6164,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)],[931]) ).

thf(714,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(5213,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(1212,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)],[1211]) ).

thf(1214,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)],[1212]) ).

thf(861,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ m2_nat_lat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_nat_lat) ).

thf(5865,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)],[861]) ).

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/sandbox2/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).

thf(2349,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(1006,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v1_lattice2 )
      <=> ( ( A @ v13_lattices )
          & ( A @ v3_filter_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice2) ).

thf(6501,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)],[1006]) ).

thf(21484,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)],[21482,1083]) ).

thf(21485,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)],[21484]) ).

thf(21486,plain,
    ! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[21485:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk152 @ k9_relat_1 ) )),bind(C,$thf( sk152 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(21572,plain,
    ! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[21486]) ).

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/sandbox2/benchmark/theBenchmark.p',t8_relset_1) ).

thf(2085,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(8631,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)],[3316,1052]) ).

thf(8632,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)],[8631]) ).

thf(8633,plain,
    ! [A: $i] : ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[8632:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).

thf(23674,plain,
    ! [A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[8633,15632]) ).

thf(23676,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)],[23674,1083]) ).

thf(23677,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)],[23676]) ).

thf(23678,plain,
    ! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[23677:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk216 @ k9_relat_1 ) )),bind(C,$thf( sk216 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(23772,plain,
    ! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[23678]) ).

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/sandbox2/benchmark/theBenchmark.p',t18_lattice2) ).

thf(3555,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(576,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( B @ ( F @ m1_subset_1 ) )
                           => ( ( C @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
                       => ( ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice2) ).

thf(4457,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)],[576]) ).

thf(1016,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( C @ ( B @ ( A @ k20_filter_2 ) ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_filter_2) ).

thf(6541,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)],[1016]) ).

thf(135,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( C
          = ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
       => ( ( ( C @ k2_relat_1 )
            = ( B @ k1_tarski ) )
          & ( ( C @ k1_relat_1 )
            = ( A @ k1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relat_1) ).

thf(1889,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(2472,plain,
    k13_nat_lat @ v10_lattices,
    inference(cnfConj,[status(thm)],[2471]) ).

thf(612,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
     => ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).

thf(4621,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)],[612]) ).

thf(41562,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)],[3317,41162]) ).

thf(41563,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41562]) ).

thf(41622,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
     != sk216 )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41563]) ).

thf(1151,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)],[1149]) ).

thf(1154,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)],[1151]) ).

thf(1155,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)],[1154]) ).

thf(754,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v15_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).

thf(5387,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)],[754]) ).

thf(82,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ( ( A @ ( B @ v1_binop_1 ) )
           => ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
            <=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_binop_1) ).

thf(1478,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(702,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( C @ ( B @ ( A @ r1_lattice2 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ ( E @ m1_subset_1 ) )
                       => ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                          = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice2) ).

thf(5134,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)],[702]) ).

thf(1000,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
        = ( A @ k6_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice4) ).

thf(6475,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)],[1000]) ).

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/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).

thf(2505,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(841,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( B @ ( A @ r2_filter_2 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ ( C @ m2_filter_2 ) )
                 => ( ( C @ ( B @ r1_tarski ) )
                   => ( ( C @ ( B @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
                      | ( C
                        = ( A @ u1_struct_0 ) ) ) ) )
              & ( B
               != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_filter_2) ).

thf(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)],[841]) ).

thf(505,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
    <=> ( ( C @ ( B @ r2_hidden ) )
        & ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).

thf(4120,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)],[505]) ).

thf(8771,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)],[3318,7083]) ).

thf(8772,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)],[8771]) ).

thf(8773,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)],[8772:[bind(A,$thf( sk216 ))]]) ).

thf(15330,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)],[2270,8773]) ).

thf(15331,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)],[15330]) ).

thf(15352,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)],[15331]) ).

thf(15399,plain,
    ( ( sk216 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15352]) ).

thf(997,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( A @ l3_lattices )
                  & ( A @ v3_filter_0 )
                  & ( A @ v10_lattices )
                  & ~ ( A @ v3_struct_0 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D
                        = ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
                    <=> ( ! [E: $i] :
                            ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                           => ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                             => ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
                        & ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_0) ).

thf(6450,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)],[997]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ! [D: $i] :
                  ( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                    & ~ ( D @ v1_xboole_0 ) )
                 => ( ( ( C = D )
                      & ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
                        = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) ) )
                   => ( ( ( C @ ( A @ k19_filter_2 ) )
                        = ( D @ ( B @ k19_filter_2 ) ) )
                      & ( ( C @ ( A @ k3_filter_2 ) )
                        = ( D @ ( B @ k3_filter_2 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l48_filter_2) ).

thf(3967,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)],[481]) ).

thf(797,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ k1_lattice4 ) @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
                = ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattice4) ).

thf(5576,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)],[797]) ).

thf(29901,plain,
    ! [A: $i] :
      ( ( A != k13_nat_lat )
      | ( k1_xboole_0 @ v6_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2480]) ).

thf(29902,plain,
    ( ( k1_xboole_0 @ v6_lattices )
    | ( k13_nat_lat @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29901:[bind(A,$thf( k13_nat_lat ))]]) ).

thf(2968,plain,
    sk188 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

thf(682,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).

thf(5063,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)],[682]) ).

thf(734,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).

thf(5317,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(52,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
                  = D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_binop_1) ).

thf(1263,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(854,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_realset1) ).

thf(5850,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)],[854]) ).

thf(11207,plain,
    ( ( ( sk71 @ k1_relat_1 )
     != ( k1_xboole_0 @ k1_relat_1 ) )
    | ( ( sk71 @ k2_relat_1 )
     != 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)],[1110,10228]) ).

thf(11227,plain,
    ( ( sk71 != k1_xboole_0 )
    | ( ( sk71 @ k2_relat_1 )
     != 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)],[11207]) ).

thf(11593,plain,
    ( ( ( sk71 @ k2_relat_1 )
     != ( k1_xboole_0 @ k2_relat_1 ) )
    | ( sk71 != k1_xboole_0 )
    | ( k1_xboole_0 != 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)],[1111,11227]) ).

thf(11594,plain,
    ( ( ( sk71 @ k2_relat_1 )
     != ( k1_xboole_0 @ k2_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(simp,[status(thm)],[11593]) ).

thf(11612,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)],[11594]) ).

thf(11618,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)],[11612]) ).

thf(12954,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[11618,2074]) ).

thf(12955,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12954]) ).

thf(7613,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)],[2545,7096]) ).

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 ) ) ) ),
    inference(simp,[status(thm)],[7613]) ).

thf(7615,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)],[7614:[bind(A,$thf( sk138 ))]]) ).

thf(12331,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,7615]) ).

thf(12332,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12331]) ).

thf(12410,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk138 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12332]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i,C: $i] :
          ( ( C
            = ( B @ ( A @ k9_relat_1 ) ) )
        <=> ! [D: $i] :
              ( ( C @ ( D @ r2_hidden ) )
            <=> ? [E: $i] :
                  ( ( D
                    = ( E @ ( A @ k1_funct_1 ) ) )
                  & ( B @ ( E @ r2_hidden ) )
                  & ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).

thf(1588,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(17449,plain,
    ! [B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( B @ k1_zfmisc_1 ) )
      | ( ( A @ sk249 )
       != ( k1_xboole_0 @ k1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[1955,13049]) ).

thf(17450,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != ( k1_xboole_0 @ k1_tarski ) ),
    inference(pattern_uni,[status(thm)],[17449:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).

thf(406,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v17_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
               => ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
                  & ( A @ v17_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice4) ).

thf(3541,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)],[406]) ).

thf(8807,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)],[3318,7046]) ).

thf(8808,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)],[8807]) ).

thf(8809,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)],[8808:[bind(A,$thf( sk216 ))]]) ).

thf(15272,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)],[2270,8809]) ).

thf(15273,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)],[15272]) ).

thf(15364,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)],[15273]) ).

thf(15369,plain,
    ( ( sk216 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15364]) ).

thf(749,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_0) ).

thf(5374,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)],[749]) ).

thf(3787,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk249 @ m1_subset_1 ) ),
    inference(cnfConj,[status(thm)],[3786]) ).

thf(79,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ~ ( ! [C: $i] :
              ~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
          & ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).

thf(1456,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(1379,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1372]) ).

thf(1381,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ sk25 ) @ k1_relat_1 )
        = B )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1379]) ).

thf(1382,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ sk25 ) @ k1_relat_1 )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[1381]) ).

thf(3059,plain,
    sk196 @ v5_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(30827,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,1027]) ).

thf(30828,plain,
    ( ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
    | ( sk2 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30827:[bind(A,$thf( sk2 ))]]) ).

thf(968,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
              & ( A @ l3_lattices )
              & ( A @ v13_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B
                = ( A @ u1_struct_0 ) )
              & ( B
                = ( A @ k1_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_0) ).

thf(6331,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)],[968]) ).

thf(498,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k1_lattice4 ) @ ( A @ k7_lattices ) )
            = ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice4) ).

thf(4068,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)],[498]) ).

thf(751,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_setwiseo ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_lattice2) ).

thf(5380,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)],[751]) ).

thf(8747,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,5198]) ).

thf(8748,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8747]) ).

thf(8764,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk216 ),
    inference(simp,[status(thm)],[8748]) ).

thf(14436,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,1133]) ).

thf(14437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14436]) ).

thf(14438,plain,
    f2_s4_funct_2 @ ( sk311 @ k2_relat_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[14437:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk311 ))]]) ).

thf(1096,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)],[1095]) ).

thf(1097,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)],[1096]) ).

thf(14481,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk311 @ 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)],[14438,1097]) ).

thf(14482,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk311 @ 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)],[14481]) ).

thf(14483,plain,
    ! [A: $i] : ( sk311 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14482:[bind(A,$thf( sk311 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14509,plain,
    ! [A: $i] : ( sk311 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14483]) ).

thf(1191,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)],[1190]) ).

thf(1192,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)],[1191]) ).

thf(1060,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)],[1059]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
        = ( B @ k2_relat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).

thf(1048,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(1049,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)],[1048]) ).

thf(1050,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)],[1049]) ).

thf(3064,plain,
    sk196 @ v14_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(114,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( A @ ( C @ r1_tarski ) )
       => ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
          | ( ( A != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_2) ).

thf(1720,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(930,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v12_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 )
              & ( A @ l3_lattices )
              & ( A @ v16_lattices )
              & ( A @ v15_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v16_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
              & ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_filter_0) ).

thf(6152,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)],[930]) ).

thf(3074,plain,
    sk197 @ v6_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(34123,plain,
    ! [A: $i] :
      ( ( ( sk359 @ sk19 @ 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)],[31013,1139]) ).

thf(34124,plain,
    ! [A: $i] :
      ( ( ( sk359 @ sk19 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[34123]) ).

thf(34125,plain,
    ( ( sk359 @ sk19 @ k1_relat_1 @ ( sk359 @ sk19 @ k9_relat_1 ) )
    = ( sk359 @ sk19 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[34124:[bind(A,$thf( sk359 @ sk19 ))]]) ).

thf(565,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
    <=> ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

thf(4416,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)],[565]) ).

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/sandbox2/benchmark/theBenchmark.p',d18_binop_1) ).

thf(3364,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(3083,plain,
    sk197 @ v13_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

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/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).

thf(3162,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(70,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ( ( ( A @ k2_relat_1 )
            = k1_xboole_0 )
          | ( ( A @ k1_relat_1 )
            = k1_xboole_0 ) )
       => ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).

thf(1393,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(2370,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_relat_1 ),
    inference(cnfConj,[status(thm)],[2368]) ).

thf(776,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
        = ( C @ ( B @ k2_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).

thf(5479,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)],[776]) ).

thf(1201,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)],[1200]) ).

thf(1202,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)],[1201]) ).

thf(615,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( ~ ( C @ ( E @ r2_hidden ) )
            <=> ( D @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).

thf(4644,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)],[615]) ).

thf(2208,plain,
    ~ ( sk94 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2207]) ).

thf(28482,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)],[2074,28369]) ).

thf(28483,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)],[28482]) ).

thf(28501,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)],[28483]) ).

thf(28519,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)],[28501]) ).

thf(106,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
    <=> ~ ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).

thf(1663,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(11578,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 @ v13_lattices ) ),
    inference(paramod_ordered,[status(thm)],[1111,11072]) ).

thf(11579,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[11578]) ).

thf(11611,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[11579]) ).

thf(13625,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
      | ( sk71 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true
      | ( k1_xboole_0 @ v13_lattices ) ),
    inference(paramod_ordered,[status(thm)],[2074,11611]) ).

thf(13626,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk71 @ k1_relat_1 @ r1_tarski ) ) )
      | ( sk71 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[13625]) ).

thf(13630,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( sk71 @ k1_relat_1 )
       != k1_xboole_0 )
      | ( sk71 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[13626]) ).

thf(13643,plain,
    ( ( ( sk71 @ k1_relat_1 )
     != k1_xboole_0 )
    | ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[13630]) ).

thf(13645,plain,
    ( ( ( sk71 @ k1_relat_1 )
     != ( k1_xboole_0 @ k1_relat_1 ) )
    | ( k1_xboole_0 != k1_xboole_0 )
    | ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(paramod_ordered,[status(thm)],[1110,13643]) ).

thf(13646,plain,
    ( ( ( sk71 @ k1_relat_1 )
     != ( k1_xboole_0 @ k1_relat_1 ) )
    | ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[13645]) ).

thf(13665,plain,
    ( ( sk71 != k1_xboole_0 )
    | ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[13646]) ).

thf(13667,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[13665]) ).

thf(2423,plain,
    sk118 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(5157,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)],[5156]) ).

thf(5158,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F
          = ( E @ k1_tarski ) )
        | ~ ( F @ ( E @ ( F @ sk365 ) @ r2_hidden ) )
        | ( ( E @ ( F @ sk364 ) )
         != E ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ( ( E @ ( F @ sk365 ) )
          = E )
        | ( ( E @ ( F @ sk364 ) )
         != E ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ~ ( F @ ( E @ ( F @ sk365 ) @ r2_hidden ) )
        | ( F @ ( E @ ( F @ sk364 ) @ r2_hidden ) ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ( ( E @ ( F @ sk365 ) )
          = E )
        | ( F @ ( E @ ( F @ sk364 ) @ 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)],[5157]) ).

thf(5163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( C != A )
      | ( B
       != ( A @ k1_tarski ) ) ),
    inference(cnfConj,[status(thm)],[5158]) ).

thf(5169,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( C != A )
      | ( B
       != ( A @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[5163]) ).

thf(5170,plain,
    ! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[5169]) ).

thf(517,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ v3_lattices )
        & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).

thf(4163,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)],[517]) ).

thf(696,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ ( E @ m1_subset_1 ) )
                       => ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
                          = ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_binop_1) ).

thf(5112,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)],[696]) ).

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/sandbox2/benchmark/theBenchmark.p',d6_tarski) ).

thf(2749,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(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/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).

thf(1991,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(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/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).

thf(2788,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(733,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
      <=> ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).

thf(5310,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)],[733]) ).

thf(705,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
        = ( B @ ( C @ ( A @ k4_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).

thf(5153,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)],[705]) ).

thf(8580,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)],[1067,8520]) ).

thf(8581,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)],[8580]) ).

thf(8605,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)],[8581]) ).

thf(8614,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)],[8605]) ).

thf(37784,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)],[8614,3209]) ).

thf(37785,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)],[37784]) ).

thf(37937,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)],[2074,37785]) ).

thf(37938,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)],[37937]) ).

thf(37950,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)],[37938]) ).

thf(37983,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)],[37950]) ).

thf(541,axiom,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).

thf(4288,plain,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

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/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).

thf(2702,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(2546,plain,
    sk138 @ v2_funct_1,
    inference(cnfConj,[status(thm)],[2543]) ).

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/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_2) ).

thf(3563,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(420,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( C @ ( D @ r2_hidden ) )
            & ( A = D )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).

thf(3624,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)],[420]) ).

thf(4625,plain,
    sk313 @ v14_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

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/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).

thf(2043,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(527,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v3_filter_0 )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ! [D: $i] :
                  ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( F @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                              & ( A @ ( B @ ( C @ v1_lattice4 ) ) ) )
                           => ( F @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice4) ).

thf(4212,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)],[527]) ).

thf(654,axiom,
    ( ! [A: $i] :
        ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
       => ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
           => ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
              = ( B @ f3_s12_funct_2 ) ) )
        & ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s12_funct_2) ).

thf(4882,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)],[654]) ).

thf(4883,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk338 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
          = ( A @ f3_s12_funct_2 ) )
        | ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
        | ~ sk336 )
      & ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk338 @ m2_relset_1 ) ) )
        | ~ sk336 )
      & ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk338 @ v1_funct_2 ) ) )
        | ~ sk336 )
      & ( ( sk338 @ v1_funct_1 )
        | ~ sk336 )
      & ( sk336
        | ~ ( f2_s12_funct_2 @ ( sk337 @ f3_s12_funct_2 @ r2_hidden ) ) )
      & ( sk336
        | ( f1_s12_funct_2 @ ( sk337 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4882]) ).

thf(4889,plain,
    ( sk336
    | ( f1_s12_funct_2 @ ( sk337 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4883]) ).

thf(3183,plain,
    k6_nat_lat @ v4_lattices,
    inference(cnfConj,[status(thm)],[3176]) ).

thf(897,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_lattice2) ).

thf(6011,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)],[897]) ).

thf(2748,plain,
    sk157 @ v11_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(764,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
                      & ( C @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
                      & ( D @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
                      & ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_0) ).

thf(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 ) )
             => ! [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)],[764]) ).

thf(886,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m2_filter_2 ) )
             => ( C @ ( B @ ( A @ k21_filter_2 ) ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_2) ).

thf(5964,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)],[886]) ).

thf(949,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
                = ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattices) ).

thf(6260,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)],[949]) ).

thf(2963,plain,
    sk188 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

thf(832,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k7_lattices ) @ ( A @ k7_lattices ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattices) ).

thf(5737,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)],[832]) ).

thf(1071,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)],[1069]) ).

