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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LAT335+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 : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:47:20 AM UTC 2026

% Result   : Theorem 163.11s 48.65s
% Output   : Refutation 169.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      : 1100
% Syntax   : Number of formulae    : 3425 ( 634 unt;   0 typ;  67 def)
%            Number of atoms       : 19380 (3159 equ;   0 cnn)
%            Maximal formula atoms :   58 (   5 avg)
%            Number of connectives : 65216 (4877   ~;2535   |;7100   &;45183   @)
%                                         ( 243 <=>;5278  =>;   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;  80 con; 0-9 aty)
%            Number of variables   : 8088 (  51   ^;7621   !; 349   ?;8088   :)
%                                         (   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(v3_filter_0_decl,type,
    v3_filter_0: $i > $o ).

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

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

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

thf(v1_relat_1_decl,type,
    v1_relat_1: $i > $o ).

thf(k2_tarski_decl,type,
    k2_tarski: $i > $i > $i ).

thf(k4_tarski_decl,type,
    k4_tarski: $i > $i > $i ).

thf(k1_relat_1_decl,type,
    k1_relat_1: $i > $i ).

thf(k2_relat_1_decl,type,
    k2_relat_1: $i > $i ).

thf(v1_funct_1_decl,type,
    v1_funct_1: $i > $o ).

thf(r2_hidden_decl,type,
    r2_hidden: $i > $i > $o ).

thf(k1_funct_1_decl,type,
    k1_funct_1: $i > $i > $i ).

thf(v1_funct_2_decl,type,
    v1_funct_2: $i > $i > $i > $o ).

thf(m2_relset_1_decl,type,
    m2_relset_1: $i > $i > $i > $o ).

thf(k2_funct_2_decl,type,
    k2_funct_2: $i > $i > $i > $i > $i ).

thf(r1_tarski_decl,type,
    r1_tarski: $i > $i > $o ).

thf(k9_relat_1_decl,type,
    k9_relat_1: $i > $i > $i ).

thf(v1_partfun1_decl,type,
    v1_partfun1: $i > $i > $i > $o ).

thf(k1_xboole_0_decl,type,
    k1_xboole_0: $i ).

thf(k2_zfmisc_1_decl,type,
    k2_zfmisc_1: $i > $i > $i ).

thf(r1_binop_1_decl,type,
    r1_binop_1: $i > $i > $i > $o ).

thf(k1_binop_1_decl,type,
    k1_binop_1: $i > $i > $i > $i ).

thf(k3_funct_2_decl,type,
    k3_funct_2: $i > $i > $i > $i > $i ).

thf(k4_xboole_0_decl,type,
    k4_xboole_0: $i > $i > $i ).

thf(r6_binop_1_decl,type,
    r6_binop_1: $i > $i > $i > $o ).

thf(k1_tarski_decl,type,
    k1_tarski: $i > $i ).

thf(k1_zfmisc_1_decl,type,
    k1_zfmisc_1: $i > $i ).

thf(k6_subset_1_decl,type,
    k6_subset_1: $i > $i > $i > $i ).

thf(m1_realset1_decl,type,
    m1_realset1: $i > $i > $i > $o ).

thf(k1_realset1_decl,type,
    k1_realset1: $i > $i > $i ).

thf(v1_xboole_0_decl,type,
    v1_xboole_0: $i > $o ).

thf(r4_binop_1_decl,type,
    r4_binop_1: $i > $i > $i > $o ).

thf(r5_binop_1_decl,type,
    r5_binop_1: $i > $i > $i > $o ).

thf(k1_funct_2_decl,type,
    k1_funct_2: $i > $i > $i ).

thf(v2_funct_1_decl,type,
    v2_funct_1: $i > $o ).

thf(k2_funct_1_decl,type,
    k2_funct_1: $i > $i ).

thf(m1_relset_1_decl,type,
    m1_relset_1: $i > $i > $i > $o ).

thf(v3_binop_1_decl,type,
    v3_binop_1: $i > $i > $o ).

thf(m2_realset1_decl,type,
    m2_realset1: $i > $i > $i > $o ).

thf(k5_partfun1_decl,type,
    k5_partfun1: $i > $i > $i > $i ).

thf(k2_partfun1_decl,type,
    k2_partfun1: $i > $i > $i > $i > $i ).

thf(r2_binop_1_decl,type,
    r2_binop_1: $i > $i > $i > $o ).

thf(k3_relat_1_decl,type,
    k3_relat_1: $i > $i ).

thf(v1_binop_1_decl,type,
    v1_binop_1: $i > $i > $o ).

thf(r3_binop_1_decl,type,
    r3_binop_1: $i > $i > $i > $o ).

thf(k1_funct_4_decl,type,
    k1_funct_4: $i > $i > $i ).

thf(v2_binop_1_decl,type,
    v2_binop_1: $i > $i > $o ).

thf(k3_subset_1_decl,type,
    k3_subset_1: $i > $i > $i ).

thf(k1_lattice2_decl,type,
    k1_lattice2: $i > $i ).

thf(v3_lattices_decl,type,
    v3_lattices: $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(l2_lattices_decl,type,
    l2_lattices: $i > $o ).

thf(u2_lattices_decl,type,
    u2_lattices: $i > $i ).

thf(l1_lattices_decl,type,
    l1_lattices: $i > $o ).

thf(u1_lattices_decl,type,
    u1_lattices: $i > $i ).

thf(g3_lattices_decl,type,
    g3_lattices: $i > $i > $i > $i ).

thf(a_2_3_domain_1_decl,type,
    a_2_3_domain_1: $i > $i > $i ).

thf(k2_binop_1_decl,type,
    k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).

thf(v6_group_1_decl,type,
    v6_group_1: $i > $o ).

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

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

thf(v13_lattices_decl,type,
    v13_lattices: $i > $o ).

thf(r2_tarski_decl,type,
    r2_tarski: $i > $i > $o ).

thf(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(v11_lattices_decl,type,
    v11_lattices: $i > $o ).

thf(v12_lattices_decl,type,
    v12_lattices: $i > $o ).

thf(r7_binop_1_decl,type,
    r7_binop_1: $i > $i > $i > $o ).

thf(k6_nat_lat_decl,type,
    k6_nat_lat: $i ).

thf(a_3_3_domain_1_decl,type,
    a_3_3_domain_1: $i > $i > $i > $i ).

thf(r1_relat_2_decl,type,
    r1_relat_2: $i > $i > $o ).

thf(k8_funct_2_decl,type,
    k8_funct_2: $i > $i > $i > $i > $i ).

thf(a_1_0_domain_1_decl,type,
    a_1_0_domain_1: $i > $i ).

thf(m3_realset1_decl,type,
    m3_realset1: $i > $i > $i > $o ).

thf(k7_funct_2_decl,type,
    k7_funct_2: $i > $i > $i > $i > $i > $i ).

thf(m2_filter_2_decl,type,
    m2_filter_2: $i > $i > $o ).

thf(k21_filter_2_decl,type,
    k21_filter_2: $i > $i > $i > $i ).

thf(k20_filter_2_decl,type,
    k20_filter_2: $i > $i > $i > $i ).

thf(k2_lattices_decl,type,
    k2_lattices: $i > $i > $i > $i ).

thf(r2_filter_2_decl,type,
    r2_filter_2: $i > $i > $o ).

thf(v1_filter_0_decl,type,
    v1_filter_0: $i > $i > $o ).

thf(k15_filter_2_decl,type,
    k15_filter_2: $i > $i > $i ).

thf(m1_filter_0_decl,type,
    m1_filter_0: $i > $i > $o ).

thf(k5_filter_0_decl,type,
    k5_filter_0: $i > $i > $i > $i ).

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

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

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

thf(v17_lattices_decl,type,
    v17_lattices: $i > $o ).

thf(k17_filter_2_decl,type,
    k17_filter_2: $i > $i ).

thf(v1_filter_2_decl,type,
    v1_filter_2: $i > $i > $o ).

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

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

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

thf(k5_lattices_decl,type,
    k5_lattices: $i > $i ).

thf(v15_lattices_decl,type,
    v15_lattices: $i > $o ).

thf(v16_lattices_decl,type,
    v16_lattices: $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_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(k10_filter_2_decl,type,
    k10_filter_2: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

thf(k3_lattices_decl,type,
    k3_lattices: $i > $i > $i > $i ).

thf(k7_filter_0_decl,type,
    k7_filter_0: $i > $i > $i > $i ).

thf(k8_filter_0_decl,type,
    k8_filter_0: $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(k24_filter_2_decl,type,
    k24_filter_2: $i > $i > $i ).

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

thf(k18_filter_2_decl,type,
    k18_filter_2: $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(m3_lattice4_decl,type,
    m3_lattice4: $i > $i > $o ).

thf(m1_struct_0_decl,type,
    m1_struct_0: $i > $i > $i > $o ).

thf(k7_setwiseo_decl,type,
    k7_setwiseo: $i > $i > $i > $i > $i > $i ).

thf(k12_domain_1_decl,type,
    k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(a_1_2_domain_1_decl,type,
    a_1_2_domain_1: $i > $i ).

thf(a_3_6_domain_1_decl,type,
    a_3_6_domain_1: $i > $i > $i > $i ).

thf(f1_s4_funct_2_decl,type,
    f1_s4_funct_2: $i ).

thf(f2_s4_funct_2_decl,type,
    f2_s4_funct_2: $i ).

thf(f3_s4_funct_2_decl,type,
    f3_s4_funct_2: $i > $i ).

thf(k1_finsub_1_decl,type,
    k1_finsub_1: $i > $i > $i > $i ).

thf(k2_filter_0_decl,type,
    k2_filter_0: $i > $i > $i ).

thf(a_3_5_domain_1_decl,type,
    a_3_5_domain_1: $i > $i > $i > $i ).

thf(v1_lattice4_decl,type,
    v1_lattice4: $i > $i > $i > $o ).

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

thf(a_3_4_domain_1_decl,type,
    a_3_4_domain_1: $i > $i > $i > $i ).

thf(k9_domain_1_decl,type,
    k9_domain_1: $i > $i > $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(k6_filter_0_decl,type,
    k6_filter_0: $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(k11_filter_0_decl,type,
    k11_filter_0: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sk20_decl,type,
    sk20: $i > $i ).

thf(sk26_decl,type,
    sk26: $i > $i > $i ).

thf(sk72_decl,type,
    sk72: $i ).

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

thf(sk82_decl,type,
    sk82: $i > $i > $i ).

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

thf(sk96_decl,type,
    sk96: $i ).

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

thf(sk112_decl,type,
    sk112: $i > $i > $i ).

thf(sk119_decl,type,
    sk119: $i ).

thf(sk139_decl,type,
    sk139: $i ).

thf(sk153_decl,type,
    sk153: $i ).

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

thf(sk194_decl,type,
    sk194: $i > $i ).

thf(sk204_decl,type,
    sk204: $i ).

thf(sk213_decl,type,
    sk213: $i ).

thf(sk215_decl,type,
    sk215: $i ).

thf(sk231_decl,type,
    sk231: $i > $i > $i > $o ).

thf(sk232_decl,type,
    sk232: $i > $i > $i > $i ).

thf(sk233_decl,type,
    sk233: $i > $i > $i > $i ).

thf(sk251_decl,type,
    sk251: $i > $i ).

thf(sk275_decl,type,
    sk275: $i ).

thf(sk293_decl,type,
    sk293: $i ).

thf(sk297_decl,type,
    sk297: $i ).

thf(sk310_decl,type,
    sk310: $i ).

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

thf(sk315_decl,type,
    sk315: $i ).

thf(sk317_decl,type,
    sk317: $i ).

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

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

thf(sk333_decl,type,
    sk333: $o ).

thf(sk334_decl,type,
    sk334: $i ).

thf(sk335_decl,type,
    sk335: $i ).

thf(sk341_decl,type,
    sk341: $o ).

thf(sk342_decl,type,
    sk342: $i ).

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

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

thf(sk348_decl,type,
    sk348: $i ).

thf(sk349_decl,type,
    sk349: $o ).

thf(sk350_decl,type,
    sk350: $i ).

thf(sk351_decl,type,
    sk351: $i ).

thf(sk353_decl,type,
    sk353: $i > $i ).

thf(sk357_decl,type,
    sk357: $i ).

thf(sk358_decl,type,
    sk358: $i ).

thf(sk361_decl,type,
    sk361: $i ).

thf(sk366_decl,type,
    sk366: $i > $i > $i ).

thf(sk367_decl,type,
    sk367: $i > $i > $i ).

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

thf(sk373_decl,type,
    sk373: $i ).

thf(sk374_decl,type,
    sk374: $i ).

thf(sk388_decl,type,
    sk388: $i > $i ).

thf(sk410_decl,type,
    sk410: $i ).

thf(sk423_decl,type,
    sk423: $i ).

thf(sk448_decl,type,
    sk448: $o ).

thf(sk449_decl,type,
    sk449: $i ).

thf(sk450_decl,type,
    sk450: $i ).

thf(sk462_decl,type,
    sk462: $i ).

thf(sk475_decl,type,
    sk475: $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 ) )
               => ! [C: $i] :
                    ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                   => ( ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                        & ( A @ v3_filter_0 ) )
                     => ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ v3_filter_0 ) ) ) ) ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: $i] :
          ~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
           => ! [B: $i] :
                ( ( sk1 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
               => ( ( ( B @ ( A @ ( sk1 @ r3_lattices ) ) )
                    & ( sk1 @ v3_filter_0 ) )
                 => ( B @ ( A @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 ) ) ) ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( @+[A: $i] :
          ~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
           => ( ( ( A @ ( sk2 @ ( sk1 @ r3_lattices ) ) )
                & ( sk1 @ v3_filter_0 ) )
             => ( A @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 ) ) ) ) ) ).

thf(sk5_def,definition,
    ( sk5
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( C @ ( D @ r2_hidden ) )
           => ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ).

thf(sk6_def,definition,
    ( sk6
    = ( ^ [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(sk7_def,definition,
    ( sk7
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( C @ ( D @ m1_subset_1 ) )
           => ( ( D @ ( B @ ( A @ k1_binop_1 ) ) )
              = D ) ) ) ) ).

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 ) )
               => ! [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(sk9_def,definition,
    ( sk9
    = ( ^ [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 @ sk8 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
                    = ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
                  & ( ( E @ ( D @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) )
                    = ( E @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ) ).

thf(sk10_def,definition,
    ( sk10
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( C @ ( D @ m1_subset_1 ) )
           => ( ( ( D @ ( C @ ( B @ ( A @ sk9 ) ) @ ( C @ ( B @ ( A @ sk8 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
                = ( D @ ( C @ ( B @ ( A @ sk9 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
              & ( ( D @ ( C @ ( B @ ( A @ sk9 ) ) @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) )
                = ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk9 ) ) @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ).

thf(sk11_def,definition,
    ( sk11
    = ( ^ [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(sk12_def,definition,
    ( sk12
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
              & ( B @ k1_relat_1 @ ( B @ ( A @ sk11 ) @ r2_hidden ) ) )
           => ( ( ( ( C @ ( A @ k1_funct_1 ) )
                  = ( B @ ( A @ sk11 ) ) )
               => ( ( B @ ( A @ sk11 ) @ ( B @ k1_funct_1 ) )
                  = C ) )
              & ( ( ( B @ ( A @ sk11 ) @ ( B @ k1_funct_1 ) )
                  = C )
               => ( ( C @ ( A @ k1_funct_1 ) )
                  = ( B @ ( A @ sk11 ) ) ) ) ) ) ) ) ).

thf(sk13_def,definition,
    ( sk13
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( B @ ( C @ m1_subset_1 ) )
           => ( ( C @ ( C @ ( A @ k1_binop_1 ) ) )
              = C ) ) ) ) ).

thf(sk14_def,definition,
    ( sk14
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk15_def,definition,
    ( sk15
    = ( @+[A: $i] :
          ( ! [B: $i] :
              ( ( A @ ( B @ m1_subset_1 ) )
             => ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk19_def,definition,
    ( sk19
    = ( ^ [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(sk20_def,definition,
    ( sk20
    = ( ^ [A: $i] :
        @+[B: $i] :
          ~ ( ( ( B @ v1_funct_1 )
              & ( B @ v1_relat_1 ) )
           => ( ( ( ( B @ k1_relat_1 )
                  = A )
                & ( ( A @ sk19 @ k1_relat_1 )
                  = A ) )
             => ( ( A @ sk19 )
                = B ) ) ) ) ) ).

thf(sk26_def,definition,
    ( sk26
    = ( ^ [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(sk72_def,definition,
    ( sk72
    = ( @+[A: $i] :
          ( ( A @ v1_xboole_0 )
          & ( A @ v2_funct_1 )
          & ( A @ v1_funct_1 )
          & ( A @ v1_relat_1 ) ) ) ) ).

thf(sk81_def,definition,
    ( sk81
    = ( ^ [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(sk82_def,definition,
    ( sk82
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ( ! [D: $i] :
              ( ( A @ ( D @ r1_tarski ) )
             => ( C @ ( D @ r2_hidden ) ) )
          & ( B @ sk81 @ ( C @ r2_hidden ) ) ) ) ) ).