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/sandbox2/benchmark/theBenchmark.p',t27_filter_0) ).

thf(6378,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(29954,plain,
    ! [A: $i] :
      ( ( A
       != ( k1_xboole_0 @ k1_tarski ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,11635]) ).

thf(29955,plain,
    ! [A: $i] :
      ( ( A
       != ( k1_xboole_0 @ k1_tarski ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[29954]) ).

thf(29956,plain,
    k1_xboole_0 @ k1_tarski @ sk19 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[29955:[bind(A,$thf( k1_xboole_0 @ k1_tarski ))]]) ).

thf(34330,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ sk19 @ 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)],[29956,1139]) ).

thf(34331,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ sk19 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[34330]) ).

thf(34332,plain,
    ( ( k1_xboole_0 @ k1_tarski @ sk19 @ k1_relat_1 @ ( k1_xboole_0 @ k1_tarski @ sk19 @ k9_relat_1 ) )
    = ( k1_xboole_0 @ k1_tarski @ sk19 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[34331:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ sk19 ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',t8_filter_2) ).

thf(3639,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(17011,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk349 @ ( A @ r2_hidden ) )
       != ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4988,3034]) ).

thf(17012,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk349 @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[17011]) ).

thf(17022,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk349 )
       != k1_xboole_0 )
      | ( A != B ) ),
    inference(simp,[status(thm)],[17012]) ).

thf(17029,plain,
    ! [A: $i] :
      ( ( A @ sk349 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[17022]) ).

thf(760,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_0) ).

thf(5417,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)],[760]) ).

thf(197,axiom,
    ? [A: $i] :
      ( ( A @ v2_struct_0 )
      & ( A @ l2_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_struct_0) ).

thf(2218,plain,
    ? [A: $i] :
      ( ( A @ v2_struct_0 )
      & ( A @ l2_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(2219,plain,
    ( ( sk95 @ v2_struct_0 )
    & ( sk95 @ l2_struct_0 ) ),
    inference(cnf,[status(esa)],[2218]) ).

thf(2221,plain,
    sk95 @ v2_struct_0,
    inference(cnfConj,[status(thm)],[2219]) ).

thf(867,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ m1_filter_0 ) )
                     => ( ( ( E @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
                          & ( E @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
                       => ( E @ ( D @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_0) ).

thf(5887,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)],[867]) ).

thf(699,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k11_filter_2 ) )
        = ( B @ ( A @ k8_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_filter_2) ).

thf(5126,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)],[699]) ).

thf(262,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k4_tarski ) )
      = ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

thf(2662,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(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 ) )
      & ( ( 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)],[1182]) ).

thf(1185,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)],[1183]) ).

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/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).

thf(2338,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(11582,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 @ v13_lattices ) ),
    inference(paramod_ordered,[status(thm)],[1111,11032]) ).

thf(11583,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[11582]) ).

thf(11609,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk138 @ k1_relat_1 @ r1_tarski ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[11583]) ).

thf(11712,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 @ v13_lattices ) ),
    inference(paramod_ordered,[status(thm)],[1110,11609]) ).

thf(11736,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[11712]) ).

thf(11747,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( k1_xboole_0 @ r1_tarski ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[11736]) ).

thf(12952,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ $true
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(rewrite,[status(thm)],[11747,2074]) ).

thf(12953,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12952]) ).

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/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).

thf(2275,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(1876,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1875]) ).

thf(1877,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1876]) ).

thf(38620,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)],[1877,38609]) ).

thf(38621,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ sk13 ) )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[38620:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',t49_domain_1) ).

thf(2602,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(538,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m3_lattice4 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                     => ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
                        & ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattice4) ).

thf(4269,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)],[538]) ).

thf(839,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ r3_lattice4 ) ) )
              <=> ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                  = ( B @ k5_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice4) ).

thf(5758,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)],[839]) ).

thf(756,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
              <=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                  = C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).

thf(5400,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)],[756]) ).

thf(801,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( D @ ( B @ r2_hidden ) )
                   => ( D @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_0) ).

thf(5598,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)],[801]) ).

thf(818,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k1_struct_0 ) )
        = ( B @ k1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).

thf(5679,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)],[818]) ).

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/sandbox2/benchmark/theBenchmark.p',rc1_lattice4) ).

thf(6368,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(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/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).

thf(2729,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(191,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).

thf(2161,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(2162,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[2161]) ).

thf(13443,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)],[1955,2162]) ).

thf(13444,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
    inference(pattern_uni,[status(thm)],[13443:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(115,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ~ ( ! [C: $i] :
              ~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
          & ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).

thf(1727,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(963,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k1_lattice4 ) )
            = ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_lattice4) ).

thf(6314,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)],[963]) ).

thf(9021,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk292 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,2439]) ).

thf(9022,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9021]) ).

thf(9040,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk292 ),
    inference(simp,[status(thm)],[9022]) ).

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/sandbox2/benchmark/theBenchmark.p',d16_binop_1) ).

thf(3130,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(507,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
               => ! [D: $i] :
                    ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ? [E: $i] :
                        ( ( D
                          = ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
                        & ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice4) ).

thf(4131,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)],[507]) ).

thf(996,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v3_filter_0 )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ? [D: $i] :
                    ( ! [E: $i] :
                        ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( C @ ( E @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
                         => ( D @ ( E @ ( A @ r1_lattices ) ) ) ) )
                    & ( C @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
                    & ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_0) ).

thf(6437,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)],[996]) ).

thf(23575,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)],[23573,1083]) ).

thf(23576,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)],[23575]) ).

thf(23577,plain,
    ! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[23576:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk207 @ k9_relat_1 ) )),bind(C,$thf( sk207 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(23667,plain,
    ! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[23577]) ).

thf(621,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ( ( B
                = ( A @ k6_lattices ) )
            <=> ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                      = B )
                    & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                      = B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattices) ).

thf(4685,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)],[621]) ).

thf(847,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) )
            = ( A @ k6_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattices) ).

thf(5808,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)],[847]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ v1_funct_1 )
        & ( D @ v1_relat_1 ) )
     => ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
          & ( B @ ( A @ r2_hidden ) )
          & ( ( D @ k1_relat_1 )
            = ( A @ k1_tarski ) ) )
       => ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
          & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).

thf(1098,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(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 ) )
      & ( ( 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)],[1098]) ).

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 @ k1_relat_1 )
       != ( A @ k1_tarski ) )
      | ~ ( D @ v1_funct_1 )
      | ~ ( D @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1099]) ).

thf(1103,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)],[1101]) ).

thf(941,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k18_filter_2 ) )
              = ( B @ ( A @ k2_filter_2 ) ) )
            & ( ( B @ ( A @ k18_filter_2 ) )
              = ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k2_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_2) ).

thf(6203,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)],[941]) ).

thf(467,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_lattices @ k1_realset1 ) @ m2_relset_1 ) ) )
            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_lattices @ k1_realset1 ) @ v1_funct_2 ) ) )
            & ( B @ ( A @ u1_lattices @ k1_realset1 ) @ v1_funct_1 )
            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u2_lattices @ k1_realset1 ) @ m2_relset_1 ) ) )
            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ u2_lattices @ k1_realset1 ) @ v1_funct_2 ) ) )
            & ( B @ ( A @ u2_lattices @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_filter_2) ).

thf(3890,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)],[467]) ).

thf(729,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ r2_hidden ) )
                    <=> ( C @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_2) ).

thf(5278,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)],[729]) ).

thf(857,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).

thf(5855,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)],[857]) ).

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 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( D @ ( B @ ( A @ r3_lattices ) ) )
                      & ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                   => ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_filter_0) ).

thf(6084,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)],[915]) ).

thf(3079,plain,
    sk197 @ v7_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(536,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                 => ( C @ ( D @ r2_hidden ) ) ) )
           => ( C @ ( B @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).

thf(4256,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)],[536]) ).

thf(570,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).

thf(4438,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)],[570]) ).

thf(693,axiom,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
      & ( A @ k1_subset_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).

thf(5095,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)],[693]) ).

thf(4359,plain,
    sk296 @ l1_struct_0,
    inference(cnf,[status(esa)],[4358]) ).

thf(408,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ! [G: $i] :
                                ( ( B @ ( G @ m1_subset_1 ) )
                               => ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
                                  = ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
                       => ( D = E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_binop_1) ).

thf(3547,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)],[408]) ).

thf(139,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
          & ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
       => ( ( B @ ( A @ k2_tarski ) @ ( C @ k9_relat_1 ) )
          = ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k2_tarski ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_1) ).

thf(1916,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(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/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).

thf(3255,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(451,axiom,
    f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s7_domain_1) ).

thf(3811,plain,
    f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(962,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k2_filter_0 ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_0) ).

thf(6312,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)],[962]) ).

thf(3081,plain,
    sk197 @ v4_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(9055,plain,
    ! [A: $i] :
      ( ( ( sk311 @ 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)],[4590,7096]) ).

thf(9056,plain,
    ! [A: $i] :
      ( ( ( sk311 @ 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)],[9055]) ).

thf(9057,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[9056:[bind(A,$thf( sk311 ))]]) ).

thf(121,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
       => ( ( ( A @ k1_relat_1 )
            = ( A @ k2_funct_1 @ k2_relat_1 ) )
          & ( ( A @ k2_relat_1 )
            = ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).

thf(1795,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(22,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).

thf(1124,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(828,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_filter_0 )
        = ( A @ u1_struct_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_filter_0) ).

thf(5720,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)],[828]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ( A @ l1_lattices )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).

thf(4144,plain,
    ! [A: $i] :
      ( ( A @ l1_lattices )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(8009,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,3129]) ).

thf(8010,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8009]) ).

thf(8015,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk152 ),
    inference(simp,[status(thm)],[8010]) ).

thf(672,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
                            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
                            & ( F @ v1_funct_1 ) )
                         => ( ( ( D @ ( C @ ( A @ r1_lattice2 ) ) )
                              & ( F
                                = ( B @ ( D @ k1_realset1 ) ) )
                              & ( E
                                = ( B @ ( C @ k1_realset1 ) ) ) )
                           => ( F @ ( E @ ( B @ r1_lattice2 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_filter_2) ).

thf(4998,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)],[672]) ).

thf(3070,plain,
    sk196 @ v15_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(279,axiom,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).

thf(2727,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(11632,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk71 ) ),
    inference(paramod_ordered,[status(thm)],[1955,7565]) ).

thf(11633,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk71 ),
    inference(pattern_uni,[status(thm)],[11632:[bind(A,$thf( k1_xboole_0 ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',d17_binop_1) ).

thf(3319,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(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/sandbox2/benchmark/theBenchmark.p',t60_lattice2) ).

thf(3636,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(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/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).

thf(2048,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(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/sandbox2/benchmark/theBenchmark.p',t119_funct_2) ).

thf(2938,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(774,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v13_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ( ( A @ k5_lattices )
              = ( B @ k5_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_filter_2) ).

thf(5474,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)],[774]) ).

thf(398,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

thf(3504,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(684,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
        = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).

thf(5067,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)],[684]) ).

thf(545,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_struct_0 ) ) )
         => ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_struct_0) ).

thf(4309,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)],[545]) ).

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/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).

thf(3086,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(8902,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)],[1067,8773]) ).

thf(8903,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)],[8902]) ).

thf(8926,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)],[8903]) ).

thf(8935,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)],[8926]) ).

thf(39586,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)],[8935,3316]) ).

thf(39587,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)],[39586]) ).

thf(39602,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk1 @ ( sk216 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk216 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3739,39587]) ).

thf(39603,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk1 @ ( sk216 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk216 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[39602]) ).

thf(39771,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( A
       != ( sk216 @ k1_relat_1 ) )
      | ( ( sk216 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[39603]) ).

thf(39808,plain,
    ( ( ( sk216 @ k1_relat_1 )
     != sk1 )
    | ( ( sk216 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[39771]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v17_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v16_lattices )
          & ( A @ v15_lattices )
          & ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ( A @ v11_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).

thf(4677,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)],[620]) ).

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/sandbox2/benchmark/theBenchmark.p',t31_relat_1) ).

thf(2674,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(805,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
       => ! [B: $i] :
            ( ( A @ ( B @ m1_filter_0 ) )
           => ~ ( ! [C: $i] :
                    ( ( A @ ( C @ m1_filter_0 ) )
                   => ~ ( ( A @ ( C @ v1_filter_0 ) )
                        & ( C @ ( B @ r1_tarski ) ) ) )
                & ( B
                 != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_0) ).

thf(5612,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)],[805]) ).

thf(493,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
        = ( C @ ( B @ ( A @ k2_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).

thf(4032,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)],[493]) ).

thf(577,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                    & ~ ( D @ v1_xboole_0 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
                        & ~ ( E @ v1_xboole_0 ) )
                     => ( ( ( E @ ( C @ r2_hidden ) )
                          & ( D @ ( B @ r2_hidden ) ) )
                       => ( ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
                          & ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_0) ).

thf(4465,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)],[577]) ).

thf(469,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( B @ ( A @ r2_filter_2 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
                    | ( B @ ( C @ r2_hidden ) ) ) )
              & ( B
               != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_2) ).

thf(3900,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)],[469]) ).

thf(91,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).

thf(1535,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(3291,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
    inference(cnf,[status(esa)],[3290]) ).

thf(3292,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) )
      = ( A @ k2_subset_1 ) ),
    inference(lifteq,[status(thm)],[3291]) ).

thf(39004,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k3_subset_1 ) )
      = A ),
    inference(rewrite,[status(thm)],[3292,2549,3094]) ).

thf(727,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(5271,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)],[727]) ).

thf(741,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k19_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_filter_2) ).

thf(5350,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)],[741]) ).

thf(89,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
    <=> ( ( ( A = B )
          | ( C @ ( B @ r2_hidden ) ) )
        & ~ ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).

thf(1520,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(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/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).

thf(3404,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(460,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ m1_subset_1 ) )
     => ( ( B @ ( A @ r2_hidden ) )
        | ( B @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

thf(3868,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)],[460]) ).

thf(7483,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)],[1065,7417]) ).

thf(7484,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)],[7483]) ).

thf(7519,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)],[7484]) ).

thf(7545,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)],[7519]) ).

thf(9808,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)],[7545,1974]) ).

thf(9809,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)],[9808]) ).

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)],[2074,9809]) ).

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(13007,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(13022,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)],[13007]) ).

thf(636,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_domain_1) ).

thf(4769,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)],[636]) ).

thf(2959,plain,
    sk188 @ v3_filter_0,
    inference(cnfConj,[status(thm)],[2957]) ).

thf(30311,plain,
    ! [A: $i] :
      ( ( A != sk138 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,15398]) ).

thf(30312,plain,
    ! [A: $i] :
      ( ( A != sk138 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[30311]) ).

thf(30313,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( sk138 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30312:[bind(A,$thf( sk138 ))]]) ).

thf(13031,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( B @ k1_tarski @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,5198]) ).

thf(13032,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( B @ k1_tarski @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[13031]) ).

thf(13054,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( B @ k1_tarski ) ),
    inference(simp,[status(thm)],[13032]) ).

thf(769,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v3_filter_0 )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ! [G: $i] :
                              ( ( C @ ( G @ m1_filter_0 ) )
                             => ! [H: $i] :
                                  ( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
                                 => ! [I: $i] :
                                      ( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
                                     => ! [J: $i] :
                                          ( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
                                         => ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
                                                & ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                                             => ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                                            & ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
                                                & ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
                                             => ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_filter_0) ).

thf(5449,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)],[769]) ).

thf(2425,plain,
    sk118 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(2474,plain,
    ~ ( k13_nat_lat @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2471]) ).

thf(793,axiom,
    ! [A: $i] :
      ( ( a_0_0_domain_1 @ ( A @ r2_hidden ) )
    <=> ? [B: $i] :
          ( ( B @ p1_s7_domain_1 )
          & ( A = B )
          & ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).

thf(5556,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)],[793]) ).

thf(1013,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k17_filter_2 @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_filter_2) ).

thf(6525,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)],[1013]) ).

thf(74,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
         => ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
              & ( C @ v1_funct_1 ) )
           => ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
              & ( B @ ( A @ ( C @ v1_partfun1 ) ) )
              & ( C @ v1_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).

thf(1428,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(593,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( B @ ( A @ r2_hidden ) ) )
     => ( C @ ( A @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

thf(4537,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)],[593]) ).

thf(448,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).

thf(3796,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)],[448]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ v1_relat_1 )
         => ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).

thf(1503,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(8749,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,2439]) ).

thf(8750,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8749]) ).

thf(8767,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk216 ),
    inference(simp,[status(thm)],[8750]) ).

thf(790,axiom,
    f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s9_domain_1) ).

thf(5546,plain,
    f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(441,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( ( C @ ( A @ k1_lattice2 @ k3_filter_2 ) )
                  = ( C @ ( A @ k8_filter_2 ) @ ( A @ k19_filter_2 ) ) )
                & ( ( C @ ( A @ k8_filter_2 ) @ ( A @ k3_filter_2 ) )
                  = ( C @ ( A @ k1_lattice2 @ k19_filter_2 ) ) )
                & ( ( B @ ( A @ k3_filter_2 ) )
                  = ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k19_filter_2 ) ) )
                & ( ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k3_filter_2 ) )
                  = ( B @ ( A @ k19_filter_2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_2) ).

thf(3751,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)],[441]) ).

thf(506,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( ! [E: $i] :
                  ( B
                 != ( E @ k1_tarski ) )
              & ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
           => ( C @ ( D @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_funct_2) ).

thf(4127,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)],[506]) ).

thf(2220,plain,
    sk95 @ l2_struct_0,
    inference(cnfConj,[status(thm)],[2219]) ).

thf(976,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ r2_lattice4 ) ) )
              <=> ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                  = ( B @ k6_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lattice4) ).

thf(6357,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)],[976]) ).

thf(15300,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)],[2270,7615]) ).

thf(15301,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)],[15300]) ).

thf(15345,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)],[15301]) ).

thf(15391,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15345]) ).

thf(3077,plain,
    sk197 @ v5_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(859,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_setwiseo ) )
       => ( ( A @ k5_lattices )
          = ( A @ u2_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice2) ).

thf(5859,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)],[859]) ).

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/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).

thf(3330,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(2738,plain,
    sk157 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(513,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
         => ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_2) ).

thf(4149,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)],[513]) ).

thf(425,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k12_filter_2 ) )
        = ( B @ ( A @ k8_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_filter_2) ).

thf(3663,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)],[425]) ).

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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).

thf(2935,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(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/sandbox2/benchmark/theBenchmark.p',t10_lattice2) ).

thf(3002,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(564,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
        = ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).

thf(4413,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)],[564]) ).

thf(918,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
                   => ( B @ ( C @ ( D @ ( A @ r1_filter_0 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_filter_0) ).

thf(6091,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)],[918]) ).

thf(959,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m3_lattice4 ) )
                 => ( ( ( D @ ( C @ r2_hidden ) )
                      & ( D @ ( B @ r2_hidden ) ) )
                   => ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice4) ).

thf(6302,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)],[959]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
              & ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
           => ( ( B @ ( A @ a_2_1_lattice4 ) )
              = ( B @ ( A @ k3_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice4) ).

thf(3594,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)],[418]) ).

thf(12281,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,9048]) ).

thf(12282,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12281]) ).

thf(12393,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk311 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12282]) ).

thf(12451,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12393]) ).

thf(601,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ ( B @ v1_filter_0 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
                    | ( B @ ( C @ r2_hidden ) ) ) )
              & ( B
               != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_0) ).

thf(4573,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)],[601]) ).

thf(691,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_domain_1) ).

thf(5086,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)],[691]) ).

thf(1239,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)],[1238]) ).

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/sandbox2/benchmark/theBenchmark.p',fc2_realset1) ).

thf(2442,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(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/sandbox2/benchmark/theBenchmark.p',cc2_lattice2) ).

thf(3436,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(7496,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)],[1065,7130]) ).

thf(7497,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)],[7496]) ).

thf(7525,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)],[7497]) ).

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)],[7525]) ).

thf(8058,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)],[7535,2544]) ).

thf(8059,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)],[8058]) ).

thf(1089,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)],[1085]) ).

thf(1092,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)],[1089]) ).

thf(457,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v14_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
                          = ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
                       => ( ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) )
                          = ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_lattice2) ).

thf(3832,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)],[457]) ).

thf(787,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice4) ).

thf(5539,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)],[787]) ).

thf(3604,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != B )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(cnfConj,[status(thm)],[3599]) ).

thf(3618,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != B )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(lifteq,[status(thm)],[3604]) ).

thf(3619,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ r2_hidden ) ),
    inference(simp,[status(thm)],[3618]) ).

thf(136,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ! [E: $i] :
          ~ ( ! [F: $i] :
                ~ ( ( E
                    = ( F @ ( D @ k1_funct_1 ) ) )
                  & ( C @ ( F @ r2_hidden ) )
                  & ( A @ ( F @ r2_hidden ) ) )
            & ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).

thf(1897,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(4640,plain,
    sk313 @ v6_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

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/sandbox2/benchmark/theBenchmark.p',fc1_filter_2) ).

thf(6372,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(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/sandbox2/benchmark/theBenchmark.p',dt_g2_struct_0) ).

thf(3568,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(102,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).

thf(1638,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(1223,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)],[1222]) ).

thf(1224,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)],[1223]) ).

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/sandbox2/benchmark/theBenchmark.p',t168_funct_2) ).

thf(2148,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(27465,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)],[2047,3619]) ).

thf(27466,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
    inference(pattern_uni,[status(thm)],[27465:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(27507,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
    inference(simp,[status(thm)],[27466]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
                <=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_binop_1) ).

thf(1356,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(428,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v17_lattices )
      <=> ( ( A @ v11_lattices )
          & ( A @ v16_lattices )
          & ( A @ v15_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_lattices) ).

thf(3678,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)],[428]) ).

thf(1001,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_lattice2) ).

thf(6478,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)],[1001]) ).

thf(41172,plain,
    ( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,41008]) ).

thf(41173,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41172]) ).

thf(41231,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk216 ),
    inference(simp,[status(thm)],[41173]) ).

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/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).

thf(2721,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(15284,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)],[2270,8556]) ).

thf(15285,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)],[15284]) ).

thf(15358,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)],[15285]) ).

thf(15406,plain,
    ( ( sk207 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15358]) ).

thf(531,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ( A @ v5_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ r1_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattices) ).

thf(4228,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)],[531]) ).

thf(30848,plain,
    ! [A: $i] :
      ( ( A != sk14 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,8155]) ).

thf(30849,plain,
    ! [A: $i] :
      ( ( A != sk14 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[30848]) ).

thf(30850,plain,
    sk14 @ sk19 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[30849:[bind(A,$thf( sk14 ))]]) ).

thf(34020,plain,
    ! [A: $i] :
      ( ( ( sk14 @ sk19 @ 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)],[30850,1139]) ).

thf(34021,plain,
    ! [A: $i] :
      ( ( ( sk14 @ sk19 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[34020]) ).

thf(34022,plain,
    ( ( sk14 @ sk19 @ k1_relat_1 @ ( sk14 @ sk19 @ k9_relat_1 ) )
    = ( sk14 @ sk19 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[34021:[bind(A,$thf( sk14 @ sk19 ))]]) ).

thf(2422,plain,
    sk118 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(2955,plain,
    sk187 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(552,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( A @ ( H @ m1_subset_1 ) )
        & ( A @ ( G @ m1_subset_1 ) )
        & ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_domain_1) ).

thf(4337,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)],[552]) ).

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/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).

thf(2679,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(15335,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2270,9087]) ).

thf(15336,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15335]) ).

thf(15362,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk311 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[15336]) ).

thf(15367,plain,
    ( ( sk311 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[15362]) ).

thf(6305,plain,
    ( ( k13_nat_lat @ l3_lattices )
    & ( k13_nat_lat @ v10_lattices )
    & ~ ( k13_nat_lat @ v3_struct_0 ) ),
    inference(cnf,[status(esa)],[6304]) ).

thf(6308,plain,
    k13_nat_lat @ l3_lattices,
    inference(cnfConj,[status(thm)],[6305]) ).

thf(816,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( B @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_2) ).

thf(5671,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)],[816]) ).

thf(583,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
            = ( D @ k1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t164_funct_2) ).

thf(4498,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)],[583]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ v1_relat_1 )
         => ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).

thf(1282,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(2478,plain,
    k13_nat_lat @ v9_lattices,
    inference(cnfConj,[status(thm)],[2471]) ).

thf(2214,plain,
    sk94 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

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/sandbox2/benchmark/theBenchmark.p',d14_binop_1) ).

thf(2383,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(722,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
              <=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                  = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattices) ).

thf(5244,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)],[722]) ).

thf(940,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                  = C ) )
           => ( B
              = ( A @ k5_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice2) ).

thf(6197,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)],[940]) ).

thf(623,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
                                = B ) ) )
                       => ( ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) )
                            = B )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice2) ).

thf(4699,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)],[623]) ).

thf(850,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_nat_lat ) )
         => ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_nat_lat) ).

thf(5827,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)],[850]) ).

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/sandbox2/benchmark/theBenchmark.p',fc3_lattice2) ).

thf(3270,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(93,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
          <=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
              & ( C @ ( B @ ( A @ r4_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_binop_1) ).

thf(1542,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(716,axiom,
    ( ! [A: $i] :
        ( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
       => ? [B: $i] :
            ( ( B @ ( A @ p1_s3_funct_2 ) )
            & ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
           => ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
        & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_2) ).

thf(5219,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)],[716]) ).

thf(5220,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( sk372 @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) )
        | ~ ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
        | ~ sk370 )
      & ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk372 @ m2_relset_1 ) ) )
        | ~ sk370 )
      & ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk372 @ v1_funct_2 ) ) )
        | ~ sk370 )
      & ( ( sk372 @ v1_funct_1 )
        | ~ sk370 )
      & ( sk370
        | ~ ( A @ ( sk371 @ p1_s3_funct_2 ) )
        | ~ ( f2_s3_funct_2 @ ( A @ m1_subset_1 ) ) )
      & ( sk370
        | ( f1_s3_funct_2 @ ( sk371 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[5219]) ).

thf(5222,plain,
    ( sk370
    | ( f1_s3_funct_2 @ ( sk371 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[5220]) ).

thf(509,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice2) ).

thf(4139,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)],[509]) ).

thf(1144,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)],[1141]) ).

thf(2943,plain,
    sk187 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(15242,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2270,9048]) ).

thf(15243,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15242]) ).

thf(15354,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk311 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15243]) ).

thf(15401,plain,
    ( ( sk311 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15354]) ).

thf(2945,plain,
    sk187 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(611,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ~ ( ! [E: $i] :
                          ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                         => ~ ( ( C @ ( E @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                              & ( B @ ( E @ r2_hidden ) ) ) )
                      & ( B @ ( D @ ( A @ k2_filter_0 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice4) ).

thf(4616,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)],[611]) ).

thf(740,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
                  <=> ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_filter_0) ).

thf(5346,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)],[740]) ).

thf(122,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
                          = ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_binop_1) ).

thf(1801,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(514,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k11_filter_0 ) )
        = ( B @ ( A @ k10_filter_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).

thf(4154,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)],[514]) ).

thf(31978,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ l3_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,1025]) ).

thf(31979,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ( sk1 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[31978:[bind(A,$thf( sk1 ))]]) ).

thf(521,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( B @ l3_lattices )
        & ( B @ v17_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i,E: $i] :
            ( ( C @ ( E @ r2_hidden ) )
            & ( C @ ( D @ r2_hidden ) )
            & ( A
              = ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
            & ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
            & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).

thf(4176,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)],[521]) ).

thf(8171,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)],[3160,7096]) ).

thf(8172,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)],[8171]) ).

thf(8173,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)],[8172:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15211,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8173,2270]) ).

thf(15212,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15211]) ).

thf(559,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
             => ( ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ( ( B @ ( E @ r2_hidden ) )
                    <=> ( ~ ( D @ ( E @ r2_hidden ) )
                        & ( C @ ( E @ r2_hidden ) ) ) ) )
               => ( B
                  = ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).

thf(4374,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( A @ 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)],[559]) ).

thf(3182,plain,
    k6_nat_lat @ v10_lattices,
    inference(cnfConj,[status(thm)],[3176]) ).

thf(3066,plain,
    sk196 @ v16_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

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/sandbox2/benchmark/theBenchmark.p',t81_lattice2) ).

thf(3586,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(14169,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk311 @ 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)],[14123,1097]) ).

thf(14170,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk311 @ 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)],[14169]) ).

thf(14171,plain,
    ! [A: $i] : ( sk311 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14170:[bind(A,$thf( sk311 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14198,plain,
    ! [A: $i] : ( sk311 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14171]) ).

thf(77,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
          & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) )
       => ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
          | ( ( A != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_funct_2) ).

thf(1439,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(8780,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)],[3318,7096]) ).

thf(8781,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)],[8780]) ).

thf(8782,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)],[8781:[bind(A,$thf( sk216 ))]]) ).

thf(12324,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,8782]) ).

thf(12325,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12324]) ).

thf(12369,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk216 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12325]) ).

thf(725,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k14_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_filter_2) ).

thf(5267,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)],[725]) ).

thf(560,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ v17_lattices )
        & ( A @ k1_lattice2 @ v16_lattices )
        & ( A @ k1_lattice2 @ v15_lattices )
        & ( A @ k1_lattice2 @ v14_lattices )
        & ( A @ k1_lattice2 @ v13_lattices )
        & ( A @ k1_lattice2 @ v12_lattices )
        & ( A @ k1_lattice2 @ v11_lattices )
        & ( A @ k1_lattice2 @ v10_lattices )
        & ( A @ k1_lattice2 @ v9_lattices )
        & ( A @ k1_lattice2 @ v8_lattices )
        & ( A @ k1_lattice2 @ v7_lattices )
        & ( A @ k1_lattice2 @ v6_lattices )
        & ( A @ k1_lattice2 @ v5_lattices )
        & ( A @ k1_lattice2 @ v4_lattices )
        & ( A @ k1_lattice2 @ v3_lattices )
        & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_filter_2) ).

thf(4388,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)],[560]) ).

thf(1173,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)],[1167]) ).

thf(1175,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)],[1173]) ).

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/sandbox2/benchmark/theBenchmark.p',fc2_filter_0) ).

thf(2180,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(792,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).

thf(5552,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)],[792]) ).

thf(4635,plain,
    sk313 @ v8_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(568,axiom,
    ! [A: $i,B: $i] :
      ~ ( ! [C: $i] :
            ~ ( ! [D: $i] :
                  ~ ( ( C @ ( D @ r2_hidden ) )
                    & ( B @ ( D @ r2_hidden ) ) )
              & ( B @ ( C @ r2_hidden ) ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).

thf(4430,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)],[568]) ).

thf(1079,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)],[1078]) ).

thf(1080,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)],[1079]) ).

thf(30924,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ v13_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,1028]) ).

thf(30925,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ( sk1 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30924:[bind(A,$thf( sk1 ))]]) ).

thf(127,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_2) ).

thf(1821,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(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/sandbox2/benchmark/theBenchmark.p',t12_filter_2) ).

thf(4208,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(276,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).

thf(2710,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(712,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ~ ( C @ ( D @ r2_hidden ) )
            & ( A = D )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).

thf(5202,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)],[712]) ).

thf(13037,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk359 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,5125]) ).

thf(13038,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk359 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[13037]) ).

thf(13050,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != sk359 ),
    inference(simp,[status(thm)],[13038]) ).

thf(2742,plain,
    sk157 @ v13_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(573,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ m2_relset_1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ v1_funct_2 ) ) )
        & ( A @ k5_lattice4 @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice4) ).

thf(4445,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)],[573]) ).

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/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).

thf(2605,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(504,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v16_lattices )
          & ( A @ v15_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
      <=> ( ( A @ k1_lattice2 @ l3_lattices )
          & ( A @ k1_lattice2 @ v16_lattices )
          & ( A @ k1_lattice2 @ v15_lattices )
          & ( A @ k1_lattice2 @ v10_lattices )
          & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_2) ).

thf(4103,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)],[504]) ).

thf(5893,plain,
    ( ~ ( sk420 @ v3_struct_0 )
    & ( sk420 @ l2_struct_0 ) ),
    inference(cnf,[status(esa)],[5892]) ).

thf(5894,plain,
    sk420 @ l2_struct_0,
    inference(cnfConj,[status(thm)],[5893]) ).

thf(690,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
                            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
                            & ( F @ v1_funct_1 ) )
                         => ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
                              & ( F
                                = ( B @ ( D @ k1_realset1 ) ) )
                              & ( E
                                = ( B @ ( C @ k1_realset1 ) ) ) )
                           => ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_2) ).

thf(5082,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)],[690]) ).

thf(599,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m1_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_struct_0) ).

thf(4569,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)],[599]) ).

thf(4911,plain,
    sk340 @ l1_lattices,
    inference(cnf,[status(esa)],[4910]) ).

thf(3073,plain,
    sk197 @ l3_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(41228,plain,
    ( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,41008]) ).

thf(41229,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41228]) ).

thf(41235,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk71 ),
    inference(simp,[status(thm)],[41229]) ).

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/sandbox2/benchmark/theBenchmark.p',l59_filter_2) ).

thf(3572,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(656,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ~ ( D @ ( E @ r2_hidden ) )
            & ( C @ ( E @ r2_hidden ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).

thf(4897,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)],[656]) ).

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/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).

thf(2923,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(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/sandbox2/benchmark/theBenchmark.p',t12_binop_1) ).

thf(2593,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(649,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_lattice4 ) @ ( A @ k7_lattices ) )
            = ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice4) ).

thf(4850,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)],[649]) ).

thf(813,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v15_lattices )
      <=> ( ( A @ v14_lattices )
          & ( A @ v13_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattices) ).

thf(5656,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)],[813]) ).

thf(965,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) )
                      = ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
       => ( A @ v11_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattices) ).

thf(6319,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)],[965]) ).