thf(sk95_def,definition,
    ( sk95
    = ( @+[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(sk96_def,definition,
    ( sk96
    = ( @+[A: $i] :
          ( ( A @ v2_struct_0 )
          & ( A @ l2_struct_0 ) ) ) ) ).

thf(sk111_def,definition,
    ( sk111
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ( ( C @ v1_funct_1 )
          & ( C @ v1_relat_1 )
          & ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).

thf(sk112_def,definition,
    ( sk112
    = ( ^ [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(sk119_def,definition,
    ( sk119
    = ( @+[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(sk139_def,definition,
    ( sk139
    = ( @+[A: $i] :
          ( ( A @ v2_funct_1 )
          & ( A @ v1_funct_1 )
          & ( A @ v1_relat_1 ) ) ) ) ).

thf(sk153_def,definition,
    ( sk153
    = ( @+[A: $i] :
          ( ( A @ v1_relat_1 )
          & ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk187_def,definition,
    ( sk187
    = ( @+[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(sk194_def,definition,
    ( sk194
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).

thf(sk204_def,definition,
    ( sk204
    = ( @+[A: $i] :
          ( ( A @ v1_funct_1 )
          & ( A @ v1_relat_1 ) ) ) ) ).

thf(sk213_def,definition,
    ( sk213
    = ( @+[A: $i] :
          ( ( A @ v1_funct_1 )
          & ( A @ v1_xboole_0 )
          & ( A @ v1_relat_1 ) ) ) ) ).

thf(sk215_def,definition,
    ( sk215
    = ( @+[A: $i] :
          ( ( A @ v1_relat_1 )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk232_def,definition,
    ( sk232
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( A @ ( D @ r2_hidden ) )
           => ( ( D = B )
              | ( D = C ) ) ) ) ) ).

thf(sk233_def,definition,
    ( sk233
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( ( D = B )
              | ( D = C ) )
           => ( A @ ( D @ r2_hidden ) ) ) ) ) ).

thf(sk251_def,definition,
    ( sk251
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ( B @ v1_xboole_0 )
          & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).

thf(sk275_def,definition,
    ( sk275
    = ( @+[A: $i] :
          ( ~ ( A @ v3_struct_0 )
          & ( A @ l1_struct_0 ) ) ) ) ).

thf(sk293_def,definition,
    ( sk293
    = ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).

thf(sk297_def,definition,
    ( sk297
    = ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).

thf(sk310_def,definition,
    ( sk310
    = ( @+[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(sk313_def,definition,
    ( sk313
    = ( @+[A: $i] :
          ( ! [B: $i] :
              ( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
             => ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
                = ( B @ f3_s4_funct_2 ) ) )
          & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
          & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
          & ( A @ v1_funct_1 ) ) ) ) ).

thf(sk315_def,definition,
    ( sk315
    = ( @+[A: $i] :
          ( ( A @ v17_lattices )
          & ( A @ v16_lattices )
          & ( A @ v15_lattices )
          & ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk317_def,definition,
    ( sk317
    = ( @+[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(sk328_def,definition,
    ( sk328
    = ( @+[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(sk329_def,definition,
    ( sk329
    = ( @+[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(sk334_def,definition,
    ( sk334
    = ( @+[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(sk335_def,definition,
    ( sk335
    = ( @+[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(sk342_def,definition,
    ( sk342
    = ( @+[A: $i] :
          ~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
           => ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).

thf(sk343_def,definition,
    ( sk343
    = ( @+[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(sk345_def,definition,
    ( sk345
    = ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).

thf(sk348_def,definition,
    ( sk348
    = ( @+[A: $i] :
          ( ( A @ v3_lattices )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk350_def,definition,
    ( sk350
    = ( @+[A: $i] :
          ~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
           => ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).

thf(sk351_def,definition,
    ( sk351
    = ( @+[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(sk353_def,definition,
    ( sk353
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ~ ? [C: $i] :
                ( ~ ( B @ ( C @ r2_hidden ) )
                & ~ ( B @ ( C @ r2_tarski ) )
                & ( B @ ( C @ r1_tarski ) ) )
          & ! [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
             => ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( C @ ( D @ r1_tarski ) )
                & ( B @ ( C @ r2_hidden ) ) )
             => ( B @ ( D @ r2_hidden ) ) )
          & ( B @ ( A @ r2_hidden ) ) ) ) ) ).

thf(sk357_def,definition,
    ( sk357
    = ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).

thf(sk358_def,definition,
    ( sk358
    = ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).

thf(sk361_def,definition,
    ( sk361
    = ( @+[A: $i] :
          ~ ( A @ v1_xboole_0 ) ) ) ).

thf(sk366_def,definition,
    ( sk366
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( A @ ( C @ r2_hidden ) )
           => ( C = B ) ) ) ) ).

thf(sk367_def,definition,
    ( sk367
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( C = B )
           => ( A @ ( C @ r2_hidden ) ) ) ) ) ).

thf(sk373_def,definition,
    ( sk373
    = ( @+[A: $i] :
          ~ ( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
           => ? [B: $i] :
                ( ( B @ ( A @ p1_s3_funct_2 ) )
                & ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) ) ) ) ).

thf(sk374_def,definition,
    ( sk374
    = ( @+[A: $i] :
          ( ! [B: $i] :
              ( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
             => ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
          & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
          & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
          & ( A @ v1_funct_1 ) ) ) ) ).

thf(sk388_def,definition,
    ( sk388
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).

thf(sk410_def,definition,
    ( sk410
    = ( @+[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(sk423_def,definition,
    ( sk423
    = ( @+[A: $i] :
          ( ~ ( A @ v3_struct_0 )
          & ( A @ l2_struct_0 ) ) ) ) ).

thf(sk449_def,definition,
    ( sk449
    = ( @+[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(sk450_def,definition,
    ( sk450
    = ( @+[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(sk462_def,definition,
    ( sk462
    = ( @+[A: $i] :
          ( ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk475_def,definition,
    ( sk475
    = ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).

thf(580,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(4447,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)],[580]) ).

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(2094,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(202,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).

thf(2265,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(2266,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    inference(cnf,[status(esa)],[2265]) ).

thf(342,axiom,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(3127,plain,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(3128,plain,
    ( ( sk204 @ v1_funct_1 )
    & ( sk204 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[3127]) ).

thf(3130,plain,
    sk204 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3128]) ).

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

thf(1071,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)],[1070]) ).

thf(1072,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)],[1071]) ).

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 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                  & ( A @ v3_filter_0 ) )
               => ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ v3_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_filter_2) ).

thf(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 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                    & ( A @ v3_filter_0 ) )
                 => ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ v3_filter_0 ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(1035,plain,
    ~ ! [A: $i] :
        ( ( ( A @ l3_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                    & ( A @ v3_filter_0 ) )
                 => ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( A @ k23_filter_2 ) @ v3_filter_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1036,plain,
    ( ~ ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 )
    & ( sk3 @ ( sk2 @ ( sk1 @ r3_lattices ) ) )
    & ( sk1 @ v3_filter_0 )
    & ( sk1 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ) )
    & ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
    & ( sk1 @ l3_lattices )
    & ( sk1 @ v10_lattices )
    & ~ ( sk1 @ v3_struct_0 ) ),
    inference(cnf,[status(esa)],[1035]) ).

thf(1039,plain,
    sk1 @ v10_lattices,
    inference(cnfConj,[status(thm)],[1036]) ).

thf(7071,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)],[1072,1039]) ).

thf(7072,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[7071:[bind(A,$thf( sk1 ))]]) ).

thf(7334,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)],[7072]) ).

thf(8555,plain,
    ! [A: $i] :
      ( ( ( sk204 @ 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)],[3130,7334]) ).

thf(8556,plain,
    ! [A: $i] :
      ( ( ( sk204 @ 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)],[8555]) ).

thf(8557,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8556:[bind(A,$thf( sk204 ))]]) ).

thf(15679,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8557]) ).

thf(15680,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15679]) ).

thf(15687,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk204 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15680]) ).

thf(15720,plain,
    ( ( sk204 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15687]) ).

thf(739,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
        = ( A @ k6_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice4) ).

thf(5329,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
        = ( A @ k6_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(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(1100,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(1101,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
        | ( ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
         != ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
        | ( ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) )
         != ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( 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 @ sk10 ) ) @ 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 @ 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 ) )
      & ( ( ( 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)],[1100]) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk10 ) ) @ 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)],[1101]) ).

thf(636,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(4722,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)],[636]) ).

thf(4723,plain,
    ( ( sk317 @ v15_lattices )
    & ( sk317 @ v14_lattices )
    & ( sk317 @ v13_lattices )
    & ( sk317 @ v10_lattices )
    & ( sk317 @ v9_lattices )
    & ( sk317 @ v8_lattices )
    & ( sk317 @ v7_lattices )
    & ( sk317 @ v6_lattices )
    & ( sk317 @ v5_lattices )
    & ( sk317 @ v4_lattices )
    & ( sk317 @ v3_lattices )
    & ~ ( sk317 @ v3_struct_0 )
    & ( sk317 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4722]) ).

thf(4729,plain,
    sk317 @ v5_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(226,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(2410,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)],[226]) ).

thf(2411,plain,
    ( ( sk119 @ v1_lattice2 )
    & ( sk119 @ v10_lattices )
    & ( sk119 @ v9_lattices )
    & ( sk119 @ v8_lattices )
    & ( sk119 @ v7_lattices )
    & ( sk119 @ v6_lattices )
    & ( sk119 @ v5_lattices )
    & ( sk119 @ v4_lattices )
    & ~ ( sk119 @ v3_struct_0 )
    & ( sk119 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2410]) ).

thf(2412,plain,
    sk119 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2411]) ).

thf(323,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(3036,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)],[323]) ).

thf(3037,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)],[3036]) ).

thf(3038,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)],[3037]) ).

thf(3040,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3038]) ).

thf(3042,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3040]) ).

thf(3043,plain,
    k1_xboole_0 @ v1_xboole_0,
    inference(simp,[status(thm)],[3042]) ).

thf(721,axiom,
    ? [A: $i] :
      ~ ( A @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(5220,plain,
    ? [A: $i] :
      ~ ( A @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(5221,plain,
    ~ ! [A: $i] : ( A @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[5220]) ).

thf(5222,plain,
    ~ ( sk361 @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[5221]) ).

thf(6850,plain,
    ( ( ( sk361 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3043,5222]) ).

thf(6851,plain,
    ( ( sk361 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6850]) ).

thf(6855,plain,
    sk361 != k1_xboole_0,
    inference(simp,[status(thm)],[6851]) ).

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(1082,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(1083,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)],[1082]) ).

thf(901,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(6074,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_lattice4 ) )
            = ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(1008,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(6555,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)],[1008]) ).

thf(4728,plain,
    sk317 @ v9_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(887,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(6014,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)],[887]) ).

thf(750,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ r2_hidden ) )
               => ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).

thf(5385,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ r2_hidden ) )
               => ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(832,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(5810,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)],[832]) ).

thf(804,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(5659,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)],[804]) ).

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(1322,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(768,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
                  <=> ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_filter_0) ).

thf(5509,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
                     => ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) ) )
                    & ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
                     => ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(812,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(5686,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)],[812]) ).

thf(904,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(6085,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)],[904]) ).

thf(695,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(5116,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)],[695]) ).

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 ) )
             => ( ( 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(5561,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)],[783]) ).

thf(514,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(4094,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)],[514]) ).

thf(859,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(5918,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)],[859]) ).

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(1369,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(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(1182,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(1183,plain,
    ! [B: $i,A: $i] :
      ( ( ( B
          = ( A @ k2_funct_1 ) )
        | ( ( A @ ( B @ sk11 ) @ ( A @ k1_funct_1 ) )
         != ( A @ ( B @ sk12 ) ) )
        | ( ( A @ ( B @ sk12 ) @ ( B @ 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 @ sk12 ) @ ( B @ k1_funct_1 ) )
          = ( A @ ( B @ sk11 ) ) )
        | ( ( A @ ( B @ sk12 ) @ ( B @ 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 ) @ ( A @ k1_funct_1 ) )
         != ( A @ ( B @ sk12 ) ) )
        | ( ( A @ ( B @ sk11 ) @ ( A @ k1_funct_1 ) )
          = ( A @ ( B @ sk12 ) ) )
        | ( ( 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 @ sk12 ) @ ( B @ k1_funct_1 ) )
          = ( A @ ( B @ sk11 ) ) )
        | ( ( A @ ( B @ sk11 ) @ ( A @ k1_funct_1 ) )
          = ( A @ ( B @ sk12 ) ) )
        | ( ( 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 @ sk12 ) @ 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 @ 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(cnf,[status(esa)],[1182]) ).

thf(1189,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ k2_funct_1 ) )
      | ( ( A @ ( B @ sk12 ) @ ( B @ k1_funct_1 ) )
        = ( A @ ( B @ sk11 ) ) )
      | ( ( A @ ( B @ sk11 ) @ ( A @ k1_funct_1 ) )
        = ( A @ ( B @ sk12 ) ) )
      | ( ( 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)],[1183]) ).

thf(1190,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 @ sk12 ) @ ( B @ k1_funct_1 ) )
        = ( A @ ( B @ sk11 ) ) )
      | ( ( A @ ( B @ sk12 ) )
        = ( A @ ( B @ sk11 ) @ ( A @ k1_funct_1 ) ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1189]) ).

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(1306,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(1307,plain,
    ! [A: $i] :
      ( ( ( A = k1_xboole_0 )
        | ( ( A @ sk19 )
         != ( A @ sk20 ) ) )
      & ( ( A = k1_xboole_0 )
        | ( ( A @ sk20 @ k1_relat_1 )
          = A ) )
      & ( ( A = k1_xboole_0 )
        | ( ( A @ sk19 @ k1_relat_1 )
          = A ) )
      & ( ( A = k1_xboole_0 )
        | ( A @ sk20 @ v1_funct_1 ) )
      & ( ( A = k1_xboole_0 )
        | ( A @ sk20 @ v1_relat_1 ) )
      & ( ( A = k1_xboole_0 )
        | ( A @ sk19 @ v1_funct_1 ) )
      & ( ( A = k1_xboole_0 )
        | ( A @ sk19 @ v1_relat_1 ) ) ),
    inference(cnf,[status(esa)],[1306]) ).

thf(1313,plain,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1307]) ).

thf(1316,plain,
    ! [A: $i] :
      ( ( A @ sk20 @ v1_relat_1 )
      | ( A = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1313]) ).

thf(145,axiom,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).

thf(1956,plain,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(1957,plain,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[1956]) ).

thf(496,axiom,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(3979,plain,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(3980,plain,
    ~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[3979]) ).

thf(3981,plain,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[3980]) ).

thf(8514,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3043,3981]) ).

thf(8515,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8514]) ).

thf(8526,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[8515]) ).

thf(11439,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)],[1957,8526]) ).

thf(11440,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[11439:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(29835,plain,
    ! [A: $i] :
      ( ( A
       != ( k1_xboole_0 @ k1_tarski ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,11440]) ).

thf(29836,plain,
    ! [A: $i] :
      ( ( A
       != ( k1_xboole_0 @ k1_tarski ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[29835]) ).

thf(29837,plain,
    k1_xboole_0 @ k1_tarski @ sk20 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[29836:[bind(A,$thf( k1_xboole_0 @ k1_tarski ))]]) ).

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(1153,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(1154,plain,
    ! [A: $i] :
      ( ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1153]) ).

thf(1155,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_relat_1 )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1154]) ).

thf(33915,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ sk20 @ 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)],[29837,1155]) ).

thf(33916,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ sk20 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[33915]) ).

thf(33917,plain,
    ( ( k1_xboole_0 @ k1_tarski @ sk20 @ k1_relat_1 @ ( k1_xboole_0 @ k1_tarski @ sk20 @ k9_relat_1 ) )
    = ( k1_xboole_0 @ k1_tarski @ sk20 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[33916:[bind(A,$thf( k1_xboole_0 @ k1_tarski @ sk20 ))]]) ).

thf(380,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(3345,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)],[380]) ).

thf(585,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(4464,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)],[585]) ).

thf(318,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(3008,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)],[318]) ).

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(2127,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(2128,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)],[2127]) ).

thf(2129,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ sk81 @ ( F @ r2_hidden ) )
        | ( A @ sk81 @ ( F @ r2_tarski ) )
        | ~ ( A @ sk81 @ ( F @ r1_tarski ) ) )
      & ( ( A @ ( D @ sk82 ) @ ( E @ r2_hidden ) )
        | ~ ( D @ ( E @ r1_tarski ) )
        | ~ ( A @ sk81 @ ( D @ r2_hidden ) ) )
      & ( ( A @ sk81 @ ( A @ ( D @ sk82 ) @ r2_hidden ) )
        | ~ ( A @ sk81 @ ( D @ r2_hidden ) ) )
      & ( ( A @ sk81 @ ( C @ r2_hidden ) )
        | ~ ( B @ ( C @ r1_tarski ) )
        | ~ ( A @ sk81 @ ( B @ r2_hidden ) ) )
      & ( A @ sk81 @ ( A @ r2_hidden ) ) ),
    inference(cnf,[status(esa)],[2128]) ).

thf(2131,plain,
    ! [A: $i] : ( A @ sk81 @ ( A @ r2_hidden ) ),
    inference(cnfConj,[status(thm)],[2129]) ).