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/sandbox2/benchmark/theBenchmark.p',t32_relat_1) ).

thf(2874,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(866,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice2) ).

thf(5885,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)],[866]) ).

thf(62,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).

thf(1344,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(1020,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) )
           => ( A @ v13_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_2) ).

thf(6553,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)],[1020]) ).

thf(1170,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)],[1167]) ).

thf(1177,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)],[1170]) ).

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/sandbox2/benchmark/theBenchmark.p',fc2_lattice2) ).

thf(2461,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(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/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).

thf(2974,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(758,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( B @ ( A @ k7_lattices ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lattices) ).

thf(5410,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)],[758]) ).

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/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).

thf(2329,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(30010,plain,
    ! [A: $i] :
      ( ( A != sk313 )
      | ( k1_xboole_0 @ v15_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,4638]) ).

thf(30011,plain,
    ( ( k1_xboole_0 @ v15_lattices )
    | ( sk313 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30010:[bind(A,$thf( sk313 ))]]) ).

thf(853,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r2_lattices ) ) )
              <=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                    = ( A @ k5_lattices ) )
                  & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                    = ( A @ k5_lattices ) )
                  & ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                    = ( A @ k6_lattices ) )
                  & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                    = ( A @ k6_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_lattices) ).

thf(5838,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)],[853]) ).

thf(1061,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)],[1059]) ).

thf(891,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( B @ ( C @ ( A @ k20_filter_2 ) ) @ ( C @ ( B @ ( A @ k20_filter_2 ) ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_2) ).

thf(5987,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)],[891]) ).

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/sandbox2/benchmark/theBenchmark.p',rc1_nat_lat) ).

thf(2578,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(533,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ! [C: $i] :
                  ( ( A @ ( C @ m2_filter_2 ) )
                 => ~ ( ( C @ ( A @ r2_filter_2 ) )
                      & ( C @ ( B @ r2_hidden ) ) ) )
              & ( B
               != ( A @ k6_lattices ) )
              & ( A @ v14_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_filter_2) ).

thf(4232,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)],[533]) ).

thf(877,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ! [E: $i] :
                      ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( C = F )
                              & ( B = E ) )
                           => ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                                = ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k4_lattices ) ) ) )
                              & ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                                = ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_0) ).

thf(5931,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)],[877]) ).

thf(715,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v11_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ k4_lattices ) ) )
                        = ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_lattice2) ).

thf(5216,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)],[715]) ).

thf(777,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) )
                          = ( E @ ( A @ k6_filter_2 ) @ ( D @ ( A @ k6_filter_2 ) @ ( A @ k4_lattices ) ) ) )
                        & ( ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) )
                          = ( E @ ( A @ k6_filter_2 ) @ ( D @ ( A @ k6_filter_2 ) @ ( A @ k3_lattices ) ) ) )
                        & ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                          = ( C @ ( A @ k5_filter_2 ) @ ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
                        & ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                          = ( C @ ( A @ k5_filter_2 ) @ ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_2) ).

thf(5482,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)],[777]) ).

thf(427,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ ( B @ ( A @ k10_filter_2 ) @ m2_lattice4 ) )
        & ~ ( B @ ( A @ k10_filter_2 ) @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_2) ).

thf(3674,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)],[427]) ).

thf(76,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
       => ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
          & ( B @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).

thf(1435,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(830,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v11_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
                      = ( D @ ( B @ ( A @ k2_lattices ) ) @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_lattices) ).

thf(5725,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)],[830]) ).

thf(543,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D != k1_xboole_0 )
                       => ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ k4_lattices ) ) )
                          = ( E @ ( B @ ( A @ u1_lattices @ ( C @ ( A @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_lattice2) ).

thf(4304,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)],[543]) ).

thf(14453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk311 @ k2_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[14438,1083]) ).

thf(14454,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk311 @ k2_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14453]) ).

thf(14455,plain,
    ! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk311 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14454:[bind(A,$thf( sk311 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14511,plain,
    ! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk311 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14455]) ).

thf(14588,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( A @ ( sk311 @ 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)],[14511,1083]) ).

thf(14589,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( A @ ( sk311 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14588]) ).

thf(14590,plain,
    ! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk311 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14589:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk311 @ k2_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f2_s4_funct_2 )),bind(D,$thf( D ))]]) ).

thf(14656,plain,
    ! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk311 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14590]) ).

thf(8751,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,3129]) ).

thf(8752,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8751]) ).

thf(8763,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk216 ),
    inference(simp,[status(thm)],[8752]) ).

thf(41263,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,41075]) ).

thf(41264,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk292 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41263]) ).

thf(41311,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk292 ),
    inference(simp,[status(thm)],[41264]) ).

thf(8004,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,2439]) ).

thf(8005,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8004]) ).

thf(8007,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk71 ),
    inference(simp,[status(thm)],[8005]) ).

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/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).

thf(3480,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(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/sandbox2/benchmark/theBenchmark.p',t165_funct_2) ).

thf(2075,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(2418,plain,
    ~ ( sk118 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2415]) ).

thf(660,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).

thf(4933,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)],[660]) ).

thf(1195,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)],[1194]) ).

thf(1198,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)],[1195]) ).

thf(972,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k6_filter_2 ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_filter_2) ).

thf(6345,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)],[972]) ).

thf(680,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C
                  = ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
               => ( ( C @ ( A @ k3_filter_0 ) )
                  = ( B @ ( A @ k2_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_0) ).

thf(5057,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)],[680]) ).

thf(2962,plain,
    sk188 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

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/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).

thf(2362,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(2363,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)],[2362]) ).

thf(2365,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_relat_1 ),
    inference(cnfConj,[status(thm)],[2363]) ).

thf(38327,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5170,1247]) ).

thf(38328,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
     != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[38327]) ).

thf(38361,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[38328]) ).

thf(38382,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
     != ( B @ k1_tarski ) ),
    inference(simp,[status(thm)],[38361]) ).

thf(748,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).

thf(5372,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)],[748]) ).

thf(8195,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3160,7074]) ).

thf(8196,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8195]) ).

thf(8197,plain,
    ( ( k1_xboole_0 @ v13_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)],[8196:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15215,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8197,2270]) ).

thf(15216,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15215]) ).

thf(766,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
                      & ( D @ ( B @ r2_hidden ) ) )
                   => ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_0) ).

thf(5442,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)],[766]) ).

thf(2212,plain,
    sk94 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

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/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).

thf(3423,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(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/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).

thf(2550,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(15586,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)],[2544,1139]) ).

thf(15587,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)],[15586]) ).

thf(15588,plain,
    ( ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) )
    = ( sk138 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15587:[bind(A,$thf( sk138 ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).

thf(2481,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(956,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m3_lattice4 ) )
                 => ( ( ( D @ ( C @ r2_hidden ) )
                      & ( D @ ( B @ r2_hidden ) ) )
                   => ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattice4) ).

thf(6288,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)],[956]) ).

thf(953,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ ( A @ k20_filter_2 ) ) )
                = ( C @ ( B @ ( A @ a_3_0_filter_2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_2) ).

thf(6270,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)],[953]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( C @ v1_relat_1 )
             => ( ( C
                  = ( B @ ( A @ k10_filter_0 ) ) )
              <=> ( ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ! [E: $i] :
                          ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                         => ( ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
                          <=> ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) )
                  & ( A @ u1_struct_0 @ ( C @ k3_relat_1 @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_filter_0) ).

thf(3917,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)],[472]) ).

thf(944,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).

thf(6223,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)],[944]) ).

thf(31893,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_zfmisc_1 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,8160]) ).

thf(31894,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_zfmisc_1 ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[31893]) ).

thf(31895,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ sk19 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[31894:[bind(A,$thf( C @ k1_zfmisc_1 )),bind(B,$thf( C ))]]) ).

thf(33084,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ sk19 @ v1_relat_1 ),
    inference(simp,[status(thm)],[31895]) ).

thf(430,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                    & ~ ( D @ v1_xboole_0 ) )
                 => ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( D @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r2_hidden ) )
                   => ( D @ ( A @ k3_filter_0 ) @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_0) ).

thf(3687,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)],[430]) ).

thf(15274,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2270,9057]) ).

thf(15275,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15274]) ).

thf(15357,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk311 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15275]) ).

thf(15405,plain,
    ( ( sk311 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15357]) ).

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/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).

thf(2288,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(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] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ r4_lattice4 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                      = ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice4) ).

thf(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] :
              ( ( 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)],[888]) ).

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/sandbox2/benchmark/theBenchmark.p',t16_lattice2) ).

thf(3016,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(12357,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,8773]) ).

thf(12358,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12357]) ).

thf(12409,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk216 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12358]) ).

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/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).

thf(2633,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(2967,plain,
    sk188 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
          = ( C @ k2_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).

thf(1250,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(902,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
                = ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_0) ).

thf(6027,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)],[902]) ).

thf(3178,plain,
    k6_nat_lat @ v3_lattices,
    inference(cnfConj,[status(thm)],[3176]) ).

thf(4626,plain,
    sk313 @ v5_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(1004,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ m1_filter_0 ) )
        & ( B @ ( C @ m1_filter_0 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ? [F: $i] :
                ( ? [G: $i] :
                    ( ( D @ ( G @ r2_hidden ) )
                    & ( C @ ( F @ r2_hidden ) )
                    & ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
                    & ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
                & ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
            & ( A = E )
            & ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).

thf(6485,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)],[1004]) ).

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/sandbox2/benchmark/theBenchmark.p',t7_lattice2) ).

thf(2693,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(99,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i] :
          ( ( ( B @ v1_funct_1 )
            & ( B @ v1_relat_1 ) )
         => ( ( A @ ( B @ r1_tarski ) )
           => ( ( B @ ( A @ k1_funct_4 ) )
              = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice2) ).

thf(1626,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(2952,plain,
    sk187 @ v14_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(508,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
                = ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice4) ).

thf(4136,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)],[508]) ).

thf(592,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
      <=> ? [C: $i] :
            ( ( A = C )
            & ( B @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).

thf(4529,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)],[592]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( ( A @ k1_relat_1 @ v1_relat_1 )
        & ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).

thf(1340,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(464,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_funct_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(3881,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_funct_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(814,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ r1_lattice4 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                          = ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice4) ).

thf(5661,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)],[814]) ).

thf(1031,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)],[1030]) ).

thf(1033,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)],[1031]) ).

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 ) @ k1_relat_1 )
        = ( C @ ( A @ k2_tarski ) ) ) ),
    inference(simp,[status(thm)],[1033]) ).

thf(821,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k4_lattice4 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice4) ).

thf(5688,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)],[821]) ).

thf(657,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( C @ v1_xboole_0 )
        & ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

thf(4907,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)],[657]) ).

thf(5582,plain,
    ( ( ( f3_s11_funct_2 @ ( sk404 @ ( 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)],[5580]) ).

thf(5587,plain,
    ( ( ( f3_s11_funct_2 @ ( sk404 @ ( 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)],[5582]) ).

thf(8551,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3210,7074]) ).

thf(8552,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8551]) ).

thf(8553,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8552:[bind(A,$thf( sk207 ))]]) ).

thf(15337,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2270,8553]) ).

thf(15338,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15337]) ).

thf(15353,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[15338]) ).

thf(15400,plain,
    ( ( sk207 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[15353]) ).

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/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).

thf(3193,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(7508,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)],[1065,7127]) ).

thf(7509,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)],[7508]) ).

thf(7521,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)],[7509]) ).

thf(7529,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)],[7521]) ).

thf(7895,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)],[7529,1974]) ).

thf(7896,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)],[7895]) ).

thf(783,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( C = E )
                          & ( B = D )
                          & ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
                       => ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_lattice2) ).

thf(5528,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)],[783]) ).

thf(1203,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)],[1201]) ).

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/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).

thf(3576,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(955,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ( ( B
                = ( A @ k5_lattices ) )
            <=> ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                      = B )
                    & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                      = B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).

thf(6276,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)],[955]) ).

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/sandbox2/benchmark/theBenchmark.p',t12_lattice2) ).

thf(2665,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(6725,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)],[2544,1052]) ).

thf(6726,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)],[6725]) ).

thf(6727,plain,
    ! [A: $i] : ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6726:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).

thf(19399,plain,
    ! [A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6727,15588]) ).

thf(641,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
     => ( ( B @ ( A @ r1_tarski ) )
       => ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).

thf(4813,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)],[641]) ).

thf(937,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k6_filter_0 ) ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_0) ).

thf(6185,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)],[937]) ).

thf(12318,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,7238]) ).

thf(12319,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12318]) ).

thf(12368,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk138 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12319]) ).

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/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).

thf(2271,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(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/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).

thf(3293,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(605,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( B @ ( A @ r2_filter_2 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r2_hidden ) )
                <=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_2) ).

thf(4598,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)],[605]) ).

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/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).

thf(2878,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(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/sandbox2/benchmark/theBenchmark.p',dt_k3_binop_1) ).

thf(2503,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(549,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
                    = ( D @ ( C @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice2) ).

thf(4319,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)],[549]) ).

thf(12977,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)],[2074,7896]) ).

thf(12978,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)],[12977]) ).

thf(13000,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)],[12978]) ).

thf(13015,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)],[13000]) ).

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/sandbox2/benchmark/theBenchmark.p',d12_binop_1) ).

thf(3146,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(30099,plain,
    ! [A: $i] :
      ( ( A != sk94 )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2216]) ).

thf(30100,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ( sk94 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30099:[bind(A,$thf( sk94 ))]]) ).

thf(482,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ! [C: $i] :
                ( ( A @ ( C @ m1_filter_2 ) )
               => ( B @ ( C @ m1_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_filter_2) ).

thf(3975,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)],[482]) ).

thf(5674,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)],[5673]) ).

thf(5678,plain,
    k6_nat_lat @ l3_lattices,
    inference(cnfConj,[status(thm)],[5674]) ).

thf(598,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v14_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( B @ ( A @ k6_lattices @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_filter_0) ).

thf(4566,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)],[598]) ).

thf(12285,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,9090]) ).

thf(12286,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12285]) ).

thf(12367,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk311 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12286]) ).

thf(12434,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12367]) ).

thf(1010,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k5_filter_2 ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).

thf(6517,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)],[1010]) ).

thf(389,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
     => ( B @ v1_finset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finsub_1) ).

thf(3455,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(933,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k2_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_2) ).

thf(6170,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)],[933]) ).

thf(744,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ v14_lattices ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_0) ).

thf(5358,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)],[744]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
         => ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).

thf(1180,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(1181,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)],[1180]) ).

thf(4168,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(cnf,[status(esa)],[4167]) ).

thf(893,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( B @ ( A @ k1_lattice4 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice4) ).

thf(5991,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)],[893]) ).

thf(94,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
        = A )
    <=> ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).

thf(1547,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(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/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).

thf(3376,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(87,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).

thf(1516,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(723,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ~ ( ( C @ ( E @ r2_hidden ) )
              <=> ( D @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).

thf(5250,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)],[723]) ).

thf(186,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).

thf(2143,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(9023,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk292 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,3129]) ).

thf(9024,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9023]) ).

thf(9037,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk292 ),
    inference(simp,[status(thm)],[9024]) ).

thf(6367,plain,
    sk456 @ v3_lattices,
    inference(cnfConj,[status(thm)],[6364]) ).

thf(29861,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ ( B @ k1_funct_2 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,8154]) ).

thf(29862,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ ( B @ k1_funct_2 ) ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[29861]) ).

thf(29863,plain,
    ! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk19 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[29862:[bind(A,$thf( D @ ( D @ k1_funct_2 ) )),bind(B,$thf( D ))]]) ).

thf(33085,plain,
    ! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk19 @ v1_relat_1 ),
    inference(simp,[status(thm)],[29863]) ).

thf(525,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D = E )
                       => ( ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
                            = ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k2_lattice2 ) ) ) ) )
                          & ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
                            = ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattice2) ).

thf(4200,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)],[525]) ).

thf(30232,plain,
    ! [A: $i] :
      ( ( A != sk118 )
      | ( k1_xboole_0 @ v9_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2420]) ).

thf(30233,plain,
    ( ( k1_xboole_0 @ v9_lattices )
    | ( sk118 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30232:[bind(A,$thf( sk118 ))]]) ).

thf(44144,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)],[1974,1232]) ).

thf(44145,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)],[44144]) ).

thf(44146,plain,
    ! [A: $i] : ( A @ ( sk71 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44145:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).

thf(768,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_0) ).

thf(5446,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)],[768]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ! [D: $i] :
                  ( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                    & ~ ( D @ v1_xboole_0 ) )
                 => ! [E: $i] :
                      ( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
                        & ~ ( E @ v1_xboole_0 ) )
                     => ( ( ( E @ ( A @ k8_filter_2 ) @ ( D @ ( A @ k8_filter_2 ) @ ( A @ k20_filter_2 ) ) )
                          = ( E @ ( D @ ( A @ k1_lattice2 @ k5_filter_0 ) ) ) )
                        & ( ( E @ ( D @ ( A @ k1_lattice2 @ k20_filter_2 ) ) )
                          = ( E @ ( A @ k8_filter_2 ) @ ( D @ ( A @ k8_filter_2 ) @ ( A @ k5_filter_0 ) ) ) )
                        & ( ( C @ ( A @ k7_filter_2 ) @ ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k20_filter_2 ) ) )
                          = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) )
                        & ( ( C @ ( B @ ( A @ k20_filter_2 ) ) )
                          = ( C @ ( A @ k7_filter_2 ) @ ( B @ ( A @ k7_filter_2 ) @ ( A @ k1_lattice2 @ k5_filter_0 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_2) ).

thf(3988,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)],[485]) ).

thf(632,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( B @ ( A @ k10_filter_0 ) @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_0) ).

thf(4749,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)],[632]) ).

thf(149,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ v10_lattices )
        & ( A @ k1_lattice2 @ v9_lattices )
        & ( A @ k1_lattice2 @ v8_lattices )
        & ( A @ k1_lattice2 @ v7_lattices )
        & ( A @ k1_lattice2 @ v6_lattices )
        & ( A @ k1_lattice2 @ v5_lattices )
        & ( A @ k1_lattice2 @ v4_lattices )
        & ( A @ k1_lattice2 @ v3_lattices )
        & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).

thf(1961,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(494,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C
                  = ( B @ ( A @ k3_filter_0 ) ) )
              <=> ( ! [D: $i] :
                      ( ( A @ ( D @ m1_filter_0 ) )
                     => ( ( D @ ( B @ r1_tarski ) )
                       => ( D @ ( C @ r1_tarski ) ) ) )
                  & ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_filter_0) ).

thf(4035,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)],[494]) ).

thf(558,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m2_filter_2 ) )
             => ( ( C
                  = ( B @ ( A @ k19_filter_2 ) ) )
              <=> ( ! [D: $i] :
                      ( ( A @ ( D @ m2_filter_2 ) )
                     => ( ( D @ ( B @ r1_tarski ) )
                       => ( D @ ( C @ r1_tarski ) ) ) )
                  & ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_2) ).

thf(4360,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)],[558]) ).

thf(876,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
                      & ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_0) ).

thf(5927,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)],[876]) ).

thf(780,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k2_filter_2 ) )
        = ( B @ ( A @ k2_filter_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).

thf(5514,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)],[780]) ).

thf(803,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ v11_lattices ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_0) ).

thf(5602,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)],[803]) ).

thf(652,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ~ ( D @ v1_xboole_0 )
        & ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i,F: $i] :
            ( ( D @ ( F @ r2_hidden ) )
            & ( C @ ( E @ r2_hidden ) )
            & ( A
              = ( F @ ( E @ ( B @ k4_lattices ) ) ) )
            & ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
            & ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).

thf(4864,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)],[652]) ).

thf(987,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
                    = ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattices) ).

thf(6399,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)],[987]) ).

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/sandbox2/benchmark/theBenchmark.p',cc4_lattice2) ).

thf(2060,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(4939,plain,
    sk343 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4937]) ).

thf(42134,plain,
    ! [A: $i] :
      ( ( A
       != ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,41233]) ).

thf(42135,plain,
    ! [A: $i] :
      ( ( A
       != ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[42134]) ).

thf(42136,plain,
    sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ sk19 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[42135:[bind(A,$thf( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ))]]) ).

thf(3082,plain,
    sk197 @ v9_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(619,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v3_filter_0 )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v3_lattice4 ) ) )
               => ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
                  & ( A @ v3_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice4) ).

thf(4673,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)],[619]) ).

thf(588,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ ( A @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(4517,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ ( A @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(614,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( A @ ( F @ r2_hidden ) )
        & ( F @ ( E @ r2_hidden ) )
        & ( E @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).

thf(4641,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)],[614]) ).

thf(578,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D != k1_xboole_0 )
                       => ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ k3_lattices ) ) )
                          = ( E @ ( B @ ( A @ u2_lattices @ ( C @ ( A @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice2) ).

thf(4469,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)],[578]) ).

thf(634,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
        = ( C @ ( B @ k2_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).

thf(4754,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)],[634]) ).

thf(665,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v3_filter_0 )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ! [D: $i] :
                  ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice4) ).

thf(4961,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)],[665]) ).

thf(3058,plain,
    sk196 @ v7_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(44228,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk14 @ sk19 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[30850,1232]) ).

thf(44229,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk14 @ sk19 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[44228]) ).

thf(44230,plain,
    ! [A: $i] : ( A @ ( sk14 @ sk19 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44229:[bind(A,$thf( A )),bind(B,$thf( sk14 @ sk19 ))]]) ).

thf(4630,plain,
    sk313 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(1229,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)],[1227]) ).

thf(1230,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)],[1229]) ).

thf(41248,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,41075]) ).

thf(41249,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41248]) ).

thf(41307,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk216 ),
    inference(simp,[status(thm)],[41249]) ).

thf(562,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( A @ v1_finset_1 )
       => ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).

thf(4409,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)],[562]) ).

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/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).

thf(2165,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(124,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i,C: $i] :
          ( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
          = ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).

thf(1813,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(35,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A
         != ( B @ k1_tarski ) )
        & ( A != k1_xboole_0 )
        & ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
          = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).

thf(1186,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(919,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k8_filter_0 ) @ l3_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
        & ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_0) ).

thf(6093,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)],[919]) ).

thf(119,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).

thf(1785,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(927,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k5_lattices )
        = ( A @ k1_lattice2 @ k6_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_lattice2) ).

thf(6125,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)],[927]) ).

thf(789,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k5_lattices @ ( A @ k4_lattices ) ) )
            = ( A @ k5_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattices) ).

thf(5543,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)],[789]) ).

thf(435,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
                & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
                & ( D @ v1_funct_1 ) )
             => ! [E: $i] :
                  ( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
                    & ( B @ ( A @ ( E @ v1_funct_2 ) ) )
                    & ( E @ v1_funct_1 ) )
                 => ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
                      = ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
                  <=> ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( C @ ( F @ r2_hidden ) )
                         => ( ( F @ ( E @ k1_funct_1 ) )
                            = ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice2) ).

thf(3715,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)],[435]) ).

thf(113,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A @ ( B @ v2_binop_1 ) )
      <=> ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
                      = ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_binop_1) ).

thf(1711,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(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/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).

thf(3019,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(3080,plain,
    ~ ( sk197 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[3072]) ).

thf(2747,plain,
    sk157 @ v12_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(590,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
      <=> ( C @ ( B @ ( A @ r1_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).

thf(4522,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)],[590]) ).

thf(547,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D @ ( C @ r2_hidden ) )
                       => ( E @ ( D @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice2) ).

thf(4314,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)],[547]) ).

thf(763,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v3_filter_0 )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r8_relat_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_filter_0) ).

thf(5431,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)],[763]) ).

thf(29859,plain,
    ! [A: $i] :
      ( ( A != sk157 )
      | ( k1_xboole_0 @ v14_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2744]) ).

thf(29860,plain,
    ( ( k1_xboole_0 @ v14_lattices )
    | ( sk157 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29859:[bind(A,$thf( sk157 ))]]) ).

thf(19401,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)],[19399,1083]) ).

thf(19402,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)],[19401]) ).

thf(19403,plain,
    ! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[19402:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk138 @ k9_relat_1 ) )),bind(C,$thf( sk138 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(19475,plain,
    ! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[19403]) ).

thf(534,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
             => ( ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ( ( B @ ( E @ r2_hidden ) )
                    <=> ( ( D @ ( E @ r2_hidden ) )
                        | ( C @ ( E @ r2_hidden ) ) ) ) )
               => ( B
                  = ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).

thf(4240,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)],[534]) ).

thf(6233,plain,
    ( ( f2_s4_subset_1 = f3_s4_subset_1 )
    | ( sk447 @ p1_s4_subset_1 )
    | ( f3_s4_subset_1 @ ( sk447 @ r2_hidden ) )
    | sk445 ),
    inference(cnfConj,[status(thm)],[6226]) ).

thf(6244,plain,
    ( ( sk447 @ p1_s4_subset_1 )
    | ( f3_s4_subset_1 @ ( sk447 @ r2_hidden ) )
    | sk445
    | ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
    inference(lifteq,[status(thm)],[6233]) ).

thf(761,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_0) ).

thf(5420,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)],[761]) ).

thf(473,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
              & ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
               => ~ ( ! [D: $i] :
                        ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                       => ~ ( ( ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
                              = ( D @ ( A @ k2_lattice4 ) ) )
                            & ( B @ ( A @ k4_lattice4 ) @ ( D @ r1_tarski ) ) ) )
                    & ( B @ ( A @ k4_lattice4 ) @ ( C @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice4) ).

thf(3940,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)],[473]) ).

thf(29905,plain,
    ! [A: $i] :
      ( ( A != k6_nat_lat )
      | ( k1_xboole_0 @ v6_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,3185]) ).

thf(29906,plain,
    ( ( k1_xboole_0 @ v6_lattices )
    | ( k6_nat_lat @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29905:[bind(A,$thf( k6_nat_lat ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).

thf(2224,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(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/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).

thf(2454,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(3063,plain,
    sk196 @ v4_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(1018,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_0) ).

thf(6545,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)],[1018]) ).

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/sandbox2/benchmark/theBenchmark.p',cc6_lattice2) ).

thf(3344,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(837,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( A @ ( B @ m2_lattice4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_lattice4) ).

thf(5753,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)],[837]) ).

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/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).

thf(3202,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(529,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).

thf(4222,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(881,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k11_filter_2 ) @ m2_lattice4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_filter_2) ).

thf(5948,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)],[881]) ).

thf(12322,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,8529]) ).

thf(12323,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12322]) ).

thf(12419,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk207 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12323]) ).

thf(456,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) )
           => ( A @ ( B @ m2_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_2) ).

thf(3823,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)],[456]) ).

thf(129,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
        = ( B @ ( A @ k2_tarski ) ) )
    <=> ( ~ ( C @ ( B @ r2_hidden ) )
        & ~ ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).

thf(1830,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(16152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s11_funct_2 @ ( sk404 @ 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)],[14730,1083]) ).

thf(16153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s11_funct_2 @ ( sk404 @ 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)],[16152]) ).

thf(16154,plain,
    ! [A: $i] :
      ( ( f1_s11_funct_2 @ ( A @ ( sk404 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[16153:[bind(A,$thf( sk404 @ k1_relat_1 )),bind(B,$thf( f1_s11_funct_2 )),bind(C,$thf( C ))]]) ).

thf(16234,plain,
    ! [A: $i] :
      ( ( f1_s11_funct_2 @ ( A @ ( sk404 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[16154]) ).

thf(935,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( C = E )
                          & ( B = D ) )
                       => ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                            = ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
                          & ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                            = ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattice2) ).

thf(6174,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)],[935]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ k2_funct_1 @ v1_funct_1 )
        & ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).

thf(1538,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(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/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).

thf(3095,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(6712,plain,
    ( ( ( sk359 @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,5125]) ).

thf(6713,plain,
    ( ( sk359 @ v1_xboole_0 )
   != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6712]) ).

thf(6715,plain,
    sk359 != sk71,
    inference(simp,[status(thm)],[6713]) ).

thf(709,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                            = ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
                          & ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                            = ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice4) ).

thf(5186,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)],[709]) ).

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/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).

thf(2468,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(12306,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,8809]) ).

thf(12307,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12306]) ).

thf(12424,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk216 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12307]) ).

thf(2948,plain,
    ~ ( sk187 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2942]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).

thf(1257,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(664,axiom,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).

thf(4959,plain,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(1023,plain,
    ~ ( sk2 @ ( sk1 @ k5_lattices @ ( sk1 @ k22_filter_2 ) ) @ ( sk2 @ ( sk1 @ k18_filter_2 ) @ ( sk1 @ u1_struct_0 @ r1_filter_2 ) ) ),
    inference(cnfConj,[status(thm)],[1022]) ).

thf(38610,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)],[1123,38609]) ).

thf(38611,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ sk13 ) )
      = A ),
    inference(pattern_uni,[status(thm)],[38610:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(721,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ ( B @ ( A @ k12_filter_2 ) @ m2_lattice4 ) )
        & ~ ( B @ ( A @ k12_filter_2 ) @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_filter_2) ).

thf(5240,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)],[721]) ).

thf(809,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k5_lattices )
        = ( A @ u2_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_lattice2) ).

thf(5633,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)],[809]) ).

thf(41187,plain,
    ( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,41008]) ).

thf(41188,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk292 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41187]) ).

thf(41230,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk292 ),
    inference(simp,[status(thm)],[41188]) ).

thf(15302,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)],[2270,7127]) ).

thf(15303,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)],[15302]) ).

thf(15350,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)],[15303]) ).

thf(15397,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15350]) ).

thf(800,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m2_filter_2 ) )
        & ( A @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k21_filter_2 ) ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k21_filter_2) ).

thf(5596,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)],[800]) ).

thf(5895,plain,
    ~ ( sk420 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[5893]) ).

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/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).

thf(3398,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(429,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
     => ( ( B @ ( A @ k2_tarski ) )
        = ( C @ k1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).

thf(3684,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)],[429]) ).

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/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).

thf(2411,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(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/sandbox2/benchmark/theBenchmark.p',d15_binop_1) ).

thf(3488,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(3407,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)],[3406]) ).

thf(3408,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)],[3407]) ).

thf(3410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
      | ( A
       != ( C @ k1_tarski ) ) ),
    inference(cnfConj,[status(thm)],[3408]) ).

thf(3414,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
      | ( A
       != ( C @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[3410]) ).

thf(3415,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ k1_tarski @ r1_tarski ) ),
    inference(simp,[status(thm)],[3414]) ).

thf(910,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
           => ( A @ v14_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_filter_0) ).

thf(6073,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)],[910]) ).

thf(228,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).

thf(2426,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
     => ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).

thf(1981,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(56,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( B @ ( D @ r2_hidden ) )
            & ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
            & ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).

thf(1284,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(41566,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)],[2660,41162]) ).

thf(41567,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41566]) ).

thf(41627,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
     != sk152 )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41567]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
       => ( ( A @ k2_funct_1 @ k2_funct_1 )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).

thf(1353,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(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/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).

thf(2279,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(770,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
      <=> ? [B: $i] :
            ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                    = B )
                  & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                    = B ) ) )
            & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).

thf(5453,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)],[770]) ).

thf(44198,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)],[3209,1232]) ).

thf(44199,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)],[44198]) ).

thf(44200,plain,
    ! [A: $i] : ( A @ ( sk207 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44199:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ! [B: $i,C: $i] :
            ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
            = ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
       => ( A @ v2_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).

thf(1585,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(4634,plain,
    sk313 @ v9_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(916,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
        = ( B @ ( C @ ( A @ k2_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).

thf(6086,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)],[916]) ).

thf(1090,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)],[1085]) ).

thf(1094,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)],[1090]) ).

thf(820,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k4_filter_0 ) ) )
            = ( A @ k6_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_0) ).

thf(5685,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)],[820]) ).

thf(4093,plain,
    sk276 @ l1_struct_0,
    inference(cnfConj,[status(thm)],[4092]) ).

thf(2949,plain,
    sk187 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(773,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
               => ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattices) ).

thf(5472,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)],[773]) ).

thf(998,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ k1_filter_0 )
          = ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_0) ).

thf(6467,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)],[998]) ).

thf(1009,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
                  = C ) )
           => ( B
              = ( A @ k5_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattice2) ).

thf(6511,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)],[1009]) ).

thf(54,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ( ( C @ ( B @ r2_hidden ) )
        & ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).

thf(1272,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(4639,plain,
    sk313 @ v17_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(393,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
     => ( B @ v1_finset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_finsub_1) ).

thf(3478,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(44273,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)],[3316,1232]) ).

thf(44274,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)],[44273]) ).

thf(44275,plain,
    ! [A: $i] : ( A @ ( sk216 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44274:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',t56_subset_1) ).

thf(2696,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(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/sandbox2/benchmark/theBenchmark.p',t27_binop_1) ).

thf(2870,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(662,axiom,
    ( ! [A: $i] :
        ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
       => ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
           => ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
              = ( B @ f3_s13_funct_2 ) ) )
        & ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s13_funct_2) ).

thf(4940,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)],[662]) ).

thf(4941,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk346 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
          = ( A @ f3_s13_funct_2 ) )
        | ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
        | ~ sk344 )
      & ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk346 @ m2_relset_1 ) ) )
        | ~ sk344 )
      & ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk346 @ v1_funct_2 ) ) )
        | ~ sk344 )
      & ( ( sk346 @ v1_funct_1 )
        | ~ sk344 )
      & ( sk344
        | ~ ( f2_s13_funct_2 @ ( sk345 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
      & ( sk344
        | ( f1_s13_funct_2 @ ( sk345 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4940]) ).

thf(4944,plain,
    ( sk344
    | ( f1_s13_funct_2 @ ( sk345 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4941]) ).

thf(2215,plain,
    sk94 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

thf(10157,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,4606]) ).

thf(10158,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[10157]) ).

thf(10169,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk152 ),
    inference(simp,[status(thm)],[10158]) ).

thf(26495,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)],[2047,10169]) ).

thf(26496,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk152 ),
    inference(pattern_uni,[status(thm)],[26495:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(26516,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk152 ),
    inference(simp,[status(thm)],[26496]) ).