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(2109,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(653,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(4824,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)],[653]) ).

thf(661,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(4898,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)],[661]) ).

thf(4899,plain,
    ( ( sk329 @ v1_lattice2 )
    & ( sk329 @ v3_filter_0 )
    & ( sk329 @ v13_lattices )
    & ( sk329 @ v10_lattices )
    & ( sk329 @ v9_lattices )
    & ( sk329 @ v8_lattices )
    & ( sk329 @ v7_lattices )
    & ( sk329 @ v6_lattices )
    & ( sk329 @ v5_lattices )
    & ( sk329 @ v4_lattices )
    & ( sk329 @ v3_lattices )
    & ~ ( sk329 @ v3_struct_0 )
    & ( sk329 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4898]) ).

thf(4909,plain,
    ~ ( sk329 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4899]) ).

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(2031,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(486,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(3930,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)],[486]) ).

thf(1040,plain,
    sk1 @ l3_lattices,
    inference(cnfConj,[status(thm)],[1036]) ).

thf(30307,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ l3_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1040]) ).

thf(30308,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ( sk1 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30307:[bind(A,$thf( sk1 ))]]) ).

thf(299,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(2909,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)],[299]) ).

thf(2910,plain,
    ( ( sk187 @ v3_filter_0 )
    & ( 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)],[2909]) ).

thf(2921,plain,
    sk187 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(331,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(3077,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)],[331]) ).

thf(3078,plain,
    ( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
    & ( k1_xboole_0 @ v1_funct_1 ) ),
    inference(miniscope,[status(thm)],[3077]) ).

thf(3079,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
      & ( k1_xboole_0 @ v1_funct_1 ) ),
    inference(cnf,[status(esa)],[3078]) ).

thf(3080,plain,
    k1_xboole_0 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3079]) ).

thf(8560,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)],[3080,7334]) ).

thf(8561,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)],[8560]) ).

thf(8562,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)],[8561:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15557,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8562,2266]) ).

thf(15558,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15557]) ).

thf(949,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [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(6285,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)],[949]) ).

thf(389,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(3397,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)],[389]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
    <=> ! [B: $i] :
          ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

thf(2979,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)],[312]) ).

thf(2980,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)],[2979]) ).

thf(2981,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C = k1_xboole_0 )
        | ( C @ ( C @ sk194 @ r2_hidden ) ) )
      & ( ~ ( A @ ( B @ r2_hidden ) )
        | ( A != k1_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[2980]) ).

thf(2982,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ r2_hidden ) )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[2981]) ).

thf(2984,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ r2_hidden ) )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[2982]) ).

thf(2985,plain,
    ! [A: $i] :
      ~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[2984]) ).

thf(15221,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk81 @ ( A @ r2_hidden ) )
       != ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2131,2985]) ).

thf(15222,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk81 @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[15221]) ).

thf(15237,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk81 )
       != k1_xboole_0 )
      | ( A != B ) ),
    inference(simp,[status(thm)],[15222]) ).

thf(15242,plain,
    ! [A: $i] :
      ( ( A @ sk81 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[15237]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ 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(3830,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)],[465]) ).

thf(239,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(2499,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)],[239]) ).

thf(892,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(6042,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)],[892]) ).

thf(628,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(4668,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)],[628]) ).

thf(4669,plain,
    ( ( sk315 @ v17_lattices )
    & ( sk315 @ v16_lattices )
    & ( sk315 @ v15_lattices )
    & ( sk315 @ v14_lattices )
    & ( sk315 @ v13_lattices )
    & ( sk315 @ v11_lattices )
    & ( sk315 @ v10_lattices )
    & ( sk315 @ v9_lattices )
    & ( sk315 @ v8_lattices )
    & ( sk315 @ v7_lattices )
    & ( sk315 @ v6_lattices )
    & ( sk315 @ v5_lattices )
    & ( sk315 @ v4_lattices )
    & ( sk315 @ v3_lattices )
    & ~ ( sk315 @ v3_struct_0 )
    & ( sk315 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4668]) ).

thf(4682,plain,
    sk315 @ v11_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(699,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(5131,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)],[699]) ).

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(1549,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(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(1554,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(4904,plain,
    sk329 @ v10_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(1102,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)],[1101]) ).

thf(1110,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)],[1102]) ).

thf(336,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(3095,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)],[336]) ).

thf(3096,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)],[3095]) ).

thf(3098,plain,
    k6_nat_lat @ v4_lattices,
    inference(cnfConj,[status(thm)],[3096]) ).

thf(29811,plain,
    ! [A: $i] :
      ( ( A != k6_nat_lat )
      | ( k1_xboole_0 @ v4_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,3098]) ).

thf(29812,plain,
    ( ( k1_xboole_0 @ v4_lattices )
    | ( k6_nat_lat @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29811:[bind(A,$thf( k6_nat_lat ))]]) ).

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(1156,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(1157,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)],[1156]) ).

thf(1158,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)],[1157]) ).

thf(924,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(6177,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)],[924]) ).

thf(705,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( A @ ( I @ m1_subset_1 ) )
        & ( A @ ( H @ m1_subset_1 ) )
        & ( A @ ( G @ m1_subset_1 ) )
        & ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_domain_1) ).

thf(5168,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( A @ ( I @ m1_subset_1 ) )
        & ( A @ ( H @ m1_subset_1 ) )
        & ( A @ ( G @ m1_subset_1 ) )
        & ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(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(1067,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(1068,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)],[1067]) ).

thf(306,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(2953,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)],[306]) ).

thf(707,axiom,
    ? [A: $i] : ( A @ l2_lattices ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).

thf(5172,plain,
    ? [A: $i] : ( A @ l2_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(5173,plain,
    sk358 @ l2_lattices,
    inference(cnf,[status(esa)],[5172]) ).

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(1140,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(1141,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
       != k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1140]) ).

thf(1142,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
       != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1141]) ).

thf(616,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(4619,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)],[616]) ).

thf(4620,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk313 @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
          = ( A @ f3_s4_funct_2 ) )
        | ~ ( f1_s4_funct_2 @ ( A @ m1_subset_1 ) ) )
      & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
      & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ v1_funct_2 ) ) )
      & ( sk313 @ v1_funct_1 ) ),
    inference(cnf,[status(esa)],[4619]) ).

thf(4623,plain,
    f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ),
    inference(cnfConj,[status(thm)],[4620]) ).

thf(610,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(4580,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)],[610]) ).

thf(4581,plain,
    ( ( sk310 @ v14_lattices )
    & ( sk310 @ v13_lattices )
    & ( sk310 @ v12_lattices )
    & ( sk310 @ v11_lattices )
    & ( sk310 @ v10_lattices )
    & ( sk310 @ v9_lattices )
    & ( sk310 @ v8_lattices )
    & ( sk310 @ v7_lattices )
    & ( sk310 @ v6_lattices )
    & ( sk310 @ v5_lattices )
    & ( sk310 @ v4_lattices )
    & ( sk310 @ v3_lattices )
    & ~ ( sk310 @ v3_struct_0 )
    & ( sk310 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4580]) ).

thf(4592,plain,
    sk310 @ v14_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(218,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(2363,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)],[218]) ).

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(1198,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(1199,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)],[1198]) ).

thf(1200,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)],[1199]) ).

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(1146,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(1147,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)],[1146]) ).

thf(1149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
    inference(cnfConj,[status(thm)],[1147]) ).

thf(15031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,1149]) ).

thf(15032,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15031]) ).

thf(15033,plain,
    f2_s4_funct_2 @ ( sk313 @ k2_relat_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[15032:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk313 ))]]) ).

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(1097,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(1098,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(miniscope,[status(thm)],[1097]) ).

thf(1099,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ ( B @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[1098]) ).

thf(15062,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk313 @ k2_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15033,1099]) ).

thf(15063,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk313 @ k2_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15062]) ).

thf(15064,plain,
    ! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[15063:[bind(A,$thf( sk313 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(15098,plain,
    ! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[15064]) ).

thf(195,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(2202,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)],[195]) ).

thf(2203,plain,
    ( ( sk95 @ v10_lattices )
    & ( sk95 @ v9_lattices )
    & ( sk95 @ v8_lattices )
    & ( sk95 @ v7_lattices )
    & ( sk95 @ v6_lattices )
    & ( sk95 @ v5_lattices )
    & ( sk95 @ v4_lattices )
    & ( sk95 @ v3_lattices )
    & ~ ( sk95 @ v3_struct_0 )
    & ( sk95 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2202]) ).

thf(2210,plain,
    sk95 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

thf(355,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(3204,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(3205,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
    inference(cnf,[status(esa)],[3204]) ).

thf(3206,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) )
      = ( A @ k2_subset_1 ) ),
    inference(lifteq,[status(thm)],[3205]) ).

thf(246,axiom,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).

thf(2543,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(2544,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(cnf,[status(esa)],[2543]) ).

thf(2545,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(lifteq,[status(thm)],[2544]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).

thf(3012,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(3013,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[3012]) ).

thf(3014,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[3013]) ).

thf(38726,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k3_subset_1 ) )
      = A ),
    inference(rewrite,[status(thm)],[3206,2545,3014]) ).

thf(834,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(5820,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)],[834]) ).

thf(910,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ 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(6106,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)],[910]) ).

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(1891,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(1892,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1891]) ).

thf(1893,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1892]) ).

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(1221,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(1222,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != ( A @ ( B @ k4_xboole_0 ) ) ) ),
    inference(cnf,[status(esa)],[1221]) ).

thf(1223,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != ( A @ ( B @ k4_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[1222]) ).

thf(1224,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[1223]) ).

thf(1225,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk14 ) )
      = A ),
    inference(cnf,[status(esa)],[1224]) ).

thf(39164,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk14 ) )
      = A ),
    inference(lifteq,[status(thm)],[1225]) ).

thf(39187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
       != ( C @ ( B @ k4_xboole_0 ) ) )
      | ( ( k1_xboole_0 @ ( C @ sk14 ) )
        = B ) ),
    inference(paramod_ordered,[status(thm)],[1893,39164]) ).

thf(39188,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ sk14 ) )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[39187:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).

thf(595,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(4515,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)],[595]) ).

thf(459,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(3813,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)],[459]) ).

thf(360,axiom,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_xboole_0 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(3228,plain,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_xboole_0 )
      & ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(3229,plain,
    ( ( sk213 @ v1_funct_1 )
    & ( sk213 @ v1_xboole_0 )
    & ( sk213 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[3228]) ).

thf(3230,plain,
    sk213 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3229]) ).

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(1073,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(960,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(6338,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)],[960]) ).

thf(632,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(4711,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)],[632]) ).

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(1202,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(1203,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)],[1202]) ).

thf(1204,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)],[1203]) ).

thf(1205,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)],[1204]) ).

thf(557,axiom,
    ? [A: $i] : ( A @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(4326,plain,
    ? [A: $i] : ( A @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(728,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(5251,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)],[728]) ).

thf(5252,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)],[5251]) ).

thf(5253,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F
          = ( E @ k1_tarski ) )
        | ~ ( F @ ( E @ ( F @ sk367 ) @ r2_hidden ) )
        | ( ( E @ ( F @ sk366 ) )
         != E ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ( ( E @ ( F @ sk367 ) )
          = E )
        | ( ( E @ ( F @ sk366 ) )
         != E ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ~ ( F @ ( E @ ( F @ sk367 ) @ r2_hidden ) )
        | ( F @ ( E @ ( F @ sk366 ) @ r2_hidden ) ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ( ( E @ ( F @ sk367 ) )
          = E )
        | ( F @ ( E @ ( F @ sk366 ) @ r2_hidden ) ) )
      & ( ( B @ ( D @ r2_hidden ) )
        | ( D != A )
        | ( B
         != ( A @ k1_tarski ) ) )
      & ( ( C = A )
        | ~ ( B @ ( C @ r2_hidden ) )
        | ( B
         != ( A @ k1_tarski ) ) ) ),
    inference(cnf,[status(esa)],[5252]) ).

thf(5259,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( C != A )
      | ( B
       != ( A @ k1_tarski ) ) ),
    inference(cnfConj,[status(thm)],[5253]) ).

thf(5264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( C != A )
      | ( B
       != ( A @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[5259]) ).

thf(5265,plain,
    ! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[5264]) ).

thf(289,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(2854,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)],[289]) ).

thf(725,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(5237,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)],[725]) ).

thf(1017,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(6602,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)],[1017]) ).

thf(1037,plain,
    sk1 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ),
    inference(cnfConj,[status(thm)],[1036]) ).

thf(32722,plain,
    ! [A: $i] :
      ( ( A
       != ( sk1 @ u1_struct_0 ) )
      | ( k1_xboole_0 @ ( sk3 @ m1_subset_1 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1037]) ).

thf(32723,plain,
    ( ( k1_xboole_0 @ ( sk3 @ m1_subset_1 ) )
    | ( sk1 @ u1_struct_0 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[32722:[bind(A,$thf( sk1 @ u1_struct_0 ))]]) ).

thf(798,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_0) ).

thf(5614,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(935,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(6214,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)],[935]) ).

thf(1041,plain,
    ~ ( sk1 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[1036]) ).

thf(588,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(4479,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)],[588]) ).

thf(321,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(3017,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)],[321]) ).

thf(971,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [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(6391,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)],[971]) ).

thf(513,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(4090,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)],[513]) ).

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(1756,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(324,axiom,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).

thf(3044,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(685,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(5059,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)],[685]) ).

thf(5060,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)],[5059]) ).

thf(5061,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ sk353 @ ( E @ r2_hidden ) )
        | ( A @ sk353 @ ( E @ r2_tarski ) )
        | ~ ( A @ sk353 @ ( E @ r1_tarski ) ) )
      & ( ( A @ sk353 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
        | ~ ( A @ sk353 @ ( D @ r2_hidden ) ) )
      & ( ( A @ sk353 @ ( C @ r2_hidden ) )
        | ~ ( B @ ( C @ r1_tarski ) )
        | ~ ( A @ sk353 @ ( B @ r2_hidden ) ) )
      & ( A @ sk353 @ ( A @ r2_hidden ) ) ),
    inference(cnf,[status(esa)],[5060]) ).

thf(5062,plain,
    ! [A: $i] : ( A @ sk353 @ ( A @ r2_hidden ) ),
    inference(cnfConj,[status(thm)],[5061]) ).

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(1256,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(1257,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)],[1256]) ).

thf(1258,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)],[1257]) ).

thf(1260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != C )
      | ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[1258]) ).

thf(1262,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
      | ( A != C ) ),
    inference(lifteq,[status(thm)],[1260]) ).

thf(1263,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ r2_hidden ) ),
    inference(simp,[status(thm)],[1262]) ).

thf(38320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk353 @ ( A @ r2_hidden ) )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5062,1263]) ).

thf(38321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk353 @ ( A @ r2_hidden ) )
     != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[38320]) ).

thf(38339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk353 )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[38321]) ).

thf(38352,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
     != ( B @ sk353 ) ),
    inference(simp,[status(thm)],[38339]) ).

thf(1029,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(6655,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)],[1029]) ).

thf(464,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(3826,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( A != B )
        & ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(1042,plain,
    sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ),
    inference(cnfConj,[status(thm)],[1036]) ).

thf(30670,plain,
    ! [A: $i] :
      ( ( A
       != ( sk1 @ u1_struct_0 ) )
      | ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1042]) ).

thf(30671,plain,
    ( ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
    | ( sk1 @ u1_struct_0 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30670:[bind(A,$thf( sk1 @ u1_struct_0 ))]]) ).

thf(476,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(3895,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)],[476]) ).

thf(1025,axiom,
    ? [A: $i] : ( A @ l3_lattices ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).

thf(6640,plain,
    ? [A: $i] : ( A @ l3_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(148,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(1974,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)],[148]) ).

thf(1975,plain,
    ( ( sk72 @ v1_xboole_0 )
    & ( sk72 @ v2_funct_1 )
    & ( sk72 @ v1_funct_1 )
    & ( sk72 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1974]) ).

thf(1977,plain,
    sk72 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[1975]) ).

thf(6966,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)],[1072,1041]) ).

thf(6967,plain,
    ! [A: $i] :
      ( ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[6966:[bind(A,$thf( sk1 ))]]) ).

thf(7278,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)],[6967]) ).

thf(7496,plain,
    ! [A: $i] :
      ( ( ( sk72 @ 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)],[1977,7278]) ).

thf(7497,plain,
    ! [A: $i] :
      ( ( ( sk72 @ 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)],[7496]) ).

thf(7498,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7497:[bind(A,$thf( sk72 ))]]) ).

thf(15659,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7498]) ).

thf(15660,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15659]) ).

thf(15698,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk72 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15660]) ).

thf(15735,plain,
    ( ( sk72 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15698]) ).

thf(8147,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1083,7498]) ).

thf(8148,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8147]) ).

thf(8169,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 )
       != k1_xboole_0 )
      | ( A != sk1 )
      | ( B != sk72 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8148]) ).

thf(8185,plain,
    ( ( ( sk72 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk72 @ k1_relat_1 @ r1_tarski ) )
    | ~ ( sk72 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8169]) ).

thf(1976,plain,
    sk72 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[1975]) ).

thf(38843,plain,
    ( ( ( sk72 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk72 @ k1_relat_1 @ r1_tarski ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8185,1976]) ).

thf(38844,plain,
    ( ( ( sk72 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk72 @ k1_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[38843]) ).

thf(245,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(2538,plain,
    ? [A: $i] :
      ( ( A @ v2_funct_1 )
      & ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(2539,plain,
    ( ( sk139 @ v2_funct_1 )
    & ( sk139 @ v1_funct_1 )
    & ( sk139 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[2538]) ).

thf(2541,plain,
    sk139 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[2539]) ).

thf(8549,plain,
    ! [A: $i] :
      ( ( ( sk139 @ 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)],[2541,7334]) ).

thf(8550,plain,
    ! [A: $i] :
      ( ( ( sk139 @ 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)],[8549]) ).

thf(8551,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8550:[bind(A,$thf( sk139 ))]]) ).

thf(325,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).

thf(3047,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(3048,plain,
    ~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[3047]) ).

thf(3049,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[3048]) ).