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/sandbox2/benchmark/theBenchmark.p',t168_partfun1) ).

thf(3039,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(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/sandbox2/benchmark/theBenchmark.p',t32_lattice2) ).

thf(1998,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(851,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) )
              <=> ( C @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_2) ).

thf(5832,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)],[851]) ).

thf(878,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k18_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k18_filter_2) ).

thf(5939,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)],[878]) ).

thf(474,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
       => ( B @ ( C @ ( A @ r1_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).

thf(3946,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)],[474]) ).

thf(19069,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)],[1955,5321]) ).

thf(19070,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[19069:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(19104,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ),
    inference(rewrite,[status(thm)],[19070,2541]) ).

thf(539,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k4_filter_2 ) ) )
        = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_filter_2) ).

thf(4278,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)],[539]) ).

thf(863,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m2_filter_2 ) )
                 => ( ( D @ ( B @ r2_hidden ) )
                   => ( ( D @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
                      & ( D @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_2) ).

thf(5873,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)],[863]) ).

thf(14514,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( A @ ( sk311 @ 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)],[14199,1083]) ).

thf(14515,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( A @ ( sk311 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14514]) ).

thf(14516,plain,
    ! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk311 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14515:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk311 @ k1_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f1_s4_funct_2 )),bind(D,$thf( D ))]]) ).

thf(14586,plain,
    ! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk311 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14516]) ).

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/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).

thf(3457,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(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/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).

thf(2352,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(2479,plain,
    k13_nat_lat @ v8_lattices,
    inference(cnfConj,[status(thm)],[2471]) ).

thf(992,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_filter_2 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_2) ).

thf(6425,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)],[992]) ).

thf(411,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).

thf(3565,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(380,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A
        = ( A @ a_1_0_domain_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).

thf(3401,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A
        = ( A @ a_1_0_domain_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(873,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
               => ! [D: $i] :
                    ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( ( C = E )
                            & ( B = D ) )
                         => ( D @ ( E @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattice2) ).

thf(5917,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)],[873]) ).

thf(416,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).

thf(3589,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(80,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ! [B: $i] :
        ? [C: $i] :
          ( ( ( C @ k2_relat_1 )
            = ( B @ k1_tarski ) )
          & ( ( C @ k1_relat_1 )
            = A )
          & ( C @ v1_funct_1 )
          & ( C @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).

thf(1459,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(31168,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk349 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,17029]) ).

thf(31169,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk349 ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[31168]) ).

thf(31170,plain,
    ! [A: $i] : ( A @ sk349 @ sk19 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[31169:[bind(A,$thf( C @ sk349 )),bind(B,$thf( C ))]]) ).

thf(32988,plain,
    ! [A: $i] : ( A @ sk349 @ sk19 @ v1_relat_1 ),
    inference(simp,[status(thm)],[31170]) ).

thf(3067,plain,
    sk196 @ v3_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(898,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m3_lattice4 ) )
         => ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_lattice4) ).

thf(6013,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)],[898]) ).

thf(2960,plain,
    sk188 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

thf(405,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( ( A @ ( B @ v1_filter_2 ) )
              & ( B
               != ( A @ k17_filter_2 ) ) )
          <=> ( B @ ( A @ r2_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_2) ).

thf(3533,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)],[405]) ).

thf(887,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v12_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( B @ ( A @ r1_lattices ) ) )
                     => ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
                        = ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_lattices) ).

thf(5966,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)],[887]) ).

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/sandbox2/benchmark/theBenchmark.p',t14_lattice2) ).

thf(3447,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(15293,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)],[2270,8782]) ).

thf(15294,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)],[15293]) ).

thf(15361,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)],[15294]) ).

thf(15366,plain,
    ( ( sk216 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15361]) ).

thf(985,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_lattice2 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( C @ ( A @ k6_filter_2 ) @ ( A @ k5_filter_2 ) )
                  = C )
                & ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k6_filter_2 ) )
                  = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_2) ).

thf(6390,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)],[985]) ).

thf(2209,plain,
    sk94 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2207]) ).

thf(1125,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
       != k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1124]) ).

thf(1126,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
       != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1125]) ).

thf(436,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).

thf(3725,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)],[436]) ).

thf(2743,plain,
    sk157 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(1187,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)],[1186]) ).

thf(1188,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)],[1187]) ).

thf(1189,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)],[1188]) ).

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/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).

thf(2919,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(1017,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).

thf(6543,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)],[1017]) ).

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/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).

thf(2071,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(105,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ~ ( ( A
           != ( C @ ( B @ k2_tarski ) ) )
          & ( A
           != ( C @ k1_tarski ) )
          & ( A
           != ( B @ k1_tarski ) )
          & ( A != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).

thf(1646,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(29899,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,1024]) ).

thf(29900,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ( sk1 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29899:[bind(A,$thf( sk1 ))]]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
                = ( B @ ( C @ ( A @ k5_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_0) ).

thf(5800,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)],[844]) ).

thf(595,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
        = ( B @ ( C @ ( A @ k3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).

thf(4542,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)],[595]) ).

thf(100,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
        | ( A @ ( C @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).

thf(1629,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(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/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).

thf(3235,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(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/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).

thf(2152,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(625,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ k1_lattice2 )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice2) ).

thf(4710,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)],[625]) ).

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/sandbox2/benchmark/theBenchmark.p',t31_lattice2) ).

thf(2988,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(1377,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk25 ) @ v1_funct_1 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1372]) ).

thf(1384,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk25 ) @ v1_funct_1 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1377]) ).

thf(1385,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_funct_1 ),
    inference(simp,[status(thm)],[1384]) ).

thf(912,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( C @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
               => ( B @ ( A @ k18_filter_2 ) @ ( C @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_2) ).

thf(6077,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)],[912]) ).

thf(8757,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,4006]) ).

thf(8758,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8757]) ).

thf(8769,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk216 ),
    inference(simp,[status(thm)],[8758]) ).

thf(11638,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk216 ) ),
    inference(paramod_ordered,[status(thm)],[1955,8769]) ).

thf(11639,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk216 ),
    inference(pattern_uni,[status(thm)],[11638:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(970,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ m1_filter_0 ) )
                     => ( ( ( E @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
                          & ( E @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) )
                       => ( E @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_0) ).

thf(6341,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)],[970]) ).

thf(26473,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)],[2047,10171]) ).

thf(26474,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk216 ),
    inference(pattern_uni,[status(thm)],[26473:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(26526,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk216 ),
    inference(simp,[status(thm)],[26474]) ).

thf(30829,plain,
    ! [A: $i] :
      ( ( A
       != ( sk1 @ u1_struct_0 ) )
      | ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,1027]) ).

thf(30830,plain,
    ( ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
    | ( sk1 @ u1_struct_0 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30829:[bind(A,$thf( sk1 @ u1_struct_0 ))]]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ( A @ l1_struct_0 )
     => ( ( A @ v3_struct_0 )
      <=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).

thf(3789,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)],[446]) ).

thf(617,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( B @ ( A @ ( C @ v1_lattice4 ) ) )
              <=> ( C @ v2_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice4) ).

thf(4666,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)],[617]) ).

thf(31173,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,1026]) ).

thf(31174,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ( sk1 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[31173:[bind(A,$thf( sk1 ))]]) ).

thf(8759,plain,
    ( ( ( sk218 @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3317,3328]) ).

thf(8760,plain,
    ( ( sk218 @ v1_xboole_0 )
   != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8759]) ).

thf(8766,plain,
    sk218 != sk216,
    inference(simp,[status(thm)],[8760]) ).

thf(752,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
       => ( A @ ( A @ k5_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_2) ).

thf(5382,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)],[752]) ).

thf(903,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( A @ ( B @ v1_filter_2 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
                    <=> ( ( B @ ( D @ r2_hidden ) )
                        | ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_filter_2) ).

thf(6030,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)],[903]) ).

thf(895,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( D @ ( B @ r2_hidden ) )
                   => ( ( D @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                      & ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_filter_0) ).

thf(6003,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)],[895]) ).

thf(849,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
      <=> ( ( A @ k1_lattice2 @ l3_lattices )
          & ( A @ k1_lattice2 @ v11_lattices )
          & ( A @ k1_lattice2 @ v10_lattices )
          & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_lattice2) ).

thf(5813,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)],[849]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice2) ).

thf(3748,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)],[440]) ).

thf(717,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_lattice2) ).

thf(5228,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)],[717]) ).

thf(645,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
        & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice2) ).

thf(4834,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)],[645]) ).

thf(582,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v14_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ( ( A @ k6_lattices )
              = ( B @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_filter_2) ).

thf(4495,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)],[582]) ).

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/sandbox2/benchmark/theBenchmark.p',t39_subset_1) ).

thf(2526,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(2416,plain,
    sk118 @ v1_lattice2,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(802,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_filter_2) ).

thf(5600,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)],[802]) ).

thf(537,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) )
                       => ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_lattice2) ).

thf(4261,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)],[537]) ).

thf(975,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k7_filter_2 ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).

thf(6354,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)],[975]) ).

thf(41176,plain,
    ( ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,41008]) ).

thf(41177,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41176]) ).

thf(41236,plain,
    ( ( sk14 @ sk384 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk152 ),
    inference(simp,[status(thm)],[41177]) ).

thf(3085,plain,
    sk197 @ v1_lattice2,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(483,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
                       => ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice2) ).

thf(3978,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)],[483]) ).

thf(524,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_0) ).

thf(4197,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)],[524]) ).

thf(3262,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3259]) ).

thf(3266,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3262]) ).

thf(3267,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[3266]) ).

thf(12308,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,9057]) ).

thf(12309,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk311 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12308]) ).

thf(12408,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk311 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12309]) ).

thf(12463,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk311 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12408]) ).

thf(447,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k7_filter_0 ) ) )
        = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).

thf(3793,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)],[447]) ).

thf(1015,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
              <=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
                  & ( B @ ( A @ ( C @ v1_lattice4 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice4) ).

thf(6536,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)],[1015]) ).

thf(932,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                    & ~ ( D @ v1_xboole_0 ) )
                 => ( ( B @ ( A @ k19_filter_2 ) @ ( B @ ( A @ k19_filter_2 ) @ ( A @ k19_filter_2 ) @ r1_tarski ) )
                    & ( ( D @ ( C @ r1_tarski ) )
                     => ( D @ ( A @ k19_filter_2 ) @ ( C @ ( A @ k19_filter_2 ) @ r1_tarski ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_2) ).

thf(6166,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)],[932]) ).

thf(442,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i,E: $i] :
            ( ( E @ ( D @ p1_s2_domain_1 ) )
            & ( A
              = ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
            & ( C @ ( E @ m1_subset_1 ) )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).

thf(3761,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)],[442]) ).

thf(1039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk3 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
      | ( ( C @ k1_relat_1 )
       != A )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1038]) ).

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)],[1039]) ).

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(15312,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)],[2270,8520]) ).

thf(15313,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)],[15312]) ).

thf(15356,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)],[15313]) ).

thf(15404,plain,
    ( ( sk207 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15356]) ).

thf(2944,plain,
    sk187 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(3181,plain,
    k6_nat_lat @ v5_lattices,
    inference(cnfConj,[status(thm)],[3176]) ).

thf(2475,plain,
    k13_nat_lat @ v4_lattices,
    inference(cnfConj,[status(thm)],[2471]) ).

thf(651,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ( A @ ( B @ m2_lattice4 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                     => ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                        & ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattice4) ).

thf(4855,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)],[651]) ).

thf(606,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).

thf(4602,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)],[606]) ).

thf(784,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_0) ).

thf(5532,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)],[784]) ).

thf(29931,plain,
    ! [A: $i] :
      ( ( A != sk187 )
      | ( k1_xboole_0 @ v9_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2947]) ).

thf(29932,plain,
    ( ( k1_xboole_0 @ v9_lattices )
    | ( sk187 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29931:[bind(A,$thf( sk187 ))]]) ).

thf(957,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ ( A @ k5_filter_2 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).

thf(6290,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)],[957]) ).

thf(528,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v11_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ! [G: $i] :
                                ( ( A @ ( G @ m1_subset_1 ) )
                               => ( ( B @ ( G @ r2_hidden ) )
                                 => ( ( G @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) )
                                    = ( G @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) ) ) ) )
                           => ( ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) )
                              = ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_lattice2) ).

thf(4214,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)],[528]) ).

thf(4591,plain,
    f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ v1_funct_2 ) ),
    inference(cnfConj,[status(thm)],[4589]) ).

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 ) )
         => ~ ( ! [C: $i] :
                  ( ( A @ ( C @ m1_filter_0 ) )
                 => ~ ( ( A @ ( C @ v1_filter_0 ) )
                      & ( C @ ( B @ r2_hidden ) ) ) )
              & ( B
               != ( A @ k5_lattices ) )
              & ( A @ l3_lattices )
              & ( A @ v13_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_0) ).

thf(5781,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)],[842]) ).

thf(6728,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)],[1974,1052]) ).

thf(6729,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)],[6728]) ).

thf(6730,plain,
    ! [A: $i] : ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6729:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).

thf(21387,plain,
    ! [A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6730,15605]) ).

thf(21389,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)],[21387,1083]) ).

thf(21390,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)],[21389]) ).

thf(21391,plain,
    ! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[21390:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk71 @ k9_relat_1 ) )),bind(C,$thf( sk71 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(21472,plain,
    ! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[21391]) ).

thf(1011,axiom,
    ? [A: $i] : ( A @ l3_lattices ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).

thf(6520,plain,
    ? [A: $i] : ( A @ l3_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(6521,plain,
    sk469 @ l3_lattices,
    inference(cnf,[status(esa)],[6520]) ).

thf(1076,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)],[1075]) ).

thf(1077,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)],[1076]) ).

thf(909,axiom,
    ! [A: $i] :
      ( ( a_0_2_domain_1 @ ( A @ r2_hidden ) )
    <=> ? [B: $i,C: $i] :
          ( ( C @ ( B @ p1_s9_domain_1 ) )
          & ( A
            = ( C @ ( B @ f4_s9_domain_1 ) ) )
          & ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
          & ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).

thf(6062,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)],[909]) ).

thf(713,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).

thf(5211,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)],[713]) ).

thf(500,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ( B @ ( C @ r2_hidden ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).

thf(4074,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)],[500]) ).

thf(983,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
                      & ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                   => ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_filter_0) ).

thf(6386,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)],[983]) ).

thf(5584,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ v1_funct_2 ) ) )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5580]) ).

thf(5590,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk404 @ v1_funct_2 ) ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5584]) ).

thf(781,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) )
           => ( A @ ( B @ m2_lattice4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_2) ).

thf(5517,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)],[781]) ).

thf(209,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ( ( B @ ( A @ r1_tarski ) )
       => ( A @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).

thf(2294,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(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/sandbox2/benchmark/theBenchmark.p',t6_relset_1) ).

thf(2036,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(7571,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,5198]) ).

thf(7572,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7571]) ).

thf(7574,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk71 ),
    inference(simp,[status(thm)],[7572]) ).

thf(2739,plain,
    sk157 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(826,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ k5_lattices @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_lattice2) ).

thf(5704,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)],[826]) ).

thf(730,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).

thf(5287,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)],[730]) ).

thf(3412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
      | ( A
       != ( B @ k1_tarski ) ) ),
    inference(cnfConj,[status(thm)],[3408]) ).

thf(3419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
      | ( A
       != ( B @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[3412]) ).

thf(3420,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(simp,[status(thm)],[3419]) ).

thf(2421,plain,
    sk118 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(855,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_lattice4 ) )
         => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).

thf(5852,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)],[855]) ).

thf(44201,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)],[2661,1232]) ).

thf(44202,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)],[44201]) ).

thf(44203,plain,
    ! [A: $i] : ( A @ ( sk152 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44202:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).

thf(13041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3788,4606]) ).

thf(13042,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[13041]) ).

thf(13053,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( C @ ( B @ k2_tarski ) ) ),
    inference(simp,[status(thm)],[13042]) ).

thf(27744,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 @ sk249 ) ) ),
    inference(paramod_ordered,[status(thm)],[2047,13053]) ).

thf(27745,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ k1_zfmisc_1 )
     != ( A @ sk249 ) ),
    inference(pattern_uni,[status(thm)],[27744:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 )),bind(D,$thf( E @ k1_tarski ))]]) ).

thf(27764,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ k1_zfmisc_1 )
     != ( A @ sk249 ) ),
    inference(simp,[status(thm)],[27745]) ).

thf(966,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_lattice4) ).

thf(6326,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)],[966]) ).

thf(896,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
              <=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_0) ).

thf(6007,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)],[896]) ).

thf(786,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k8_filter_2 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_2) ).

thf(5537,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)],[786]) ).

thf(627,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D @ ( C @ r2_hidden ) )
                       => ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_lattice2) ).

thf(4719,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)],[627]) ).

thf(403,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( A @ ( B @ m2_nat_lat ) )
          <=> ( ( ( B @ u1_lattices )
                = ( B @ u1_struct_0 @ ( A @ u1_lattices @ k1_realset1 ) ) )
              & ( ( B @ u2_lattices )
                = ( B @ u1_struct_0 @ ( A @ u2_lattices @ k1_realset1 ) ) )
              & ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_nat_lat) ).

thf(3521,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( ( ( B @ u1_lattices )
                  = ( B @ u1_struct_0 @ ( A @ u1_lattices @ k1_realset1 ) ) )
                & ( ( B @ u2_lattices )
                  = ( B @ u1_struct_0 @ ( A @ u2_lattices @ k1_realset1 ) ) )
                & ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) )
             => ( A @ ( B @ m2_nat_lat ) ) )
            & ( ( A @ ( B @ m2_nat_lat ) )
             => ( ( ( B @ u1_lattices )
                  = ( B @ u1_struct_0 @ ( A @ u1_lattices @ k1_realset1 ) ) )
                & ( ( B @ u2_lattices )
                  = ( B @ u1_struct_0 @ ( A @ u2_lattices @ k1_realset1 ) ) )
                & ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(775,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_0) ).

thf(5477,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)],[775]) ).

thf(104,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
     => ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
          & ( C @ v1_funct_1 ) )
       => ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).

thf(1642,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(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/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).

thf(2102,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(5677,plain,
    k6_nat_lat @ v13_lattices,
    inference(cnfConj,[status(thm)],[5674]) ).

thf(700,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
                       => ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice2) ).

thf(5129,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)],[700]) ).

thf(579,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( B @ ( A @ k6_domain_1 ) )
        = ( B @ k1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).

thf(4472,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)],[579]) ).

thf(618,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ! [B: $i] :
          ( ( B @ l3_lattices )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ( ( A @ k1_lattice2 )
              = ( B @ k1_lattice2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_filter_2) ).

thf(4670,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)],[618]) ).

thf(556,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_domain_1) ).

thf(4356,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)],[556]) ).