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(3745,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(21,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).

thf(1137,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(378,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(3332,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)],[378]) ).

thf(624,axiom,
    ! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(4647,plain,
    ! [A: $i] : ( A @ ( A @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(489,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(3942,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)],[489]) ).

thf(8566,plain,
    ! [A: $i] :
      ( ( ( sk72 @ 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)],[1977,7334]) ).

thf(8567,plain,
    ! [A: $i] :
      ( ( ( sk72 @ 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)],[8566]) ).

thf(8568,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8567:[bind(A,$thf( sk72 ))]]) ).

thf(660,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(4882,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)],[660]) ).

thf(4883,plain,
    ( ( sk328 @ v16_lattices )
    & ( sk328 @ v15_lattices )
    & ( sk328 @ v14_lattices )
    & ( sk328 @ v13_lattices )
    & ( sk328 @ v10_lattices )
    & ( sk328 @ v9_lattices )
    & ( sk328 @ v8_lattices )
    & ( sk328 @ v7_lattices )
    & ( sk328 @ v6_lattices )
    & ( sk328 @ v5_lattices )
    & ( sk328 @ v4_lattices )
    & ( sk328 @ v3_lattices )
    & ~ ( sk328 @ v3_struct_0 )
    & ( sk328 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4882]) ).

thf(4884,plain,
    sk328 @ v9_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(6339,plain,
    ( ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ ( f3_s4_subset_1 @ ( sk450 @ r2_hidden ) )
      | ~ ( sk450 @ p1_s4_subset_1 )
      | sk448 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( sk450 @ p1_s4_subset_1 )
      | ~ ( sk450 @ p1_s4_subset_1 )
      | sk448 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ ( f3_s4_subset_1 @ ( sk450 @ r2_hidden ) )
      | ( f3_s4_subset_1 @ ( sk450 @ r2_hidden ) )
      | sk448 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( sk450 @ p1_s4_subset_1 )
      | ( f3_s4_subset_1 @ ( sk450 @ r2_hidden ) )
      | sk448 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( f1_s4_subset_1 @ ( sk450 @ m1_subset_1 ) )
      | sk448 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk448
      | ~ ( f2_s4_subset_1 @ ( sk449 @ r2_hidden ) )
      | ~ ( sk449 @ p1_s4_subset_1 ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk448
      | ( sk449 @ p1_s4_subset_1 )
      | ~ ( sk449 @ p1_s4_subset_1 ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk448
      | ~ ( f2_s4_subset_1 @ ( sk449 @ r2_hidden ) )
      | ( f2_s4_subset_1 @ ( sk449 @ r2_hidden ) ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk448
      | ( sk449 @ p1_s4_subset_1 )
      | ( f2_s4_subset_1 @ ( sk449 @ r2_hidden ) ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk448
      | ( f1_s4_subset_1 @ ( sk449 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[6338]) ).

thf(6346,plain,
    ( ( f2_s4_subset_1 = f3_s4_subset_1 )
    | ( f1_s4_subset_1 @ ( sk450 @ m1_subset_1 ) )
    | sk448 ),
    inference(cnfConj,[status(thm)],[6339]) ).

thf(6359,plain,
    ( ( f1_s4_subset_1 @ ( sk450 @ m1_subset_1 ) )
    | sk448
    | ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
    inference(lifteq,[status(thm)],[6346]) ).

thf(2918,plain,
    sk187 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

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(1164,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(399,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(3446,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)],[399]) ).

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(1232,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(1233,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)],[1232]) ).

thf(1000,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(6515,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)],[1000]) ).

thf(29739,plain,
    ! [A: $i] :
      ( ( A != sk317 )
      | ( k1_xboole_0 @ v5_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,4729]) ).

thf(29740,plain,
    ( ( k1_xboole_0 @ v5_lattices )
    | ( sk317 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29739:[bind(A,$thf( sk317 ))]]) ).

thf(1044,plain,
    sk1 @ v3_filter_0,
    inference(cnfConj,[status(thm)],[1036]) ).

thf(7142,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ v3_filter_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)],[1072,1044]) ).

thf(7143,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[7142:[bind(A,$thf( sk1 ))]]) ).

thf(7367,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[7143]) ).

thf(8998,plain,
    ! [A: $i] :
      ( ( ( sk72 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1977,7367]) ).

thf(8999,plain,
    ! [A: $i] :
      ( ( ( sk72 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8998]) ).

thf(9000,plain,
    ( ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8999:[bind(A,$thf( sk72 ))]]) ).

thf(236,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(2466,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)],[236]) ).

thf(2467,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)],[2466]) ).

thf(2476,plain,
    k13_nat_lat @ v6_lattices,
    inference(cnfConj,[status(thm)],[2467]) ).

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(2168,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(1007,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ 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(6551,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)],[1007]) ).

thf(404,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(3481,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)],[404]) ).

thf(828,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(5782,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)],[828]) ).

thf(959,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(6336,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)],[959]) ).

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(1053,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(1054,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        | ~ ( B @ ( A @ ( C @ sk4 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        | ~ ( B @ ( A @ ( C @ sk4 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( C @ v1_funct_1 )
        | ~ ( B @ ( A @ ( C @ sk4 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( B @ ( A @ ( C @ sk4 ) ) )
        | ~ ( B @ ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
        | ( ( C @ k1_relat_1 )
         != A )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( B @ ( A @ ( C @ sk4 ) ) )
        | ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ r2_hidden ) )
        | ( ( C @ k1_relat_1 )
         != A )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) ) ),
    inference(cnf,[status(esa)],[1053]) ).

thf(1059,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk4 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
      | ( ( C @ k1_relat_1 )
       != A )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1054]) ).

thf(1062,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk4 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 )
      | ( ( C @ k1_relat_1 )
       != A ) ),
    inference(lifteq,[status(thm)],[1059]) ).

thf(1063,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k1_relat_1 @ ( B @ sk4 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ ( A @ ( B @ sk5 ) ) @ ( B @ k1_funct_1 ) @ r2_hidden ) )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[1062]) ).

thf(144,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).

thf(1954,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(260,axiom,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

thf(2654,plain,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(2655,plain,
    ( ( sk153 @ v1_relat_1 )
    & ( sk153 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[2654]) ).

thf(2656,plain,
    sk153 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[2655]) ).

thf(6801,plain,
    ( ( ( sk361 @ v1_xboole_0 )
     != ( sk153 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2656,5222]) ).

thf(6802,plain,
    ( ( sk361 @ v1_xboole_0 )
   != ( sk153 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6801]) ).

thf(6804,plain,
    sk361 != sk153,
    inference(simp,[status(thm)],[6802]) ).

thf(385,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(3370,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)],[385]) ).

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(1196,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(196,axiom,
    ? [A: $i] :
      ( ( A @ v2_struct_0 )
      & ( A @ l2_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_struct_0) ).

thf(2214,plain,
    ? [A: $i] :
      ( ( A @ v2_struct_0 )
      & ( A @ l2_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(2215,plain,
    ( ( sk96 @ v2_struct_0 )
    & ( sk96 @ l2_struct_0 ) ),
    inference(cnf,[status(esa)],[2214]) ).

thf(2216,plain,
    sk96 @ l2_struct_0,
    inference(cnfConj,[status(thm)],[2215]) ).

thf(528,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(4142,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)],[528]) ).

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(1122,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(1123,plain,
    ( ( ( k1_xboole_0 @ k2_relat_1 )
      = k1_xboole_0 )
    & ( ( k1_xboole_0 @ k1_relat_1 )
      = k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1122]) ).

thf(1125,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1123]) ).

thf(1127,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1125]) ).

thf(7487,plain,
    ! [A: $i] :
      ( ( ( sk204 @ 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)],[3130,7278]) ).

thf(7488,plain,
    ! [A: $i] :
      ( ( ( sk204 @ 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)],[7487]) ).

thf(7489,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7488:[bind(A,$thf( sk204 ))]]) ).

thf(8152,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1083,7489]) ).

thf(8153,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8152]) ).

thf(8170,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 )
       != k1_xboole_0 )
      | ( A != sk1 )
      | ( B != sk204 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8153]) ).

thf(8186,plain,
    ( ( ( sk204 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk204 @ k1_relat_1 @ r1_tarski ) )
    | ~ ( sk204 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8170]) ).

thf(3129,plain,
    sk204 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3128]) ).

thf(40237,plain,
    ( ( ( sk204 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk204 @ k1_relat_1 @ r1_tarski ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8186,3129]) ).

thf(40238,plain,
    ( ( ( sk204 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk204 @ k1_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[40237]) ).

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(2082,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(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(2067,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(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(1254,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(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(1746,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(3103,plain,
    k6_nat_lat @ v10_lattices,
    inference(cnfConj,[status(thm)],[3096]) ).

thf(215,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(2348,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)],[215]) ).

thf(278,axiom,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).

thf(2723,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(3232,plain,
    sk213 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3229]) ).

thf(8563,plain,
    ! [A: $i] :
      ( ( ( sk213 @ 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)],[3232,7334]) ).

thf(8564,plain,
    ! [A: $i] :
      ( ( ( sk213 @ 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)],[8563]) ).

thf(8565,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8564:[bind(A,$thf( sk213 ))]]) ).

thf(15661,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8565]) ).

thf(15662,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15661]) ).

thf(15689,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk213 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15662]) ).

thf(15723,plain,
    ( ( sk213 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15689]) ).

thf(548,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( 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(4266,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)],[548]) ).

thf(412,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(3513,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)],[412]) ).

thf(4679,plain,
    sk315 @ v5_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(334,axiom,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).

thf(3088,plain,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(454,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(3777,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)],[454]) ).

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(1935,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(2540,plain,
    sk139 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[2539]) ).

thf(6896,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk139 @ 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)],[2540,1068]) ).

thf(6897,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk139 @ 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)],[6896]) ).

thf(6898,plain,
    ! [A: $i] : ( sk139 @ k1_relat_1 @ ( sk139 @ k9_relat_1 ) @ ( A @ ( sk139 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6897:[bind(A,$thf( A )),bind(B,$thf( sk139 ))]]) ).

thf(15938,plain,
    ! [A: $i] :
      ( ( ( sk139 @ 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)],[2540,1155]) ).

thf(15939,plain,
    ! [A: $i] :
      ( ( ( sk139 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15938]) ).

thf(15940,plain,
    ( ( sk139 @ k1_relat_1 @ ( sk139 @ k9_relat_1 ) )
    = ( sk139 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15939:[bind(A,$thf( sk139 ))]]) ).

thf(19518,plain,
    ! [A: $i] : ( sk139 @ k2_relat_1 @ ( A @ ( sk139 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6898,15940]) ).

thf(442,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(3730,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)],[442]) ).

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(1645,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(825,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(5770,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)],[825]) ).

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(1601,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(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(1386,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(402,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(3466,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)],[402]) ).

thf(7024,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)],[1072,1040]) ).

thf(7025,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[7024:[bind(A,$thf( sk1 ))]]) ).

thf(7314,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)],[7025]) ).

thf(7854,plain,
    ! [A: $i] :
      ( ( ( sk204 @ 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)],[3130,7314]) ).

thf(7855,plain,
    ! [A: $i] :
      ( ( ( sk204 @ 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)],[7854]) ).

thf(7856,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7855:[bind(A,$thf( sk204 ))]]) ).

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(1724,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(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(1475,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(953,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(6306,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)],[953]) ).

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(1366,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(848,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ k1_filter_2 @ ( A @ k23_filter_2 ) )
          = ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) )
        & ( ( A @ k17_filter_2 @ ( A @ k23_filter_2 ) )
          = ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_filter_2) ).

thf(5874,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ k1_filter_2 @ ( A @ k23_filter_2 ) )
          = ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) )
        & ( ( A @ k17_filter_2 @ ( A @ k23_filter_2 ) )
          = ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(908,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(6102,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)],[908]) ).

thf(7493,plain,
    ! [A: $i] :
      ( ( ( sk213 @ 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)],[3232,7278]) ).

thf(7494,plain,
    ! [A: $i] :
      ( ( ( sk213 @ 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)],[7493]) ).

thf(7495,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7494:[bind(A,$thf( sk213 ))]]) ).

thf(12229,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7495]) ).

thf(12230,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12229]) ).

thf(12324,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk213 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12230]) ).

thf(4327,plain,
    sk293 @ v1_xboole_0,
    inference(cnf,[status(esa)],[4326]) ).

thf(229,axiom,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

thf(2433,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(2434,plain,
    ~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[2433]) ).

thf(2435,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[2434]) ).

thf(9385,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk293 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4327,2435]) ).

thf(9386,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk293 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9385]) ).

thf(9394,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk293 ),
    inference(simp,[status(thm)],[9386]) ).

thf(926,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(6182,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)],[926]) ).

thf(224,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(2405,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)],[224]) ).

thf(264,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(2667,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)],[264]) ).

thf(3045,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[3044]) ).

thf(3046,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[3045]) ).

thf(822,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(5751,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)],[822]) ).

thf(5752,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk410 @ ( 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 @ ( sk410 @ ( 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 @ ( sk410 @ ( 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 @ ( sk410 @ m2_relset_1 ) ) )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) )
      & ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ v1_funct_2 ) ) )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) )
      & ( ( sk410 @ v1_funct_1 )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) ) ),
    inference(cnf,[status(esa)],[5751]) ).

thf(5755,plain,
    ( ( sk410 @ v1_funct_1 )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5752]) ).

thf(5759,plain,
    ( ( sk410 @ v1_funct_1 )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5755]) ).

thf(857,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(5910,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)],[857]) ).

thf(171,axiom,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

thf(2080,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(2081,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    inference(cnf,[status(esa)],[2080]) ).

thf(38990,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk72 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk72 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2081,38844]) ).

thf(38991,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk72 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk72 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[38990]) ).

thf(39014,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( sk72 @ k1_relat_1 )
       != k1_xboole_0 )
      | ( ( sk72 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[38991]) ).

thf(39055,plain,
    ( ( ( sk72 @ k1_relat_1 )
     != k1_xboole_0 )
    | ( ( sk72 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[39014]) ).

thf(240,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(2501,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)],[240]) ).

thf(405,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(3485,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)],[405]) ).

thf(8524,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk153 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2656,3981]) ).

thf(8525,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk153 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8524]) ).

thf(8530,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk153 ),
    inference(simp,[status(thm)],[8525]) ).

thf(11447,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk153 ) ),
    inference(paramod_ordered,[status(thm)],[1957,8530]) ).

thf(11448,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk153 ),
    inference(pattern_uni,[status(thm)],[11447:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(621,axiom,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).

thf(4637,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(4621,plain,
    sk313 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[4620]) ).

thf(8984,plain,
    ! [A: $i] :
      ( ( ( sk313 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4621,7367]) ).

thf(8985,plain,
    ! [A: $i] :
      ( ( ( sk313 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8984]) ).

thf(8986,plain,
    ( ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8985:[bind(A,$thf( sk313 ))]]) ).

thf(12241,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8986]) ).

thf(12242,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12241]) ).

thf(12313,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk313 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[12242]) ).

thf(12351,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[12313]) ).

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(1409,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(823,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(5765,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)],[823]) ).

thf(578,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(4439,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)],[578]) ).

thf(603,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(4546,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)],[603]) ).

thf(495,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(3976,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)],[495]) ).

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(1080,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(1081,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)],[1080]) ).

thf(7942,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1081,7498]) ).

thf(7943,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7942]) ).

thf(7957,plain,
    ! [B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( B @ k1_relat_1 )
       != sk1 )
      | ( B != sk72 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7943]) ).

thf(7969,plain,
    ( ( ( sk72 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk72 @ k2_relat_1 @ r1_tarski ) )
    | ~ ( sk72 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7957]) ).

thf(9988,plain,
    ( ( ( sk72 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk72 @ k2_relat_1 @ r1_tarski ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7969,1976]) ).

thf(9989,plain,
    ( ( ( sk72 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk72 @ k2_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[9988]) ).

thf(30374,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_zfmisc_1 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,8526]) ).

thf(30375,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_zfmisc_1 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[30374]) ).

thf(30376,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ sk20 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[30375:[bind(A,$thf( C @ k1_zfmisc_1 )),bind(B,$thf( C ))]]) ).

thf(33110,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ sk20 @ v1_relat_1 ),
    inference(simp,[status(thm)],[30376]) ).

thf(212,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(2328,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)],[212]) ).

thf(2916,plain,
    sk187 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(394,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(3425,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)],[394]) ).

thf(4896,plain,
    sk328 @ v16_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

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(1430,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(151,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(1985,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)],[151]) ).