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/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(2983,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(459,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
                    = ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_lattice4) ).

thf(3865,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)],[459]) ).

thf(535,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_lattices @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_lattice2) ).

thf(4254,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)],[535]) ).

thf(12361,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,8553]) ).

thf(12362,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12361]) ).

thf(12380,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk207 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12362]) ).

thf(640,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattices) ).

thf(4811,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)],[640]) ).

thf(12343,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,8520]) ).

thf(12344,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12343]) ).

thf(12374,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk207 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12344]) ).

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/sandbox2/benchmark/theBenchmark.p',fc5_lattice2) ).

thf(2233,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(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/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).

thf(3373,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(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/sandbox2/benchmark/theBenchmark.p',t176_partfun1) ).

thf(3464,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(2951,plain,
    sk187 @ v13_lattices,
    inference(cnfConj,[status(thm)],[2942]) ).

thf(840,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_0) ).

thf(5764,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)],[840]) ).

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/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).

thf(2815,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(2736,plain,
    sk157 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

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/sandbox2/benchmark/theBenchmark.p',s2_domain_1) ).

thf(2008,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(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/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).

thf(3337,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(616,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
                = ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice4) ).

thf(4663,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)],[616]) ).

thf(929,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( B @ ( A @ k8_filter_2 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_filter_2) ).

thf(6150,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)],[929]) ).

thf(575,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).

thf(4455,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)],[575]) ).

thf(6366,plain,
    ~ ( sk456 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[6364]) ).

thf(3062,plain,
    sk196 @ v8_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

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 ) )
     => ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_0) ).

thf(5700,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)],[824]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( B
            = ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_domain_1) ).

thf(4146,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)],[512]) ).

thf(44222,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk218 @ sk19 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[31658,1232]) ).

thf(44223,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk218 @ sk19 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[44222]) ).

thf(44224,plain,
    ! [A: $i] : ( A @ ( sk218 @ sk19 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[44223:[bind(A,$thf( A )),bind(B,$thf( sk218 @ sk19 ))]]) ).

thf(125,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_relat_1 )
        & ( A @ v1_relat_1 ) )
     => ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).

thf(1816,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(669,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ l2_lattices )
        & ( A @ l1_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).

thf(4981,plain,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ l2_lattices )
        & ( A @ l1_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ? [F: $i] :
                            ( ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) )
                            & ( D @ ( F @ r2_hidden ) )
                            & ( C @ ( F @ m1_subset_1 ) ) )
                       => ( B @ ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_lattice2) ).

thf(3875,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)],[462]) ).

thf(6710,plain,
    ( ( ( sk359 @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,5125]) ).

thf(6711,plain,
    ( ( sk359 @ v1_xboole_0 )
   != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6710]) ).

thf(6714,plain,
    sk359 != sk152,
    inference(simp,[status(thm)],[6711]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ k6_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_0) ).

thf(4442,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)],[572]) ).

thf(421,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_tarski ) )
      = ( A @ ( B @ k2_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(3633,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_tarski ) )
      = ( A @ ( B @ k2_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(399,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_subset_1 ) )
             => ( ( ( B @ ( D @ ( A @ r3_binop_1 ) ) )
                  & ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_binop_1) ).

thf(3506,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)],[399]) ).

thf(765,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_2) ).

thf(5440,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)],[765]) ).

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/sandbox2/benchmark/theBenchmark.p',t29_lattice2) ).

thf(1989,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(496,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
         => ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
            & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_lattice4) ).

thf(4051,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)],[496]) ).

thf(540,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( B @ r1_tarski ) )
       => ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( C @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
          | ( ( A != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).

thf(4281,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)],[540]) ).

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/sandbox2/benchmark/theBenchmark.p',t60_domain_1) ).

thf(3277,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(39264,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)],[2047,3420]) ).

thf(39265,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[39264:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(39333,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
    inference(simp,[status(thm)],[39265]) ).

thf(39340,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)],[39333,1083]) ).

thf(39341,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)],[39340]) ).

thf(39342,plain,
    ! [B: $i,A: $i] : ( B @ k1_tarski @ k1_zfmisc_1 @ ( A @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[39341:[bind(A,$thf( G )),bind(B,$thf( k1_xboole_0 @ k1_tarski )),bind(C,$thf( G @ k1_tarski @ k1_zfmisc_1 )),bind(D,$thf( D ))]]) ).

thf(39446,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)],[39342]) ).

thf(18758,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( k1_xboole_0 @ k1_tarski @ ( A @ sk249 @ m1_subset_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[1955,3787]) ).

thf(18759,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ sk249 @ m1_subset_1 ),
    inference(pattern_uni,[status(thm)],[18758:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(4631,plain,
    sk313 @ v4_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(3177,plain,
    ~ ( k6_nat_lat @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[3176]) ).

thf(489,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ k1_lattice2 @ l3_lattices )
        & ( A @ k1_lattice2 @ v3_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).

thf(4007,plain,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ k1_lattice2 @ l3_lattices )
        & ( A @ k1_lattice2 @ v3_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(2746,plain,
    sk157 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2734]) ).

thf(515,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != C )
        & ( A != B )
        & ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).

thf(4157,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)],[515]) ).

thf(41252,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,41075]) ).

thf(41253,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[41252]) ).

thf(41312,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk152 ),
    inference(simp,[status(thm)],[41253]) ).

thf(2417,plain,
    sk118 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2415]) ).

thf(2366,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_funct_1 ),
    inference(cnfConj,[status(thm)],[2363]) ).

thf(738,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).

thf(5339,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)],[738]) ).

thf(2961,plain,
    sk188 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

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/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).

thf(2913,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(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/sandbox2/benchmark/theBenchmark.p',cc3_lattice2) ).

thf(2091,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(982,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_2 ) )
        <=> ( A @ ( B @ m1_filter_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).

thf(6380,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)],[982]) ).

thf(862,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                  = ( A @ k5_lattices ) )
              <=> ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattices) ).

thf(5867,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)],[862]) ).

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/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).

thf(3426,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(675,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
    <=> ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
         => ( B @ ( C @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

thf(5036,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)],[675]) ).

thf(659,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ k1_zfmisc_1 ) )
    <=> ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
        <=> ( A @ ( C @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

thf(4912,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)],[659]) ).

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/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).

thf(2668,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(1163,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)],[1162]) ).

thf(1165,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)],[1163]) ).

thf(954,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k8_filter_2 ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_2) ).

thf(6273,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)],[954]) ).

thf(736,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
      <=> ? [F: $i,G: $i] :
            ( ( E @ ( G @ r2_hidden ) )
            & ( D @ ( F @ r2_hidden ) )
            & ( A
              = ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
            & ( C @ ( G @ m1_subset_1 ) )
            & ( B @ ( F @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).

thf(5322,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)],[736]) ).

thf(63,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
        = ( D @ ( C @ k9_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).

thf(1346,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(961,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k6_lattices @ ( A @ k4_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattices) ).

thf(6309,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)],[961]) ).

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/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).

thf(2159,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(845,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( A @ v14_lattices )
           => ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k6_lattices )
              = ( A @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_filter_0) ).

thf(5803,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)],[845]) ).

thf(942,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ ( B @ v2_filter_0 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                    <=> ( ( B @ ( D @ r2_hidden ) )
                        | ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_0) ).

thf(6209,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)],[942]) ).

thf(719,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k16_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_filter_2) ).

thf(5236,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)],[719]) ).

thf(1116,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)],[1113]) ).

thf(1120,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)],[1116]) ).

thf(1086,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)],[1085]) ).

thf(1093,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)],[1086]) ).

thf(142,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
       => ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
          & ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
          & ( B @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).

thf(1930,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(974,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_filter_0 ) )
            = ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_0) ).

thf(6351,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)],[974]) ).

thf(728,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                = ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).

thf(5275,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)],[728]) ).

thf(1236,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)],[1234]) ).

thf(41578,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)],[3123,41162]) ).

thf(41579,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)],[41578]) ).

thf(41624,plain,
    ( ( ( sk2 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
     != k1_xboole_0 )
    | ( ( sk1 @ u1_struct_0 )
     != sk14 ) ),
    inference(simp,[status(thm)],[41579]) ).

thf(12273,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4592,8806]) ).

thf(12274,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12273]) ).

thf(12406,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk216 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12274]) ).

thf(1128,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)],[1127]) ).

thf(1129,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)],[1128]) ).

thf(2966,plain,
    sk188 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2957]) ).

thf(9025,plain,
    ( ( ( sk359 @ v1_xboole_0 )
     != ( sk292 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4308,5125]) ).

thf(9026,plain,
    ( ( sk359 @ v1_xboole_0 )
   != ( sk292 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9025]) ).

thf(9038,plain,
    sk359 != sk292,
    inference(simp,[status(thm)],[9026]) ).

thf(432,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).

thf(3701,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(3057,plain,
    sk196 @ v13_lattices,
    inference(cnfConj,[status(thm)],[3056]) ).

thf(12314,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[4592,7130]) ).

thf(12315,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk311 @ 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)],[12314]) ).

thf(12384,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk311 != sk138 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12315]) ).

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/sandbox2/benchmark/theBenchmark.p',d3_relat_2) ).

thf(2803,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(254,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(2600,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

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/sandbox2/benchmark/theBenchmark.p',cc1_lattice2) ).

thf(2898,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(846,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ v12_lattices )
           => ( B @ ( A @ k8_filter_0 ) @ v12_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_filter_0) ).

thf(5806,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)],[846]) ).

thf(668,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ m2_lattice4 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( B @ l3_lattices )
        & ( B @ v17_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( C @ ( B @ a_2_1_lattice4 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( C @ ( B @ k4_lattice4 ) @ ( D @ r1_tarski ) )
            & ( A
              = ( D @ ( B @ k2_lattice4 ) ) )
            & ( B @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).

thf(4972,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)],[668]) ).

thf(995,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m2_nat_lat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_nat_lat) ).

thf(6435,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)],[995]) ).

thf(443,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
            & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ( ( B
              = ( A @ k5_lattice4 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                  = ( C @ ( A @ k7_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice4) ).

thf(3772,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)],[443]) ).

thf(681,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( A @ ( I @ m1_subset_1 ) )
        & ( A @ ( H @ m1_subset_1 ) )
        & ( A @ ( G @ m1_subset_1 ) )
        & ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_domain_1) ).

thf(5061,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)],[681]) ).

thf(653,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ! [E: $i] :
                ( ( A @ ( E @ r2_hidden ) )
               => ( ( E @ ( C @ k1_funct_1 ) )
                  = ( E @ ( D @ k1_funct_1 ) ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).

thf(4876,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)],[653]) ).

thf(1976,plain,
    sk71 @ v2_funct_1,
    inference(cnfConj,[status(thm)],[1973]) ).

thf(454,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( B @ ( C @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
                    = ( D @ ( C @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattice4) ).

thf(3817,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)],[454]) ).

thf(999,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
                  <=> ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_0) ).

thf(6471,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
                     => ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                    & ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
                     => ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(480,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ v14_lattices )
           => ( B @ ( A @ k8_filter_0 ) @ v14_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_0) ).

thf(3965,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)],[480]) ).

thf(914,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ r2_hidden ) )
               => ( C @ ( A @ k19_filter_2 ) @ ( B @ ( A @ k18_filter_2 ) @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_2) ).

thf(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 @ 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)],[914]) ).

thf(885,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
                  = C ) )
           => ( B
              = ( A @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattice2) ).

thf(5958,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)],[885]) ).

thf(973,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
            = ( A @ k5_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattices) ).

thf(6348,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
            = ( A @ k5_lattices ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(677,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) )
                = ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice4) ).

thf(5046,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)],[677]) ).

thf(626,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ! [E: $i] :
                ( ( A @ ( E @ m1_subset_1 ) )
               => ( ( E @ ( C @ k1_funct_1 ) )
                  = ( E @ ( D @ k1_funct_1 ) ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).

thf(4713,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)],[626]) ).

thf(743,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( A @ k19_filter_2 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) )
                & ( C @ ( B @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k19_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_2) ).

thf(5354,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)],[743]) ).

thf(924,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
              & ( A @ l3_lattices )
              & ( A @ v13_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( ( B @ ( A @ k3_filter_0 ) )
                = ( A @ u1_struct_0 ) )
              & ( ( B @ ( A @ k3_filter_0 ) )
                = ( A @ k1_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_0) ).

thf(6109,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)],[924]) ).

thf(3076,plain,
    sk197 @ v10_lattices,
    inference(cnfConj,[status(thm)],[3072]) ).

thf(499,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k6_lattices )
        = ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_lattice2) ).

thf(4071,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)],[499]) ).

thf(750,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v3_filter_0 )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ ( E @ m1_filter_0 ) )
                     => ! [F: $i] :
                          ( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
                            & ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_filter_0) ).

thf(5376,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)],[750]) ).

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/sandbox2/benchmark/theBenchmark.p',t175_partfun1) ).

thf(2699,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(452,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
     => ( ( D @ ( A @ r1_tarski ) )
       => ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).

thf(3812,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)],[452]) ).

thf(554,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
                    = ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattice4) ).

thf(4345,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)],[554]) ).

thf(584,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) )
        = ( D @ ( C @ k4_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).

thf(4501,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)],[584]) ).

thf(85,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
                    = D )
                  & ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
                    = D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_binop_1) ).

thf(1505,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(71,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i,C: $i] :
          ( ( ~ ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
           => ( ( C
                = ( B @ ( A @ k1_funct_1 ) ) )
            <=> ( C = k1_xboole_0 ) ) )
          & ( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
           => ( ( C
                = ( B @ ( A @ k1_funct_1 ) ) )
            <=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).

thf(1399,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(98,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r3_binop_1 ) ) )
          <=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
              & ( C @ ( B @ ( A @ r1_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_binop_1) ).

thf(1621,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(6655,plain,
    ( ( ( sk218 @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,3328]) ).

thf(6656,plain,
    ( ( sk218 @ v1_xboole_0 )
   != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6655]) ).

thf(6658,plain,
    sk218 != sk152,
    inference(simp,[status(thm)],[6656]) ).

thf(29998,plain,
    ! [A: $i] :
      ( ( A != sk157 )
      | ( k1_xboole_0 @ v4_lattices )
      | ( A @ sk19 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1299,2740]) ).

thf(29999,plain,
    ( ( k1_xboole_0 @ v4_lattices )
    | ( sk157 @ sk19 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29998:[bind(A,$thf( sk157 ))]]) ).

thf(185,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ k2_zfmisc_1 ) )
        = ( B @ ( B @ k2_zfmisc_1 ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).

thf(2138,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(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/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).

thf(3341,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(68,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
      | ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).

thf(1367,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(779,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v1_lattice2 )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ? [D: $i] :
                    ( ! [E: $i] :
                        ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                         => ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
                    & ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                    & ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_lattice2) ).

thf(5494,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)],[779]) ).

thf(655,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
              <=> ( ( C @ k2_relat_1 )
                  = ( B @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice4) ).

thf(4891,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)],[655]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
                       => ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_lattice2) ).

thf(4161,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)],[516]) ).

thf(597,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( ( C @ ( E @ r2_hidden ) )
            <=> ~ ( D @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).

thf(4547,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)],[597]) ).

thf(880,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( B @ ( A @ k18_filter_2 ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
                & ( B @ ( A @ k18_filter_2 ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) )
                & ( B @ ( A @ k18_filter_2 ) @ ( B @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_2) ).

thf(5943,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)],[880]) ).

thf(639,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ( ( C
                  = ( B @ ( A @ k8_filter_0 ) ) )
              <=> ? [D: $i] :
                    ( ? [E: $i] :
                        ( ( C
                          = ( E @ ( D @ ( B @ g3_lattices ) ) ) )
                        & ( E
                          = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
                        & ( D
                          = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                    & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_filter_0) ).

thf(4779,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)],[639]) ).

thf(27742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ k2_tarski ) )
       != ( D @ ( C @ k2_tarski ) ) )
      | ( ( A @ k1_tarski )
       != ( B @ sk249 ) ) ),
    inference(paramod_ordered,[status(thm)],[4528,13053]) ).

thf(27743,plain,
    ! [B: $i,A: $i] :
      ( ( A @ k1_tarski )
     != ( B @ sk249 ) ),
    inference(pattern_uni,[status(thm)],[27742:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(864,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_struct_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_struct_0) ).

thf(5877,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)],[864]) ).

thf(5586,plain,
    ( ( sk404 @ v1_funct_1 )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5580]) ).

thf(5591,plain,
    ( ( sk404 @ v1_funct_1 )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5586]) ).

thf(12967,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 @ v13_lattices ) ),
    inference(paramod_ordered,[status(thm)],[2074,11032]) ).

thf(12968,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12967]) ).

thf(13001,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[12968]) ).

thf(13016,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 @ v13_lattices ) ),
    inference(simp,[status(thm)],[13001]) ).

thf(686,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_lattice4 ) )
         => ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r1_tarski ) )
                 => ( B @ ( C @ ( A @ k2_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice4) ).

thf(5073,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)],[686]) ).

thf(4627,plain,
    sk313 @ v7_lattices,
    inference(cnfConj,[status(thm)],[4624]) ).

thf(663,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( D @ ( E @ r2_hidden ) )
            & ( C @ ( E @ r2_hidden ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).

thf(4949,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)],[663]) ).

thf(1184,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)],[1183]) ).