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(2039,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(891,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(6039,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)],[891]) ).

thf(272,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(2698,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)],[272]) ).

thf(343,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(3131,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)],[343]) ).

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(1298,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(626,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(4654,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)],[626]) ).

thf(232,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(2444,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)],[232]) ).

thf(2217,plain,
    sk96 @ v2_struct_0,
    inference(cnfConj,[status(thm)],[2215]) ).

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(1826,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(1038,plain,
    ~ ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 ),
    inference(cnfConj,[status(thm)],[1036]) ).

thf(6674,plain,
    ( ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 )
     != ( sk1 @ v3_filter_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1044,1038]) ).

thf(6675,plain,
    ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 )
   != ( sk1 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[6674]) ).

thf(6676,plain,
    ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) )
   != sk1 ),
    inference(simp,[status(thm)],[6675]) ).

thf(524,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(4130,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)],[524]) ).

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(1279,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(698,axiom,
    ? [A: $i] : ( A @ l2_struct_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).

thf(5129,plain,
    ? [A: $i] : ( A @ l2_struct_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(5130,plain,
    sk357 @ l2_struct_0,
    inference(cnf,[status(esa)],[5129]) ).

thf(704,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
              & ( A @ l3_lattices )
              & ( A @ v13_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B
                = ( A @ u1_struct_0 ) )
              & ( B
                = ( A @ k1_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_0) ).

thf(5160,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
              & ( A @ l3_lattices )
              & ( A @ v13_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B
                = ( A @ u1_struct_0 ) )
              & ( B
                = ( A @ k1_filter_0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(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(1455,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(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(3749,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(711,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
        & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice2) ).

thf(5182,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
        & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(470,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(3845,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)],[470]) ).

thf(504,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(4023,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)],[504]) ).

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(1832,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(1184,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ k2_funct_1 ) )
      | ( B @ k1_relat_1 @ ( A @ ( B @ sk12 ) @ 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)],[1183]) ).

thf(1191,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_relat_1 @ ( A @ ( B @ sk12 ) @ 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)],[1184]) ).

thf(1031,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(6662,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)],[1031]) ).

thf(884,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(6006,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)],[884]) ).

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(1992,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(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(2052,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(2053,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
      = ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
    inference(cnf,[status(esa)],[2052]) ).

thf(2054,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
      = ( A @ k1_tarski @ k1_zfmisc_1 ) ),
    inference(lifteq,[status(thm)],[2053]) ).

thf(374,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(3307,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)],[374]) ).

thf(3308,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)],[3307]) ).

thf(3309,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)],[3308]) ).

thf(3311,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
      | ( A
       != ( B @ k1_tarski ) ) ),
    inference(cnfConj,[status(thm)],[3309]) ).

thf(3320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
      | ( A
       != ( B @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[3311]) ).

thf(3321,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(simp,[status(thm)],[3320]) ).

thf(39304,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)],[2054,3321]) ).

thf(39305,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[39304:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(39343,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
    inference(simp,[status(thm)],[39305]) ).

thf(39557,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)],[39343,1099]) ).

thf(39558,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)],[39557]) ).

thf(39559,plain,
    ! [B: $i,A: $i] : ( B @ k1_tarski @ k1_zfmisc_1 @ ( A @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[39558:[bind(A,$thf( G )),bind(B,$thf( k1_xboole_0 @ k1_tarski )),bind(C,$thf( G @ k1_tarski @ k1_zfmisc_1 )),bind(D,$thf( D ))]]) ).

thf(39617,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)],[39559]) ).

thf(4638,plain,
    ~ ? [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[4637]) ).

thf(4639,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[4638]) ).

thf(9595,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk153 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2656,4639]) ).

thf(9596,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk153 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9595]) ).

thf(9603,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk153 ),
    inference(simp,[status(thm)],[9596]) ).

thf(24353,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 )
       != sk153 ) ),
    inference(paramod_ordered,[status(thm)],[2054,9603]) ).

thf(24354,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk153 ),
    inference(pattern_uni,[status(thm)],[24353:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(24386,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk153 ),
    inference(simp,[status(thm)],[24354]) ).

thf(693,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(5108,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)],[693]) ).

thf(575,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(4428,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)],[575]) ).

thf(472,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(3855,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)],[472]) ).

thf(760,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
      <=> ? [B: $i] :
            ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                    = B )
                  & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                    = B ) ) )
            & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattices) ).

thf(5461,plain,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ? [B: $i] :
              ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                      = B )
                    & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                      = B ) ) )
              & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
         => ( A @ v14_lattices ) )
        & ( ( A @ v14_lattices )
         => ? [B: $i] :
              ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                      = B )
                    & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                      = B ) ) )
              & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(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 @ ( 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(6130,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)],[914]) ).

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(1247,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(4622,plain,
    f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ v1_funct_2 ) ),
    inference(cnfConj,[status(thm)],[4620]) ).

thf(762,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).

thf(5480,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(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(1494,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(587,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(4471,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)],[587]) ).

thf(3231,plain,
    sk213 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[3229]) ).

thf(900,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(6071,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)],[900]) ).

thf(820,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(5744,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)],[820]) ).

thf(2420,plain,
    sk119 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2411]) ).

thf(7995,plain,
    ! [A: $i] :
      ( ( ( sk313 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4621,7314]) ).

thf(7996,plain,
    ! [A: $i] :
      ( ( ( sk313 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7995]) ).

thf(7997,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7996:[bind(A,$thf( sk313 ))]]) ).

thf(7860,plain,
    ! [A: $i] :
      ( ( ( sk213 @ 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)],[3232,7314]) ).

thf(7861,plain,
    ! [A: $i] :
      ( ( ( sk213 @ 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)],[7860]) ).

thf(7862,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7861:[bind(A,$thf( sk213 ))]]) ).

thf(886,axiom,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l2_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).

thf(6010,plain,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l2_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(894,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(6049,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)],[894]) ).

thf(3099,plain,
    ~ ( k6_nat_lat @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[3096]) ).

thf(564,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(4353,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)],[564]) ).

thf(795,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v6_group_1 )
      <=> ( A @ k1_lattice2 @ v6_group_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_lattice2) ).

thf(5605,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ k1_lattice2 @ v6_group_1 )
         => ( A @ v6_group_1 ) )
        & ( ( A @ v6_group_1 )
         => ( A @ k1_lattice2 @ v6_group_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(2169,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[2168]) ).

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(1084,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(1085,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
        | ( ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
         != ( A @ ( B @ ( C @ sk7 ) ) ) )
        | ~ ( 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 @ 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 @ ( 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)],[1084]) ).

thf(1087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r1_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 @ ( B @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[1085]) ).

thf(8995,plain,
    ! [A: $i] :
      ( ( ( sk213 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3232,7367]) ).

thf(8996,plain,
    ! [A: $i] :
      ( ( ( sk213 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8995]) ).

thf(8997,plain,
    ( ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8996:[bind(A,$thf( sk213 ))]]) ).

thf(15669,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8997]) ).

thf(15670,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15669]) ).

thf(15692,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk213 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15670]) ).

thf(15727,plain,
    ( ( sk213 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15692]) ).

thf(716,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(5199,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)],[716]) ).

thf(919,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(6149,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)],[919]) ).

thf(7484,plain,
    ! [A: $i] :
      ( ( ( sk139 @ 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)],[2541,7278]) ).

thf(7485,plain,
    ! [A: $i] :
      ( ( ( sk139 @ 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)],[7484]) ).

thf(7486,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7485:[bind(A,$thf( sk139 ))]]) ).

thf(15620,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7486]) ).

thf(15621,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15620]) ).

thf(15705,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk139 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15621]) ).

thf(15742,plain,
    ( ( sk139 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15705]) ).

thf(1021,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(6626,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)],[1021]) ).

thf(533,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(4179,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)],[533]) ).

thf(715,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(5193,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)],[715]) ).

thf(1387,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)],[1386]) ).

thf(1388,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ sk26 ) @ k2_relat_1 @ r1_tarski ) )
        | ( B != k1_xboole_0 ) )
      & ( ( B
          = ( A @ ( B @ sk26 ) @ k1_relat_1 ) )
        | ( B != k1_xboole_0 ) )
      & ( ( A @ ( B @ sk26 ) @ v1_funct_1 )
        | ( B != k1_xboole_0 ) )
      & ( ( A @ ( B @ sk26 ) @ v1_relat_1 )
        | ( B != k1_xboole_0 ) )
      & ( ( A @ ( A @ ( B @ sk26 ) @ k2_relat_1 @ r1_tarski ) )
        | ( A = k1_xboole_0 ) )
      & ( ( B
          = ( A @ ( B @ sk26 ) @ k1_relat_1 ) )
        | ( A = k1_xboole_0 ) )
      & ( ( A @ ( B @ sk26 ) @ v1_funct_1 )
        | ( A = k1_xboole_0 ) )
      & ( ( A @ ( B @ sk26 ) @ v1_relat_1 )
        | ( A = k1_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[1387]) ).

thf(1391,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ sk26 ) @ k2_relat_1 @ r1_tarski ) )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1388]) ).

thf(1397,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ sk26 ) @ k2_relat_1 @ r1_tarski ) )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1391]) ).

thf(1398,plain,
    ! [A: $i] : ( A @ ( A @ ( k1_xboole_0 @ sk26 ) @ k2_relat_1 @ r1_tarski ) ),
    inference(simp,[status(thm)],[1397]) ).

thf(655,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(4830,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)],[655]) ).

thf(4675,plain,
    sk315 @ v7_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(403,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k23_filter_2 ) @ v10_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v9_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v8_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v7_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v6_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v5_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v4_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v3_lattices )
        & ~ ( B @ ( A @ k23_filter_2 ) @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_filter_2) ).

thf(3470,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k23_filter_2 ) @ v10_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v9_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v8_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v7_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v6_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v5_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v4_lattices )
        & ( B @ ( A @ k23_filter_2 ) @ v3_lattices )
        & ~ ( B @ ( A @ k23_filter_2 ) @ v3_struct_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(843,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(5851,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)],[843]) ).

thf(605,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(4551,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)],[605]) ).

thf(527,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).

thf(4140,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(4141,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(cnf,[status(esa)],[4140]) ).

thf(1148,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
    inference(cnfConj,[status(thm)],[1147]) ).

thf(14595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,1148]) ).

thf(14596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14595]) ).

thf(14597,plain,
    f1_s4_funct_2 @ ( sk313 @ k1_relat_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[14596:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk313 ))]]) ).

thf(907,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(6098,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)],[907]) ).

thf(619,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(4632,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)],[619]) ).

thf(467,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(3835,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)],[467]) ).

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(1362,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(147,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(1963,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)],[147]) ).

thf(423,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( A @ ( B @ m2_nat_lat ) )
          <=> ? [C: $i] :
                ( ? [D: $i] :
                    ( ? [E: $i] :
                        ( ( ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) )
                          = ( E @ ( D @ ( C @ g3_lattices ) ) ) )
                        & ( E
                          = ( C @ ( A @ u1_lattices @ k1_realset1 ) ) )
                        & ( D
                          = ( C @ ( A @ u2_lattices @ k1_realset1 ) ) )
                        & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                    & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                & ( A @ ( C @ m2_lattice4 ) )
                & ~ ( C @ v1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_filter_2) ).

thf(3602,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ? [C: $i] :
                  ( ? [D: $i] :
                      ( ? [E: $i] :
                          ( ( ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) )
                            = ( E @ ( D @ ( C @ g3_lattices ) ) ) )
                          & ( E
                            = ( C @ ( A @ u1_lattices @ k1_realset1 ) ) )
                          & ( D
                            = ( C @ ( A @ u2_lattices @ k1_realset1 ) ) )
                          & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                          & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                          & ( E @ v1_funct_1 ) )
                      & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                      & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                      & ( D @ v1_funct_1 ) )
                  & ( A @ ( C @ m2_lattice4 ) )
                  & ~ ( C @ v1_xboole_0 ) )
             => ( A @ ( B @ m2_nat_lat ) ) )
            & ( ( A @ ( B @ m2_nat_lat ) )
             => ? [C: $i] :
                  ( ? [D: $i] :
                      ( ? [E: $i] :
                          ( ( ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) )
                            = ( E @ ( D @ ( C @ g3_lattices ) ) ) )
                          & ( E
                            = ( C @ ( A @ u1_lattices @ k1_realset1 ) ) )
                          & ( D
                            = ( C @ ( A @ u2_lattices @ k1_realset1 ) ) )
                          & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                          & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                          & ( E @ v1_funct_1 ) )
                      & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                      & ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                      & ( D @ v1_funct_1 ) )
                  & ( A @ ( C @ m2_lattice4 ) )
                  & ~ ( C @ v1_xboole_0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
      <=> ? [B: $i] :
            ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                    = B )
                  & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                    = B ) ) )
            & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).

thf(3557,plain,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ? [B: $i] :
              ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                      = B )
                    & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                      = B ) ) )
              & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) )
         => ( A @ v13_lattices ) )
        & ( ( A @ v13_lattices )
         => ? [B: $i] :
              ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                      = B )
                    & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                      = B ) ) )
              & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(221,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(2388,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)],[221]) ).

thf(992,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(6487,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)],[992]) ).

thf(243,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(2533,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)],[243]) ).

thf(366,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(3258,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)],[366]) ).

thf(968,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice4) ).

thf(6382,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)],[968]) ).

thf(1014,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(6594,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)],[1014]) ).

thf(1979,plain,
    sk72 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[1975]) ).

thf(9573,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk72 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1979,3049]) ).

thf(9574,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk72 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9573]) ).

thf(9580,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk72 ),
    inference(simp,[status(thm)],[9574]) ).

thf(2657,plain,
    sk153 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[2655]) ).

thf(15952,plain,
    ! [A: $i] :
      ( ( ( sk153 @ 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)],[2657,1155]) ).

thf(15953,plain,
    ! [A: $i] :
      ( ( ( sk153 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15952]) ).

thf(15954,plain,
    ( ( sk153 @ k1_relat_1 @ ( sk153 @ k9_relat_1 ) )
    = ( sk153 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15953:[bind(A,$thf( sk153 ))]]) ).

thf(455,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(3788,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)],[455]) ).

thf(4595,plain,
    sk310 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(830,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v17_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
      <=> ( ( A @ k1_lattice2 @ l3_lattices )
          & ( A @ k1_lattice2 @ v17_lattices )
          & ( A @ k1_lattice2 @ v10_lattices )
          & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_2) ).

thf(5792,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( ( A @ k1_lattice2 @ l3_lattices )
            & ( A @ k1_lattice2 @ v17_lattices )
            & ( A @ k1_lattice2 @ v10_lattices )
            & ~ ( A @ k1_lattice2 @ v3_struct_0 ) )
         => ( ( A @ l3_lattices )
            & ( A @ v17_lattices )
            & ( A @ v10_lattices )
            & ~ ( A @ v3_struct_0 ) ) )
        & ( ( ( A @ l3_lattices )
            & ( A @ v17_lattices )
            & ( A @ v10_lattices )
            & ~ ( A @ v3_struct_0 ) )
         => ( ( A @ k1_lattice2 @ l3_lattices )
            & ( A @ k1_lattice2 @ v17_lattices )
            & ( A @ k1_lattice2 @ v10_lattices )
            & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(810,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(5682,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)],[810]) ).

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(1946,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(503,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(4018,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)],[503]) ).

thf(612,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(4600,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)],[612]) ).

thf(651,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(4820,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)],[651]) ).

thf(438,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(3702,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)],[438]) ).

thf(4724,plain,
    sk317 @ v14_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(700,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(5135,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)],[700]) ).

thf(747,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ ( B @ ( A @ k12_filter_2 ) @ m2_lattice4 ) )
        & ~ ( B @ ( A @ k12_filter_2 ) @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_filter_2) ).

thf(5360,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ ( B @ ( A @ k12_filter_2 ) @ m2_lattice4 ) )
        & ~ ( B @ ( A @ k12_filter_2 ) @ v1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(607,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(4556,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)],[607]) ).

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(2007,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(763,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).

thf(5483,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(5484,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    inference(cnf,[status(esa)],[5483]) ).

thf(19093,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)],[1957,5484]) ).

thf(19094,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[19093:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(244,axiom,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).

thf(2536,plain,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(2537,plain,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[2536]) ).

thf(19206,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ),
    inference(rewrite,[status(thm)],[19094,2537]) ).

thf(943,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( 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(6259,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)],[943]) ).

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(1415,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(2917,plain,
    sk187 @ v3_filter_0,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(6838,plain,
    ( ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 )
     != ( sk187 @ v3_filter_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2917,1038]) ).

thf(6839,plain,
    ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 )
   != ( sk187 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[6838]) ).

thf(6840,plain,
    ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) )
   != sk187 ),
    inference(simp,[status(thm)],[6839]) ).

thf(851,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(5892,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)],[851]) ).

thf(4583,plain,
    sk310 @ v11_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

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(2027,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(939,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(6227,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)],[939]) ).

thf(775,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ? [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
              & ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_0) ).

thf(5526,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ? [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
              & ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(488,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(3934,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)],[488]) ).

thf(4903,plain,
    sk329 @ v4_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(688,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(5084,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)],[688]) ).

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(1811,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(3746,plain,
    ! [A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
      & ( A @ k1_zfmisc_1 @ ( A @ sk251 @ m1_subset_1 ) ) ),
    inference(cnf,[status(esa)],[3745]) ).

thf(3748,plain,
    ! [A: $i] : ( A @ sk251 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[3746]) ).

thf(12816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk251 @ v1_xboole_0 )
       != ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3748,2435]) ).

thf(12817,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
     != ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12816]) ).

thf(12828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk251 )
     != ( C @ ( B @ k4_tarski ) ) ),
    inference(simp,[status(thm)],[12817]) ).

thf(1103,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)],[1101]) ).

thf(1109,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)],[1103]) ).

thf(1030,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(6657,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)],[1030]) ).

thf(552,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(4297,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)],[552]) ).

thf(2469,plain,
    k13_nat_lat @ v8_lattices,
    inference(cnfConj,[status(thm)],[2467]) ).

thf(4733,plain,
    sk317 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(4902,plain,
    sk329 @ v3_filter_0,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(9223,plain,
    ( ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 )
     != ( sk329 @ v3_filter_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4902,1038]) ).

thf(9224,plain,
    ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) @ v3_filter_0 )
   != ( sk329 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[9223]) ).

thf(9225,plain,
    ( ( sk3 @ ( sk2 @ ( sk1 @ k22_filter_2 ) ) @ ( sk1 @ k23_filter_2 ) )
   != sk329 ),
    inference(simp,[status(thm)],[9224]) ).

thf(1002,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(6523,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)],[1002]) ).

thf(415,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(3521,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)],[415]) ).

thf(3522,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)],[3521]) ).

thf(3523,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 @ sk233 ) ) @ r2_hidden ) )
        | ( H @ ( G @ ( F @ sk231 ) ) ) )
      & ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ( ( F @ ( G @ ( H @ sk233 ) ) )
          = G )
        | ( ( F @ ( G @ ( H @ sk233 ) ) )
          = F )
        | ( H @ ( G @ ( F @ sk231 ) ) ) )
      & ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ~ ( H @ ( G @ ( F @ sk231 ) ) )
        | ( ( F @ ( G @ ( H @ sk232 ) ) )
         != G ) )
      & ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ~ ( H @ ( G @ ( F @ sk231 ) ) )
        | ( ( F @ ( G @ ( H @ sk232 ) ) )
         != F ) )
      & ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ~ ( H @ ( G @ ( F @ sk231 ) ) )
        | ( H @ ( F @ ( G @ ( H @ sk232 ) ) @ 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)],[3522]) ).

thf(3530,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != A )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(cnfConj,[status(thm)],[3523]) ).

thf(3532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != A )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(lifteq,[status(thm)],[3530]) ).

thf(3533,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[3532]) ).

thf(26743,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)],[3533,2985]) ).

thf(26744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[26743]) ).

thf(26780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) )
       != k1_xboole_0 )
      | ( A != C ) ),
    inference(simp,[status(thm)],[26744]) ).

thf(26793,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[26780]) ).

thf(31932,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( B @ ( C @ k2_tarski ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,26793]) ).

thf(31933,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( B @ ( C @ k2_tarski ) ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[31932]) ).

thf(31934,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk20 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[31933:[bind(A,$thf( E @ ( D @ k2_tarski ) )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).

thf(32982,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk20 @ v1_relat_1 ),
    inference(simp,[status(thm)],[31934]) ).

thf(200,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(2236,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)],[200]) ).

thf(1005,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(6534,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)],[1005]) ).

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(1128,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(1129,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)],[1128]) ).

thf(1132,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)],[1129]) ).

thf(1136,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)],[1132]) ).

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(1864,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(509,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(4050,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)],[509]) ).

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(2122,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(424,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(3621,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)],[424]) ).

thf(1978,plain,
    sk72 @ v2_funct_1,
    inference(cnfConj,[status(thm)],[1975]) ).

thf(301,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(2925,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)],[301]) ).

thf(494,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(3973,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)],[494]) ).

thf(7923,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1081,7495]) ).

thf(7924,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7923]) ).

thf(7954,plain,
    ! [B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( B @ k1_relat_1 )
       != sk1 )
      | ( B != sk213 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7924]) ).

thf(7966,plain,
    ( ( ( sk213 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk213 @ k2_relat_1 @ r1_tarski ) )
    | ~ ( sk213 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7954]) ).

thf(9638,plain,
    ( ( ( sk213 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk213 @ k2_relat_1 @ r1_tarski ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7966,3230]) ).

thf(9639,plain,
    ( ( ( sk213 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk213 @ k2_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[9638]) ).

thf(12771,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk213 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk213 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2081,9639]) ).

thf(12772,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk213 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk213 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12771]) ).

thf(12784,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( sk213 @ k2_relat_1 )
       != k1_xboole_0 )
      | ( ( sk213 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12772]) ).

thf(12794,plain,
    ( ( ( sk213 @ k2_relat_1 )
     != k1_xboole_0 )
    | ( ( sk213 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12784]) ).

thf(7857,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)],[3080,7314]) ).

thf(7858,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)],[7857]) ).

thf(7859,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)],[7858:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15553,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7859,2266]) ).

thf(15554,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15553]) ).

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(1383,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(525,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( 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(4134,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)],[525]) ).

thf(383,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(3357,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)],[383]) ).

thf(418,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_tarski ) )
      = ( A @ ( B @ k2_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(3569,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_tarski ) )
      = ( A @ ( B @ k2_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(8016,plain,
    ! [A: $i] :
      ( ( ( sk313 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4621,7278]) ).

thf(8017,plain,
    ! [A: $i] :
      ( ( ( sk313 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8016]) ).

thf(8018,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8017:[bind(A,$thf( sk313 ))]]) ).

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(2034,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(1010,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(6559,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)],[1010]) ).

thf(519,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(4115,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)],[519]) ).

thf(5758,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ v1_funct_2 ) ) )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5752]) ).

thf(5761,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ v1_funct_2 ) ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5758]) ).

thf(629,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(4686,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)],[629]) ).

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(3771,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(1011,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(6562,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)],[1011]) ).

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(2017,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(838,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(5834,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)],[838]) ).

thf(1165,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)],[1164]) ).

thf(1166,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)],[1165]) ).

thf(1168,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)],[1166]) ).

thf(1169,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)],[1168]) ).

thf(744,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
                          = ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
                       => ( ( ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) )
                            = ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice2) ).

thf(5353,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
                          = ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
                       => ( ( ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) )
                            = ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(443,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(3739,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)],[443]) ).

thf(749,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ~ ( ( C @ ( E @ r2_hidden ) )
              <=> ( D @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).

thf(5370,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( ? [E: $i] :
              ( ~ ( ( ( D @ ( E @ r2_hidden ) )
                   => ( C @ ( E @ r2_hidden ) ) )
                  & ( ( C @ ( E @ r2_hidden ) )
                   => ( D @ ( E @ r2_hidden ) ) ) )
              & ( A = E )
              & ( B @ ( E @ m1_subset_1 ) ) )
         => ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) ) )
        & ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
         => ? [E: $i] :
              ( ~ ( ( ( D @ ( E @ r2_hidden ) )
                   => ( C @ ( E @ r2_hidden ) ) )
                  & ( ( C @ ( E @ r2_hidden ) )
                   => ( D @ ( E @ r2_hidden ) ) ) )
              & ( A = E )
              & ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(6893,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk153 @ 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)],[2657,1068]) ).

thf(6894,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk153 @ 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)],[6893]) ).

thf(6895,plain,
    ! [A: $i] : ( sk153 @ k1_relat_1 @ ( sk153 @ k9_relat_1 ) @ ( A @ ( sk153 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6894:[bind(A,$thf( A )),bind(B,$thf( sk153 ))]]) ).

thf(19263,plain,
    ! [A: $i] : ( sk153 @ k2_relat_1 @ ( A @ ( sk153 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6895,15954]) ).

thf(994,axiom,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).

thf(6496,plain,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(6497,plain,
    ( ( sk462 @ v3_lattices )
    & ~ ( sk462 @ v3_struct_0 )
    & ( sk462 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[6496]) ).

thf(6498,plain,
    sk462 @ l3_lattices,
    inference(cnfConj,[status(thm)],[6497]) ).

thf(554,axiom,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).

thf(4307,plain,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(506,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(4038,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)],[506]) ).

thf(376,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(3327,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)],[376]) ).

thf(15625,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7495]) ).

thf(15626,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15625]) ).

thf(15701,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk213 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15626]) ).

thf(15738,plain,
    ( ( sk213 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15701]) ).

thf(474,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(3870,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)],[474]) ).

thf(683,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(5040,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)],[683]) ).

thf(5041,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk351 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
          = ( A @ f3_s13_funct_2 ) )
        | ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
        | ~ sk349 )
      & ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk351 @ m2_relset_1 ) ) )
        | ~ sk349 )
      & ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk351 @ v1_funct_2 ) ) )
        | ~ sk349 )
      & ( ( sk351 @ v1_funct_1 )
        | ~ sk349 )
      & ( sk349
        | ~ ( f2_s13_funct_2 @ ( sk350 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
      & ( sk349
        | ( f1_s13_funct_2 @ ( sk350 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[5040]) ).

thf(5045,plain,
    ( sk349
    | ( f1_s13_funct_2 @ ( sk350 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[5041]) ).

thf(7408,plain,
    ( ( ( sk361 @ v1_xboole_0 )
     != ( sk213 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3231,5222]) ).

thf(7409,plain,
    ( ( sk361 @ v1_xboole_0 )
   != ( sk213 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7408]) ).

thf(7413,plain,
    sk361 != sk213,
    inference(simp,[status(thm)],[7409]) ).

thf(786,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_0) ).

thf(5572,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)],[786]) ).

thf(12174,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8551]) ).

thf(12175,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12174]) ).

thf(12330,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk139 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12175]) ).

thf(9583,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3043,4639]) ).

thf(9584,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9583]) ).

thf(9600,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[9584]) ).

thf(24380,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)],[2054,9600]) ).

thf(24381,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[24380:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(24401,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[24381]) ).

thf(498,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(3986,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)],[498]) ).

thf(861,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(5929,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)],[861]) ).

thf(2364,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( A @ ( B @ sk112 ) @ v1_funct_2 ) ) )
      & ( A @ ( B @ sk112 ) @ v1_funct_1 )
      & ( A @ ( B @ sk112 ) @ v1_relat_1 )
      & ( B @ ( A @ ( A @ ( B @ sk112 ) @ m1_relset_1 ) ) ) ),
    inference(cnf,[status(esa)],[2363]) ).

thf(2367,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk112 ) @ v1_funct_1 ),
    inference(cnfConj,[status(thm)],[2364]) ).

thf(230,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(2436,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(2437,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
    inference(cnf,[status(esa)],[2436]) ).

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(1928,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(981,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(6451,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)],[981]) ).

thf(1023,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(6631,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)],[1023]) ).

thf(656,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(4842,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)],[656]) ).

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(1209,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(1210,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ v3_binop_1 ) )
        | ( ( A @ ( B @ sk13 ) @ ( A @ ( B @ sk13 ) @ ( B @ k1_binop_1 ) ) )
         != ( A @ ( B @ sk13 ) ) )
        | ~ ( 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 @ sk13 ) @ 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)],[1209]) ).

thf(1213,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ v3_binop_1 ) )
      | ( ( A @ ( B @ sk13 ) @ ( A @ ( B @ sk13 ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ sk13 ) ) )
      | ~ ( 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)],[1210]) ).

thf(1215,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 @ sk13 ) @ ( A @ ( B @ sk13 ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ sk13 ) ) ) ),
    inference(lifteq,[status(thm)],[1213]) ).

thf(12818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk251 @ v1_xboole_0 )
       != ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3748,4639]) ).

thf(12819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
     != ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12818]) ).

thf(12824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk251 )
     != ( C @ ( B @ k2_tarski ) ) ),
    inference(simp,[status(thm)],[12819]) ).

thf(912,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(6110,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)],[912]) ).

thf(826,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(5772,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)],[826]) ).

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(1114,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(1115,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)],[1114]) ).

thf(1117,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)],[1115]) ).

thf(1119,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)],[1117]) ).

thf(228,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(2424,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)],[228]) ).

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(1111,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(1112,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)],[1111]) ).

thf(1113,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)],[1112]) ).

thf(14629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk313 @ k1_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[14597,1113]) ).

thf(14630,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk313 @ k1_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14629]) ).

thf(14631,plain,
    ! [A: $i] : ( sk313 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14630:[bind(A,$thf( sk313 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14658,plain,
    ! [A: $i] : ( sk313 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14631]) ).

thf(732,axiom,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(5291,plain,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(5292,plain,
    ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[5291]) ).

thf(5293,plain,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[5292]) ).

thf(8678,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk213 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3231,5293]) ).

thf(8679,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk213 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8678]) ).

thf(8691,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk213 ),
    inference(simp,[status(thm)],[8679]) ).

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(3756,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(601,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(4536,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)],[601]) ).

thf(362,axiom,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).

thf(3240,plain,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(3241,plain,
    ( ( sk215 @ v1_relat_1 )
    & ~ ( sk215 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[3240]) ).

thf(3243,plain,
    sk215 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3241]) ).

thf(623,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(4643,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)],[623]) ).

thf(1201,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)],[1199]) ).

thf(8124,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1083,7486]) ).

thf(8125,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8124]) ).

thf(8163,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 )
       != k1_xboole_0 )
      | ( A != sk1 )
      | ( B != sk139 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8125]) ).

thf(8179,plain,
    ( ( ( sk139 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk139 @ k1_relat_1 @ r1_tarski ) )
    | ~ ( sk139 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8163]) ).

thf(28932,plain,
    ( ( ( sk139 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk139 @ k1_relat_1 @ r1_tarski ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8179,2540]) ).

thf(28933,plain,
    ( ( ( sk139 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk139 @ k1_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[28932]) ).

thf(29052,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk139 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk139 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2081,28933]) ).

thf(29053,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk139 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk139 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[29052]) ).

thf(29088,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( sk139 @ k1_relat_1 )
       != k1_xboole_0 )
      | ( ( sk139 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[29053]) ).

thf(29099,plain,
    ( ( ( sk139 @ k1_relat_1 )
     != k1_xboole_0 )
    | ( ( sk139 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[29088]) ).

thf(309,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(2965,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)],[309]) ).

thf(8552,plain,
    ! [A: $i] :
      ( ( ( sk313 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4621,7334]) ).

thf(8553,plain,
    ! [A: $i] :
      ( ( ( sk313 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8552]) ).

thf(8554,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8553:[bind(A,$thf( sk313 ))]]) ).

thf(4892,plain,
    sk328 @ v4_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(4588,plain,
    ~ ( sk310 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4581]) ).

thf(479,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(3906,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)],[479]) ).

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(1521,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(618,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(4628,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)],[618]) ).

thf(538,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k23_filter_2 ) @ u1_lattices )
              = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
            & ( ( B @ ( A @ k23_filter_2 ) @ u2_lattices )
              = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
            & ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_filter_2) ).

thf(4211,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k23_filter_2 ) @ u1_lattices )
              = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
            & ( ( B @ ( A @ k23_filter_2 ) @ u2_lattices )
              = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
            & ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(408,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(3492,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)],[408]) ).

thf(390,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(3406,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)],[390]) ).

thf(2205,plain,
    ~ ( sk95 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2203]) ).

thf(352,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v5_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_partfun1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
        & ( A @ u2_lattices @ v1_funct_1 )
        & ( A @ u2_lattices @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattice2) ).

thf(3184,plain,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v5_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_partfun1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
        & ( A @ u2_lattices @ v1_funct_1 )
        & ( A @ u2_lattices @ v1_relat_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(251,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(2586,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)],[251]) ).

thf(294,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

thf(2884,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(589,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(4483,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)],[589]) ).

thf(411,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(3510,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)],[411]) ).

thf(511,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(4065,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)],[511]) ).

thf(815,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).

thf(5695,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(987,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(6474,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)],[987]) ).

thf(387,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(3378,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)],[387]) ).

thf(680,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(5012,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)],[680]) ).

thf(756,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(5443,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)],[756]) ).

thf(898,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(6064,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)],[898]) ).

thf(871,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(5968,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)],[871]) ).

thf(970,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(6388,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)],[970]) ).

thf(8516,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk213 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3231,3981]) ).

thf(8517,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk213 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8516]) ).

thf(8528,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk213 ),
    inference(simp,[status(thm)],[8517]) ).

thf(11455,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk213 ) ),
    inference(paramod_ordered,[status(thm)],[1957,8528]) ).

thf(11456,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk213 ),
    inference(pattern_uni,[status(thm)],[11455:[bind(A,$thf( k1_xboole_0 ))]]) ).

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(1604,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(29842,plain,
    ! [A: $i] :
      ( ( A != sk310 )
      | ( k1_xboole_0 @ v14_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,4592]) ).

thf(29843,plain,
    ( ( k1_xboole_0 @ v14_lattices )
    | ( sk310 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29842:[bind(A,$thf( sk310 ))]]) ).

thf(300,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(2922,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)],[300]) ).

thf(708,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
        = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).

thf(5174,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
        = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(347,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(3151,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)],[347]) ).

thf(3097,plain,
    k6_nat_lat @ v6_lattices,
    inference(cnfConj,[status(thm)],[3096]) ).