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/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).

thf(2998,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(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)],[1955,7564]) ).

thf(11631,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk152 ),
    inference(pattern_uni,[status(thm)],[11630:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(131,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k4_xboole_0 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ( ~ ( B @ ( D @ r2_hidden ) )
            & ( A @ ( D @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

thf(1848,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(8000,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2660,2439]) ).

thf(8001,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8000]) ).

thf(8006,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk152 ),
    inference(simp,[status(thm)],[8001]) ).

thf(795,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( B @ ( A @ r1_filter_1 ) )
          <=> ? [C: $i] :
                ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
                & ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattice4) ).

thf(5569,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)],[795]) ).

thf(497,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m2_filter_2 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_2) ).

thf(4056,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)],[497]) ).

thf(926,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                  = ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) )
                & ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                  = ( C @ ( B @ ( A @ k3_filter_0 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_0) ).

thf(6119,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)],[926]) ).

thf(1088,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)],[1085]) ).

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/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).

thf(2191,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(1204,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)],[1201]) ).

thf(951,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_lattice4) ).

thf(6265,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)],[951]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(2106,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

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/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).

thf(2087,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(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/sandbox2/benchmark/theBenchmark.p',t36_zfmisc_1) ).

thf(3047,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(796,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ v3_filter_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_0) ).

thf(5574,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)],[796]) ).

thf(138,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
         != ( B @ ( A @ k2_tarski ) ) )
        & ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
         != ( B @ k1_tarski ) )
        & ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
         != ( A @ k1_tarski ) )
        & ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
         != k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).

thf(1912,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(871,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
                = ( B @ ( C @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_0) ).

thf(5911,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)],[871]) ).

thf(59283,plain,
    $false,
    inference(e,[status(thm)],[2163,5422,5469,3883,32927,4169,5950,4290,3397,1840,6172,2544,6042,1818,1686,1036,2630,13052,4188,4094,1024,1469,5088,2744,41233,1190,4571,4450,5857,2109,5593,2131,8154,5896,3798,1105,4022,3666,4729,1237,5320,5654,6317,2480,1083,6263,6566,6527,1956,1950,5131,6374,1110,3172,6022,2210,7083,4339,2395,3509,3108,1142,4623,6017,38388,1041,1200,5444,2077,6057,3185,3317,11635,1290,1882,26525,30158,1068,4311,6106,5696,2953,2590,1422,34597,2947,4697,3959,3912,1073,2671,2676,3012,1205,2282,5669,4326,5265,1793,4614,1533,4747,6480,4592,6522,1671,4633,3429,5589,4011,2740,15632,1233,1640,10170,4435,2146,41626,1078,5120,3530,8765,5361,11072,1137,7573,1310,4839,5755,4528,3175,1164,7096,2448,6089,4638,6416,3781,4440,2476,1260,12398,1919,3253,6241,12421,6117,1063,1954,5636,1222,13056,5412,6046,21482,1095,1196,2216,5123,3088,5921,3898,4607,5740,3545,2972,4142,1243,1127,3915,2020,3513,7235,3308,2010,1935,5723,5056,3140,4030,4963,2825,4322,5269,5750,1904,1518,4610,6182,2405,1228,1482,3597,15605,4775,4511,5352,5342,23573,2916,4348,3689,3495,2708,2501,2217,3653,12407,2682,1313,3820,4637,3204,5953,4539,2735,1985,4422,3116,6547,34228,2269,4224,33226,8806,3061,6423,6506,3485,15394,3280,3744,5989,5289,5706,8022,13025,2126,3803,30013,1132,3043,5836,6643,2745,2571,3713,6253,33329,5604,2373,3014,3180,2533,5744,2420,1922,16721,2713,3517,3998,15214,1087,1514,38795,6396,5199,1147,1247,4358,3216,6365,26517,3084,5746,3951,2024,6098,4632,3835,42919,9039,4507,1875,6025,4771,5077,1232,4967,3268,41309,3788,4595,5792,3431,2650,6187,4815,5360,2073,1051,5682,2222,4411,2950,4988,5892,2794,15398,3887,2027,5526,4173,7564,3075,1040,6657,1632,8158,4001,6419,1682,1136,1828,13013,1978,27233,5541,5914,5156,6054,29908,5650,3357,28369,2540,5985,3290,3300,2964,3986,3739,5384,4504,9035,4825,1433,1104,4628,3406,4751,15365,2367,2437,3068,4230,2861,1215,1447,5101,1119,6221,2424,2371,44261,6498,3157,5321,4307,3955,3243,2965,5629,4519,15210,4707,3870,3211,2392,6103,4588,1696,3184,4475,38392,12375,1975,4483,2954,1074,3097,6482,3265,1306,5070,1708,4910,2000,5298,9048,4853,3229,14730,4604,15402,5406,3591,2910,4629,2473,13017,9090,1199,38390,1153,3186,11032,7859,2118,5142,6250,2047,13051,3318,6388,13049,30263,2737,5862,2296,1067,1736,2621,2660,9041,18112,5334,1047,1730,3037,1057,5049,1387,6343,2541,5002,41625,5956,15407,3154,1370,1238,9036,2441,30231,2705,12437,2409,5734,1091,15610,6079,2428,2733,2560,6328,10171,2249,6247,1021,1123,5579,5044,1174,38609,14199,1217,2969,4091,5366,3069,2032,3814,2890,2414,4836,6509,3207,7565,5924,41234,3166,5492,5465,5534,11629,33233,1159,13055,1210,3028,2741,1392,1740,2958,3948,1938,5391,5879,5702,6432,5983,4849,4192,4585,2477,3198,6427,30138,1555,2332,29930,3314,4994,4757,3137,3065,5177,5690,41306,1178,25844,6292,3877,5566,6060,1027,2213,15368,6402,44056,2211,6267,2547,4080,5993,4316,5066,8155,26531,1106,6339,1983,12382,6195,1111,30182,4636,1878,3078,6075,1360,1350,5854,12422,3467,5626,1143,2115,5145,6101,1270,2946,2990,5238,15616,1953,5673,5006,2359,1121,1064,30832,4845,8016,8768,3704,5362,3963,2858,2537,5889,4095,5811,6128,5233,3060,4817,30118,3311,5075,5181,5080,3210,5620,3010,1810,4049,5941,44218,1028,3326,2323,3179,5107,29962,1182,3094,4721,4167,4425,6363,3728,6304,2419,1075,4545,2080,41310,4938,1414,2240,4406,5588,5547,4744,1700,6164,5213,1214,5865,2349,6501,21572,7417,1207,2085,23772,3555,4457,6541,1889,2472,4621,41622,1155,5387,8159,1478,5134,1974,6475,2505,5766,4120,15399,6450,3967,5576,29902,2968,5063,5317,1263,5850,12955,12410,1588,17450,3126,3541,15369,5374,3787,1456,1382,3059,30828,6331,4068,5380,8764,1231,14509,1192,1060,1050,3064,1720,6152,3074,34125,4416,3364,3083,3162,1393,2370,5479,1202,4644,2208,28519,1663,5198,13667,2423,7074,5170,4163,5112,2749,1991,2788,5310,5153,37983,4288,2702,2546,3563,3624,4625,2043,4212,4889,3183,6011,2748,5434,5964,6260,2963,5737,1071,6378,34332,3639,17029,2440,5417,2221,1026,5887,5126,2662,1185,4004,2338,4308,12953,2275,3257,38621,2602,4269,5758,5400,5598,5679,6368,2729,13444,1727,6314,9040,3130,7046,4131,6437,23667,4685,5808,1103,6203,3890,5278,5855,6084,3079,4256,4438,2941,5095,4359,3547,1916,3255,3811,6312,5065,3081,23504,9057,1795,1124,5720,4144,8015,4998,3070,2727,11633,3319,3636,2048,2938,5474,3504,5067,4309,3086,39808,4677,8809,2674,5612,4032,4465,3900,1535,39004,5271,5350,4590,1520,3404,3868,13022,4769,2959,30313,13054,3123,5449,2425,2474,5556,6525,1428,2161,4526,4537,1139,3796,1503,8767,5546,3751,4127,2220,6357,15391,3077,5859,3330,2738,4149,3663,2935,3002,4413,6091,6302,3594,12451,4573,5086,1239,2442,3436,8059,1092,3832,5539,3619,1897,4640,6372,3568,1638,1224,2148,27507,1356,3678,6478,41231,2721,15406,4228,7130,34022,2422,3732,2955,4337,2679,15367,6308,5671,4498,1282,2478,2214,2383,5244,1048,6197,4699,5827,3270,1542,14803,5222,4139,1144,2943,15401,2945,4616,5346,1801,4154,31979,4176,15212,4374,3182,3066,3586,14198,1439,12369,3160,7238,5267,8556,4388,1175,2180,5552,4635,4430,1080,8156,30925,1821,4208,8529,8782,2710,1877,5202,13050,2742,4445,2605,4882,3055,4103,5894,5082,4569,4911,3073,41235,3572,4897,4985,3034,2923,2593,1029,4850,41162,5656,6319,2874,5885,1344,2542,10172,6553,1177,2461,2974,5410,2329,30011,5838,1061,1952,1112,5987,2578,4232,5931,5216,1066,5482,3674,1435,5725,4304,14656,8763,41311,8007,3480,2075,2418,4933,1198,6345,5057,2439,2962,2365,38382,5372,15216,5442,2212,3423,2550,15588,2481,6288,6270,3917,6223,33084,3687,15405,2288,5976,3016,12409,2633,2967,1250,6027,3178,4626,6485,2693,1626,2952,4136,4529,1340,1145,3881,5661,1034,5688,4907,5587,39587,15400,3193,7896,1166,5528,1203,3576,6276,2665,6225,19399,4813,6185,12368,2271,3293,4598,8160,41008,2878,2503,4319,13015,1134,3146,30100,1081,3975,14438,5678,4566,12434,6517,7420,3455,6170,5358,1181,4168,5991,1547,3376,1516,5250,1156,2143,9037,6367,33085,4200,3129,30233,44146,5446,3988,4749,7615,1961,4035,4360,5927,1025,5514,5602,4864,6399,2661,5125,2060,4939,1225,42136,3082,4673,4517,4641,4469,3209,4754,4961,3058,44230,4630,1230,10228,41307,1098,4409,2165,1813,1186,6093,1785,6125,5543,1130,3715,1711,3019,3080,2747,1053,4522,4314,5431,29860,19475,4240,6244,5420,3940,29906,2224,2454,3063,6545,3344,5753,3202,4222,5948,12419,9809,3823,1830,3127,16234,6174,1538,2545,3329,7127,15613,1218,3095,6715,1220,5186,2468,12424,2948,1257,4959,1023,38611,5240,5633,41230,15397,5596,5895,3398,3684,1240,2411,3488,3415,6073,27238,3124,2426,1981,1221,1284,41627,1353,2279,1955,1972,1052,5453,44200,1585,4634,6086,1094,1140,7612,5685,31658,4093,2949,5472,6467,3071,6511,14123,1272,4639,3478,44275,2696,2870,4944,2215,26516,3039,1998,5832,3168,5939,3946,19104,4278,5873,14586,3457,2352,1084,2479,6425,4606,3565,3401,5917,3589,1459,32988,2045,3092,30850,3067,1180,6013,3171,2960,3533,5966,3447,15366,6390,1216,2209,1126,3725,2743,1189,4006,2919,6543,2071,2658,5055,1646,29900,3613,5800,4542,1629,3235,10182,34405,2152,4710,2988,1385,6077,11639,6341,26526,30830,10169,3789,4666,31174,8766,5382,6030,6003,5813,3748,5228,4834,4495,2526,2416,5600,4261,6354,41236,3085,2956,3978,4197,3267,5837,12463,3793,6536,6166,3761,1045,15404,2944,3181,25750,2475,4855,4602,5532,29932,6290,4214,4591,5781,21472,6521,1193,1077,2362,2162,6062,2120,5211,4074,6386,5590,5517,2294,2036,7574,2739,5196,8520,5704,5287,1161,3420,2421,5852,44203,27764,6326,6007,8769,5537,4719,3521,5477,2218,1133,1642,2102,5677,5129,4472,4670,3785,4356,10173,2983,3865,4254,1097,12380,4811,12374,2233,3373,3464,2951,5764,2815,2736,2008,3337,1148,4663,6150,4455,6366,3062,5700,4146,3328,44224,1816,4981,3875,6714,1056,4442,3633,3506,5440,2549,1989,4051,4281,3277,39446,18759,4631,6520,3177,4007,2746,4157,41312,2417,31013,2366,5339,21387,2961,2913,2091,6380,5867,3426,5036,4912,1065,2668,1165,6273,5322,1346,6309,2159,5803,6209,5236,4936,8773,1120,1093,1930,6351,5275,15198,1236,41624,12406,1977,1129,2966,23674,9038,3701,3057,12384,2803,2600,2898,5806,4972,6435,41075,3772,5061,4876,1976,3817,6471,3965,6082,14511,5958,6348,5046,4713,5219,5354,6109,1299,3076,4071,5376,2699,3812,4345,4501,1505,1399,2270,1621,39333,6658,29999,2138,3341,1367,5494,4891,2206,4161,4547,37785,8157,5943,4779,27743,5877,5591,13016,5073,4627,8553,4949,1184,2074,2998,11631,1848,8006,5569,1037,13053,4056,6119,3316,1088,2191,9087,1204,6265,2106,2087,3047,2470,4940,5574,1912,5911]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LAT330+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40  % Computer : n020.cluster.edu
% 0.13/0.40  % Model    : x86_64 x86_64
% 0.13/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40  % Memory   : 8046.5625MB
% 0.13/0.40  % OS       : Linux 6.8.0-71-generic
% 0.13/0.40  % CPULimit : 300
% 0.13/0.40  % WCLimit  : 300
% 0.13/0.40  % DateTime : Fri Sep 25 20:57:34 UTC 2026
% 0.13/0.40  % CPUTime  : 
% 0.13/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.90/1.52  % [INFO] 	 Parsing done (549ms). 
% 2.90/1.53  % [INFO] 	 Running in sequential loop mode. 
% 3.80/1.74  % [INFO] 	 eprover registered as external prover. 
% 3.80/1.74  % [INFO] 	 Scanning for conjecture ... 
% 4.77/1.94  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3003 axioms. Running axiom selection ... 
% 7.87/2.76  % [INFO] 	 Axiom selection finished. Selected 1018 axioms (removed 1985 axioms). 
% 10.72/3.56  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 11.05/3.63  % [INFO] 	 Type checking passed. 
% 11.05/3.63  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 171.27/51.14  % External prover 'e' found a proof!
% 171.27/51.14  % [INFO] 	 Killing All external provers ... 
% 171.27/51.15  % Time passed: 50618ms (effective reasoning time: 49614ms)
% 171.27/51.15  % 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)>
% 171.27/51.15  % Axioms used in derivation (1018): 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, t130_zfmisc_1, t3_filter_2, t175_partfun1, t15_relat_1, t48_funct_2, fraenkel_a_3_7_domain_1, d16_lattice4, t70_filter_0, t72_filter_0, t48_filter_2, t46_filter_0, t40_lattice2, t64_relat_1, t138_zfmisc_1, t25_subset_1, t37_filter_0, rc11_lattices, t66_filter_2, fraenkel_a_3_0_filter_0, rc3_lattices, t52_filter_0, t108_zfmisc_1, t165_funct_2, t57_filter_0, dt_l1_lattices, dt_k12_filter_2, dt_k4_lattice4, t45_filter_2, t60_partfun1, existence_m1_realset1, 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, fraenkel_a_2_0_filter_2, d3_lattice2, t4_relset_1, t10_filter_0, t31_subset_1, t3_subset, cc1_relset_1, fc1_filter_2, t25_binop_1, d2_binop_1, d6_lattice4, t30_lattice4, s1_domain_1, t12_filter_0, t124_funct_1, t50_lattice2, t55_subset_1, t79_funct_2, dt_u1_lattices, fraenkel_a_2_1_domain_1, d13_filter_2, existence_m1_subset_1, t22_lattice4, existence_m1_filter_2, commutativity_k2_tarski, t3_relat_1, t22_filter_0, t24_relat_1, t8_relset_1, t106_zfmisc_1, t125_zfmisc_1, t73_filter_0, 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
% 171.27/51.15  % No. of inferences in proof: 3448
% 171.27/51.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 50618 ms resp. 49614 ms w/o parsing
% 177.60/52.47  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 177.60/52.49  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------