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(1234,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(1235,plain,
    ! [A: $i] :
      ( ( ~ ( A @ k1_tarski @ ( sk15 @ k4_xboole_0 ) @ v1_xboole_0 )
        | ~ ( sk15 @ ( A @ m1_subset_1 ) ) )
      & ~ ( sk15 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1234]) ).

thf(1236,plain,
    ~ ( sk15 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1235]) ).

thf(6852,plain,
    ( ( ( sk15 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3043,1236]) ).

thf(6853,plain,
    ( ( sk15 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6852]) ).

thf(6856,plain,
    sk15 != k1_xboole_0,
    inference(simp,[status(thm)],[6853]) ).

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(1206,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(614,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(4604,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)],[614]) ).

thf(4893,plain,
    sk328 @ v14_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(556,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D != k1_xboole_0 )
                       => ( ( E @ ( D @ ( A @ ( C @ 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(4323,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)],[556]) ).

thf(1043,plain,
    sk3 @ ( sk2 @ ( sk1 @ r3_lattices ) ),
    inference(cnfConj,[status(thm)],[1036]) ).

thf(31449,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk3 @ ( sk2 @ ( k1_xboole_0 @ r3_lattices ) ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1043]) ).

thf(31450,plain,
    ( ( sk3 @ ( sk2 @ ( k1_xboole_0 @ r3_lattices ) ) )
    | ( sk1 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[31449:[bind(A,$thf( sk1 ))]]) ).

thf(2204,plain,
    sk95 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

thf(776,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                  = C ) )
           => ( B
              = ( A @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice2) ).

thf(5530,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                  = C ) )
           => ( B
              = ( A @ k6_lattices ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(4589,plain,
    sk310 @ v8_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(2473,plain,
    k13_nat_lat @ v9_lattices,
    inference(cnfConj,[status(thm)],[2467]) ).

thf(250,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(2574,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)],[250]) ).

thf(4888,plain,
    sk328 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

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(1438,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(840,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [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(5839,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)],[840]) ).

thf(755,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m2_nat_lat ) )
             => ( ( C
                  = ( B @ ( A @ k23_filter_2 ) ) )
              <=> ? [D: $i] :
                    ( ? [E: $i] :
                        ( ( C
                          = ( E @ ( D @ ( B @ g3_lattices ) ) ) )
                        & ( E
                          = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
                        & ( D
                          = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                    & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_filter_2) ).

thf(5411,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m2_nat_lat ) )
             => ( ( ? [D: $i] :
                      ( ? [E: $i] :
                          ( ( C
                            = ( E @ ( D @ ( B @ g3_lattices ) ) ) )
                          & ( E
                            = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
                          & ( D
                            = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
                          & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                          & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                          & ( E @ v1_funct_1 ) )
                      & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                      & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                      & ( D @ v1_funct_1 ) )
                 => ( C
                    = ( B @ ( A @ k23_filter_2 ) ) ) )
                & ( ( C
                    = ( B @ ( A @ k23_filter_2 ) ) )
                 => ? [D: $i] :
                      ( ? [E: $i] :
                          ( ( C
                            = ( E @ ( D @ ( B @ g3_lattices ) ) ) )
                          & ( E
                            = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
                          & ( D
                            = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
                          & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                          & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                          & ( E @ v1_funct_1 ) )
                      & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                      & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                      & ( D @ v1_funct_1 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(29756,plain,
    ! [A: $i] :
      ( ( A != sk315 )
      | ( k1_xboole_0 @ v11_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,4682]) ).

thf(29757,plain,
    ( ( k1_xboole_0 @ v11_lattices )
    | ( sk315 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29756:[bind(A,$thf( sk315 ))]]) ).

thf(349,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(3169,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)],[349]) ).

thf(951,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(6296,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)],[951]) ).

thf(367,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(3265,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)],[367]) ).

thf(259,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(2646,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)],[259]) ).

thf(599,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ ( A @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(4531,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ ( A @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(12184,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7997]) ).

thf(12185,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12184]) ).

thf(12293,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk313 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12185]) ).

thf(12333,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12293]) ).

thf(567,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(4370,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)],[567]) ).

thf(19285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk153 @ k2_relat_1 @ ( A @ ( sk153 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19263,1099]) ).

thf(19286,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk153 @ k2_relat_1 @ ( A @ ( sk153 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[19285]) ).

thf(19287,plain,
    ! [B: $i,A: $i] : ( sk153 @ k2_relat_1 @ ( A @ ( B @ ( sk153 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[19286:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk153 @ k9_relat_1 ) )),bind(C,$thf( sk153 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(19329,plain,
    ! [B: $i,A: $i] : ( sk153 @ k2_relat_1 @ ( A @ ( B @ ( sk153 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[19287]) ).

thf(4910,plain,
    sk329 @ v5_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(772,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_2 ) )
         => ( ( B @ ( A @ k8_filter_0 ) )
            = ( B @ ( A @ k23_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_2) ).

thf(5519,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_2 ) )
         => ( ( B @ ( A @ k8_filter_0 ) )
            = ( B @ ( A @ k23_filter_2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(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(1736,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(531,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(4172,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)],[531]) ).

thf(731,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(5281,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)],[731]) ).

thf(665,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(4925,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)],[665]) ).

thf(905,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(6092,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)],[905]) ).

thf(1057,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
      | ~ ( B @ ( A @ ( C @ sk4 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1054]) ).

thf(930,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(6200,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)],[930]) ).

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(1161,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(1162,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)],[1161]) ).

thf(1163,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)],[1162]) ).

thf(1028,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(6652,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)],[1028]) ).

thf(663,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(4915,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)],[663]) ).

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(1091,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(883,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(6000,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)],[883]) ).

thf(889,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(6032,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)],[889]) ).

thf(743,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ k1_filter_0 )
          = ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_0) ).

thf(5349,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ k1_filter_0 )
          = ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(5757,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ m2_relset_1 ) ) )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5752]) ).

thf(5762,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ m2_relset_1 ) ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5757]) ).

thf(15040,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ 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)],[5762,1149]) ).

thf(15041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ 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)],[15040]) ).

thf(15042,plain,
    ( ( f2_s11_funct_2 @ ( sk410 @ k2_relat_1 @ r1_tarski ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[15041:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk410 ))]]) ).

thf(16216,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( sk410 @ 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)],[15042,1099]) ).

thf(16217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( sk410 @ 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)],[16216]) ).

thf(16218,plain,
    ! [A: $i] :
      ( ( f2_s11_funct_2 @ ( A @ ( sk410 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[16217:[bind(A,$thf( sk410 @ k2_relat_1 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( C ))]]) ).

thf(16264,plain,
    ! [A: $i] :
      ( ( f2_s11_funct_2 @ ( A @ ( sk410 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[16218]) ).

thf(29746,plain,
    ! [A: $i] :
      ( ( A != sk361 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,6855]) ).

thf(29747,plain,
    ! [A: $i] :
      ( ( A != sk361 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[29746]) ).

thf(29748,plain,
    sk361 @ sk20 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[29747:[bind(A,$thf( sk361 ))]]) ).

thf(33601,plain,
    ! [A: $i] :
      ( ( ( sk361 @ sk20 @ 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)],[29748,1155]) ).

thf(33602,plain,
    ! [A: $i] :
      ( ( ( sk361 @ sk20 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[33601]) ).

thf(33603,plain,
    ( ( sk361 @ sk20 @ k1_relat_1 @ ( sk361 @ sk20 @ k9_relat_1 ) )
    = ( sk361 @ sk20 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[33602:[bind(A,$thf( sk361 @ sk20 ))]]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_binop_1) ).

thf(3233,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( ! [D: $i] :
                      ( ( A @ ( D @ m1_subset_1 ) )
                     => ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                        = D ) )
                 => ( C @ ( B @ ( A @ r2_binop_1 ) ) ) )
                & ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
                 => ! [D: $i] :
                      ( ( A @ ( D @ m1_subset_1 ) )
                     => ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                        = D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(356,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
    <=> ( ( D @ ( B @ r2_hidden ) )
        & ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).

thf(3207,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( D @ ( B @ r2_hidden ) )
          & ( C @ ( A @ r2_hidden ) ) )
       => ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
      & ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( D @ ( B @ r2_hidden ) )
          & ( C @ ( A @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(508,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(4044,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)],[508]) ).

thf(684,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(5049,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)],[684]) ).

thf(252,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(2589,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)],[252]) ).

thf(903,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( 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(6079,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)],[903]) ).

thf(255,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(2601,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)],[255]) ).

thf(502,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(4016,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)],[502]) ).

thf(285,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(2805,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)],[285]) ).

thf(1018,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(6605,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)],[1018]) ).

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(1519,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(253,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(2596,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(473,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(3867,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)],[473]) ).

thf(6904,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk72 @ 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)],[1976,1068]) ).

thf(6905,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk72 @ 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)],[6904]) ).

thf(6906,plain,
    ! [A: $i] : ( sk72 @ k1_relat_1 @ ( sk72 @ k9_relat_1 ) @ ( A @ ( sk72 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6905:[bind(A,$thf( A )),bind(B,$thf( sk72 ))]]) ).

thf(15974,plain,
    ! [A: $i] :
      ( ( ( sk72 @ 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)],[1976,1155]) ).

thf(15975,plain,
    ! [A: $i] :
      ( ( ( sk72 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15974]) ).

thf(15976,plain,
    ( ( sk72 @ k1_relat_1 @ ( sk72 @ k9_relat_1 ) )
    = ( sk72 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15975:[bind(A,$thf( sk72 ))]]) ).

thf(21571,plain,
    ! [A: $i] : ( sk72 @ k2_relat_1 @ ( A @ ( sk72 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6906,15976]) ).

thf(21592,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk72 @ k2_relat_1 @ ( A @ ( sk72 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21571,1099]) ).

thf(21593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk72 @ k2_relat_1 @ ( A @ ( sk72 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[21592]) ).

thf(21594,plain,
    ! [B: $i,A: $i] : ( sk72 @ k2_relat_1 @ ( A @ ( B @ ( sk72 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[21593:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk72 @ k9_relat_1 ) )),bind(C,$thf( sk72 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(21646,plain,
    ! [B: $i,A: $i] : ( sk72 @ k2_relat_1 @ ( A @ ( B @ ( sk72 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[21594]) ).

thf(597,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(4521,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)],[597]) ).

thf(460,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v14_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
                          = ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
                       => ( ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) )
                          = ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_lattice2) ).

thf(3816,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v14_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
                          = ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
                       => ( ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) )
                          = ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(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(2150,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(691,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(5102,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)],[691]) ).

thf(2414,plain,
    ~ ( sk119 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2411]) ).

thf(791,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
                      & ( D @ ( B @ r2_hidden ) ) )
                   => ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_0) ).

thf(5594,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
                      & ( D @ ( B @ r2_hidden ) ) )
                   => ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(7919,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1081,7486]) ).

thf(7920,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7919]) ).

thf(7962,plain,
    ! [B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( B @ k1_relat_1 )
       != sk1 )
      | ( B != sk139 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7920]) ).

thf(7974,plain,
    ( ( ( sk139 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) )
    | ~ ( sk139 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7962]) ).

thf(11211,plain,
    ( ( ( sk139 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7974,2540]) ).

thf(11212,plain,
    ( ( ( sk139 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[11211]) ).

thf(998,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [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(6509,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)],[998]) ).

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(1238,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(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(2015,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(835,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(5822,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)],[835]) ).

thf(5823,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)],[5822]) ).

thf(5826,plain,
    k6_nat_lat @ v13_lattices,
    inference(cnfConj,[status(thm)],[5823]) ).

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(1837,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(4725,plain,
    sk317 @ v15_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(814,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( D @ r2_hidden ) )
                    <=> ( ( C @ ( D @ ( A @ r3_lattices ) ) )
                        & ( D @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_filter_2) ).

thf(5690,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
                          & ( D @ ( B @ ( A @ r3_lattices ) ) ) )
                       => ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( D @ r2_hidden ) ) )
                      & ( ( C @ ( B @ ( A @ k22_filter_2 ) ) @ ( D @ r2_hidden ) )
                       => ( ( C @ ( D @ ( A @ r3_lattices ) ) )
                          & ( D @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(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(1951,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(606,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ 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(4553,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)],[606]) ).

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(1687,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(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(1656,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(430,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(3647,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)],[430]) ).

thf(391,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(3408,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)],[391]) ).

thf(353,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
                = ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_domain_1) ).

thf(3191,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
                = ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(235,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(2464,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)],[235]) ).

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(1938,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(1022,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(6629,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)],[1022]) ).

thf(878,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(5983,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)],[878]) ).

thf(265,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(2670,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)],[265]) ).

thf(458,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(3810,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)],[458]) ).

thf(7571,plain,
    ( ( ( sk361 @ v1_xboole_0 )
     != ( sk293 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4327,5222]) ).

thf(7572,plain,
    ( ( sk361 @ v1_xboole_0 )
   != ( sk293 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7571]) ).

thf(7576,plain,
    sk361 != sk293,
    inference(simp,[status(thm)],[7572]) ).

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(1920,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(4585,plain,
    sk310 @ v13_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(237,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(2477,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)],[237]) ).

thf(639,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(4757,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)],[639]) ).

thf(709,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k3_lattices ) ) )
                = ( B @ ( C @ ( A @ k7_grcat_1 @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funcop_1 ) ) ) ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattice4) ).

thf(5177,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k3_lattices ) ) )
                = ( B @ ( C @ ( A @ k7_grcat_1 @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funcop_1 ) ) ) ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(880,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(5988,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)],[880]) ).

thf(27607,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
       != ( D @ ( C @ k2_tarski ) ) )
      | ( ( A @ k1_tarski @ k1_zfmisc_1 )
       != ( B @ sk251 ) ) ),
    inference(paramod_ordered,[status(thm)],[2054,12824]) ).

thf(27608,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ k1_zfmisc_1 )
     != ( A @ sk251 ) ),
    inference(pattern_uni,[status(thm)],[27607:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 )),bind(D,$thf( E @ k1_tarski ))]]) ).

thf(27621,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ k1_zfmisc_1 )
     != ( A @ sk251 ) ),
    inference(simp,[status(thm)],[27608]) ).

thf(9387,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk72 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1979,2435]) ).

thf(9388,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk72 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9387]) ).

thf(9391,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk72 ),
    inference(simp,[status(thm)],[9388]) ).

thf(780,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
              <=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                  = C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).

thf(5551,plain,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                    = C )
                 => ( C @ ( B @ ( A @ r1_lattices ) ) ) )
                & ( ( C @ ( B @ ( A @ r1_lattices ) ) )
                 => ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                    = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(8520,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk293 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4327,3981]) ).

thf(8521,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk293 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8520]) ).

thf(8529,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk293 ),
    inference(simp,[status(thm)],[8521]) ).

thf(11451,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk293 ) ),
    inference(paramod_ordered,[status(thm)],[1957,8529]) ).

thf(11452,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk293 ),
    inference(pattern_uni,[status(thm)],[11451:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(682,axiom,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).

thf(5036,plain,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ( A @ l3_lattices ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(5037,plain,
    ( ( sk348 @ v3_lattices )
    & ( sk348 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[5036]) ).

thf(5038,plain,
    sk348 @ l3_lattices,
    inference(cnfConj,[status(thm)],[5037]) ).

thf(1159,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)],[1157]) ).

thf(571,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(4402,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)],[571]) ).

thf(667,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(4936,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)],[667]) ).

thf(4937,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( sk335 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
        | ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
        | ~ sk333 )
      & ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk335 @ m2_relset_1 ) ) )
        | ~ sk333 )
      & ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk335 @ v1_funct_2 ) ) )
        | ~ sk333 )
      & ( ( sk335 @ v1_funct_1 )
        | ~ sk333 )
      & ( sk333
        | ~ ( A @ ( sk334 @ p1_s14_funct_2 ) )
        | ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
      & ( sk333
        | ( f1_s14_funct_2 @ ( sk334 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4936]) ).

thf(4942,plain,
    ( sk333
    | ( f1_s14_funct_2 @ ( sk334 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4937]) ).

thf(784,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(5566,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)],[784]) ).

thf(896,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(6060,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)],[896]) ).

thf(1074,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)],[1073]) ).

thf(1075,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E
          = ( A @ ( B @ ( C @ ( D @ ( E @ sk6 ) ) ) ) @ ( 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 @ sk6 ) ) ) ) @ 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 @ sk6 ) ) ) ) @ 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)],[1074]) ).

thf(1078,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E
        = ( A @ ( B @ ( C @ ( D @ ( E @ sk6 ) ) ) ) @ ( 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)],[1075]) ).

thf(1079,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 @ sk6 ) ) ) ) @ ( D @ k1_funct_1 ) )
        = E ) ),
    inference(lifteq,[status(thm)],[1078]) ).

thf(2213,plain,
    sk95 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

thf(322,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(3028,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)],[322]) ).

thf(484,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(3926,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ~ ( A @ ( B @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(326,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(3050,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)],[326]) ).

thf(214,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(2345,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)],[214]) ).

thf(1186,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ k2_funct_1 ) )
      | ( ( A @ ( B @ sk11 ) @ ( A @ k1_funct_1 ) )
       != ( A @ ( B @ sk12 ) ) )
      | ( ( A @ ( B @ sk12 ) @ ( B @ 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)],[1183]) ).

thf(1195,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 @ sk12 ) )
       != ( A @ ( B @ sk11 ) @ ( A @ k1_funct_1 ) ) )
      | ( ( A @ ( B @ sk12 ) @ ( B @ k1_funct_1 ) )
       != ( A @ ( B @ sk11 ) ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1186]) ).

thf(2211,plain,
    sk95 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

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(3763,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(7851,plain,
    ! [A: $i] :
      ( ( ( sk139 @ 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)],[2541,7314]) ).

thf(7852,plain,
    ! [A: $i] :
      ( ( ( sk139 @ 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)],[7851]) ).

thf(7853,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7852:[bind(A,$thf( sk139 ))]]) ).

thf(1033,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(6666,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)],[1033]) ).

thf(817,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(5729,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)],[817]) ).

thf(8987,plain,
    ! [A: $i] :
      ( ( ( sk204 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3130,7367]) ).

thf(8988,plain,
    ! [A: $i] :
      ( ( ( sk204 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8987]) ).

thf(8989,plain,
    ( ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8988:[bind(A,$thf( sk204 ))]]) ).

thf(15627,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8989]) ).

thf(15628,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15627]) ).

thf(15690,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk204 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15628]) ).

thf(15724,plain,
    ( ( sk204 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15690]) ).

thf(4732,plain,
    sk317 @ v13_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(864,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(5936,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)],[864]) ).

thf(4680,plain,
    sk315 @ v13_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(770,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice2) ).

thf(5515,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(510,axiom,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(4061,plain,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(4062,plain,
    ( ~ ( sk275 @ v3_struct_0 )
    & ( sk275 @ l1_struct_0 ) ),
    inference(cnf,[status(esa)],[4061]) ).

thf(4063,plain,
    sk275 @ l1_struct_0,
    inference(cnfConj,[status(thm)],[4062]) ).

thf(1106,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)],[1101]) ).

thf(15945,plain,
    ! [A: $i] :
      ( ( ( sk215 @ 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)],[3243,1155]) ).

thf(15946,plain,
    ! [A: $i] :
      ( ( ( sk215 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15945]) ).

thf(15947,plain,
    ( ( sk215 @ k1_relat_1 @ ( sk215 @ k9_relat_1 ) )
    = ( sk215 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15946:[bind(A,$thf( sk215 ))]]) ).

thf(150,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(1983,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)],[150]) ).

thf(15579,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7997]) ).

thf(15580,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15579]) ).

thf(15702,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk313 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15580]) ).

thf(15739,plain,
    ( ( sk313 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15702]) ).

thf(961,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ( ( 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(6360,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)],[961]) ).

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(1360,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(201,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(2245,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)],[201]) ).

thf(714,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
                            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
                            & ( F @ v1_funct_1 ) )
                         => ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
                              & ( F
                                = ( B @ ( D @ k1_realset1 ) ) )
                              & ( E
                                = ( B @ ( C @ k1_realset1 ) ) ) )
                           => ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_2) ).

thf(5189,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
                            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
                            & ( F @ v1_funct_1 ) )
                         => ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
                              & ( F
                                = ( B @ ( D @ k1_realset1 ) ) )
                              & ( E
                                = ( B @ ( C @ k1_realset1 ) ) ) )
                           => ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(3105,plain,
    k6_nat_lat @ v8_lattices,
    inference(cnfConj,[status(thm)],[3096]) ).

thf(1086,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)],[1085]) ).

thf(1089,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)],[1086]) ).

thf(480,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(3909,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)],[480]) ).

thf(855,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(5904,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)],[855]) ).

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(1143,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(796,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ( ( B @ ( A @ k18_filter_2 ) )
                = ( A @ u1_struct_0 ) )
              & ~ ! [C: $i] :
                    ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                   => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                      = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_filter_2) ).

thf(5609,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ( ( B @ ( A @ k18_filter_2 ) )
                = ( A @ u1_struct_0 ) )
              & ~ ! [C: $i] :
                    ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                   => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                      = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(690,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ l2_lattices )
        & ( A @ l1_lattices ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).

thf(5098,plain,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ l2_lattices )
        & ( A @ l1_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(340,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(3122,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)],[340]) ).

thf(314,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(2990,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)],[314]) ).

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(1534,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(807,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(5673,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)],[807]) ).

thf(594,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(4512,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)],[594]) ).

thf(287,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(2841,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)],[287]) ).

thf(928,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(6195,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)],[928]) ).

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(1120,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(1121,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(cnf,[status(esa)],[1120]) ).

thf(590,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(4486,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)],[590]) ).

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(1064,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(3525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != B )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(cnfConj,[status(thm)],[3523]) ).

thf(3542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != B )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(lifteq,[status(thm)],[3525]) ).

thf(3543,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ r2_hidden ) ),
    inference(simp,[status(thm)],[3542]) ).

thf(27295,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)],[2054,3543]) ).

thf(27296,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
    inference(pattern_uni,[status(thm)],[27295:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(27314,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
    inference(simp,[status(thm)],[27296]) ).

thf(766,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).

thf(5502,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(276,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(2709,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)],[276]) ).

thf(646,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(4789,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)],[646]) ).

thf(602,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(4544,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)],[602]) ).

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(1856,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(270,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(2692,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)],[270]) ).

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(1498,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(598,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(4525,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)],[598]) ).

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 ) )
           => ! [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(6235,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)],[941]) ).

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(1094,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(1095,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)],[1094]) ).

thf(1096,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)],[1095]) ).

thf(3102,plain,
    k6_nat_lat @ v3_lattices,
    inference(cnfConj,[status(thm)],[3096]) ).

thf(542,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(4233,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)],[542]) ).

thf(493,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(3963,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)],[493]) ).

thf(414,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(3518,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)],[414]) ).

thf(788,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(5583,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)],[788]) ).

thf(540,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(4227,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

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 ) )
         => ( ( 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(5978,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)],[876]) ).

thf(290,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(2858,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)],[290]) ).

thf(426,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(3632,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)],[426]) ).

thf(850,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(5889,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)],[850]) ).

thf(15581,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7862]) ).

thf(15582,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15581]) ).

thf(15694,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk213 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15582]) ).

thf(15729,plain,
    ( ( sk213 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15694]) ).

thf(397,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(3440,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)],[397]) ).

thf(539,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(4219,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)],[539]) ).

thf(765,axiom,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
        & ( A @ u2_lattices @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).

thf(5497,plain,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
        & ( A @ u2_lattices @ v1_funct_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(328,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(3060,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)],[328]) ).

thf(650,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(4817,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)],[650]) ).

thf(4676,plain,
    sk315 @ v16_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(1160,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)],[1157]) ).

thf(687,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(5080,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)],[687]) ).

thf(7863,plain,
    ! [A: $i] :
      ( ( ( sk72 @ 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)],[1977,7314]) ).

thf(7864,plain,
    ! [A: $i] :
      ( ( ( sk72 @ 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)],[7863]) ).

thf(7865,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7864:[bind(A,$thf( sk72 ))]]) ).

thf(12239,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7865]) ).

thf(12240,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12239]) ).

thf(12325,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk72 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12240]) ).

thf(2419,plain,
    sk119 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2411]) ).

thf(534,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(4191,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)],[534]) ).

thf(862,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(5932,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)],[862]) ).

thf(560,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(4333,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)],[560]) ).

thf(866,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(5941,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)],[866]) ).

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(1329,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(596,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(4518,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)],[596]) ).

thf(4582,plain,
    sk310 @ v5_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(350,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(3171,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)],[350]) ).

thf(3172,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)],[3171]) ).

thf(3173,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)],[3172]) ).

thf(3175,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3173]) ).

thf(3178,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3175]) ).

thf(3179,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[3178]) ).

thf(1026,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( D = F )
                              & ( C = E ) )
                           => ( ( ( D @ ( C @ ( A @ k4_lattices ) ) )
                                = ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ k4_lattices ) ) ) )
                              & ( ( D @ ( C @ ( A @ k3_lattices ) ) )
                                = ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_filter_2) ).

thf(6642,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( D = F )
                              & ( C = E ) )
                           => ( ( ( D @ ( C @ ( A @ k4_lattices ) ) )
                                = ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ k4_lattices ) ) ) )
                              & ( ( D @ ( C @ ( A @ k3_lattices ) ) )
                                = ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(962,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(6363,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)],[962]) ).

thf(32720,plain,
    ! [A: $i] :
      ( ( A != sk3 )
      | ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1037]) ).

thf(32721,plain,
    ( ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
    | ( sk3 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[32720:[bind(A,$thf( sk3 ))]]) ).

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(2172,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(395,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(3428,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)],[395]) ).

thf(1211,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)],[1210]) ).

thf(1214,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)],[1211]) ).

thf(805,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(5662,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)],[805]) ).

thf(354,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(3194,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)],[354]) ).

thf(26763,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)],[2054,3533]) ).

thf(26764,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
    inference(pattern_uni,[status(thm)],[26763:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(26784,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
    inference(simp,[status(thm)],[26764]) ).

thf(38318,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)],[26784,1263]) ).

thf(38319,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)],[38318]) ).

thf(38346,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)],[38319]) ).

thf(38359,plain,
    ! [B: $i,A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != ( k1_xboole_0 @ k1_tarski @ ( B @ k4_xboole_0 ) ) ),
    inference(simp,[status(thm)],[38346]) ).

thf(973,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(6395,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)],[973]) ).

thf(995,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(6501,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)],[995]) ).

thf(15577,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7856]) ).

thf(15578,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15577]) ).

thf(15693,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk204 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15578]) ).

thf(15728,plain,
    ( ( sk204 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15693]) ).

thf(7573,plain,
    ( ( ( sk293 @ v1_xboole_0 )
     != ( sk15 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4327,1236]) ).

thf(7574,plain,
    ( ( sk293 @ v1_xboole_0 )
   != ( sk15 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7573]) ).

thf(7577,plain,
    sk293 != sk15,
    inference(simp,[status(thm)],[7574]) ).

thf(433,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(3671,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)],[433]) ).

thf(583,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(4457,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)],[583]) ).

thf(649,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(4814,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)],[649]) ).

thf(2472,plain,
    ~ ( k13_nat_lat @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2467]) ).

thf(9379,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3043,2435]) ).

thf(9380,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9379]) ).

thf(9392,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[9380]) ).

thf(944,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(6271,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)],[944]) ).

thf(751,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(5387,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)],[751]) ).

thf(4736,plain,
    sk317 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(3242,plain,
    ~ ( sk215 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[3241]) ).

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(1451,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(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(1530,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(254,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(2598,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)],[254]) ).

thf(803,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(5639,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)],[803]) ).

thf(933,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(6207,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)],[933]) ).

thf(634,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(4717,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)],[634]) ).

thf(521,axiom,
    ! [A: $i] :
      ( ( A @ l1_lattices )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).

thf(4120,plain,
    ! [A: $i] :
      ( ( A @ l1_lattices )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(915,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(6134,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)],[915]) ).

thf(233,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(2450,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)],[233]) ).

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(2125,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(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(1150,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(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(1249,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(40392,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk204 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk204 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2081,40238]) ).

thf(40393,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk204 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk204 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[40392]) ).

thf(40417,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( sk204 @ k1_relat_1 )
       != k1_xboole_0 )
      | ( ( sk204 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[40393]) ).

thf(40462,plain,
    ( ( ( sk204 @ k1_relat_1 )
     != k1_xboole_0 )
    | ( ( sk204 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[40417]) ).

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(1266,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(382,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(3354,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)],[382]) ).

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(2153,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(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(1226,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(1227,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)],[1226]) ).

thf(1229,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)],[1227]) ).

thf(1231,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)],[1229]) ).

thf(873,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(5973,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)],[873]) ).

thf(216,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(2355,plain,
    ! [A: $i] :
      ( ( A @ v1_finset_1 )
     => ( ( A @ k5_finsub_1 )
        = ( A @ k1_zfmisc_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(1187,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ k2_funct_1 ) )
      | ( A @ 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)],[1183]) ).

thf(1192,plain,
    ! [B: $i,A: $i] :
      ( ( A @ 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)],[1187]) ).

thf(9567,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk213 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3231,3049]) ).

thf(9568,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk213 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9567]) ).

thf(9581,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk213 ),
    inference(simp,[status(thm)],[9568]) ).

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(1932,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(8686,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk153 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2656,5293]) ).

thf(8687,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk153 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8686]) ).

thf(8690,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk153 ),
    inference(simp,[status(thm)],[8687]) ).

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(1045,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(1046,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)],[1045]) ).

thf(1047,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)],[1046]) ).

thf(1049,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)],[1047]) ).

thf(1050,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)],[1049]) ).

thf(388,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(3390,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)],[388]) ).

thf(461,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(3819,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)],[461]) ).

thf(544,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(4237,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)],[544]) ).

thf(358,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( A @ ( C @ r2_hidden ) )
       => ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
          | ( B = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).

thf(3222,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( A @ ( C @ r2_hidden ) )
       => ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
          | ( B = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(666,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(4934,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)],[666]) ).

thf(238,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(2497,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)],[238]) ).

thf(14873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ 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)],[5762,1148]) ).

thf(14874,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk410 @ 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)],[14873]) ).

thf(14875,plain,
    ( ( f1_s11_funct_2 @ ( sk410 @ k1_relat_1 @ r1_tarski ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[14874:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk410 ))]]) ).

thf(671,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(4953,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)],[671]) ).

thf(7914,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1081,7853]) ).

thf(7915,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7914]) ).

thf(7958,plain,
    ! [B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( B @ k1_relat_1 )
       != sk1 )
      | ( B != sk139 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[7915]) ).

thf(7970,plain,
    ( ( ( sk139 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) )
    | ~ ( sk139 @ v1_relat_1 )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[7958]) ).

thf(10548,plain,
    ( ( ( sk139 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) )
    | ~ $true
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(rewrite,[status(thm)],[7970,2540]) ).

thf(10549,plain,
    ( ( ( sk139 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[10548]) ).

thf(12767,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk139 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(paramod_ordered,[status(thm)],[2081,10549]) ).

thf(12768,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk139 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12767]) ).

thf(12789,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( sk139 @ k2_relat_1 )
       != k1_xboole_0 )
      | ( ( sk139 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12768]) ).

thf(12800,plain,
    ( ( ( sk139 @ k2_relat_1 )
     != k1_xboole_0 )
    | ( ( sk139 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12789]) ).

thf(546,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(4259,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)],[546]) ).

thf(330,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(3074,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)],[330]) ).

thf(630,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(4689,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)],[630]) ).

thf(938,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(6224,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)],[938]) ).

thf(12814,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk251 @ v1_xboole_0 )
       != ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3748,3981]) ).

thf(12815,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
     != ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12814]) ).

thf(12831,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk251 )
     != ( B @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[12815]) ).

thf(600,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

thf(4533,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(4534,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(cnf,[status(esa)],[4533]) ).

thf(4535,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[4534]) ).

thf(425,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [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(3624,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)],[425]) ).

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(1563,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(966,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(6378,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)],[966]) ).

thf(9565,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3043,3049]) ).

thf(9566,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9565]) ).

thf(9579,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[9566]) ).

thf(32402,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ ( B @ k1_funct_2 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,9579]) ).

thf(32403,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ ( B @ k1_funct_2 ) ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[32402]) ).

thf(32404,plain,
    ! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk20 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[32403:[bind(A,$thf( D @ ( D @ k1_funct_2 ) )),bind(B,$thf( D ))]]) ).

thf(33109,plain,
    ! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk20 @ v1_relat_1 ),
    inference(simp,[status(thm)],[32404]) ).

thf(769,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k19_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_filter_2) ).

thf(5513,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k19_filter_2 ) @ m2_filter_2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(256,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(2617,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)],[256]) ).

thf(697,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(5126,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)],[697]) ).

thf(242,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(2529,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)],[242]) ).

thf(706,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).

thf(5170,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(400,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(3454,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)],[400]) ).

thf(463,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(3824,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)],[463]) ).

thf(694,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(5112,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)],[694]) ).

thf(781,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(5557,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)],[781]) ).

thf(14624,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk313 @ k1_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[14597,1099]) ).

thf(14625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk313 @ k1_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14624]) ).

thf(14626,plain,
    ! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14625:[bind(A,$thf( sk313 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14657,plain,
    ! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14626]) ).

thf(457,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(3802,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)],[457]) ).

thf(8522,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk72 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1979,3981]) ).

thf(8523,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk72 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8522]) ).

thf(8527,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk72 ),
    inference(simp,[status(thm)],[8523]) ).

thf(359,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
        = ( D @ ( C @ k1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).

thf(3225,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
        = ( D @ ( C @ k1_funct_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(551,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(4288,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)],[551]) ).

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(1241,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(247,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(2546,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)],[247]) ).

thf(535,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(4195,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)],[535]) ).

thf(2208,plain,
    sk95 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

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(2043,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(4889,plain,
    ~ ( sk328 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4883]) ).

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(1712,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(7410,plain,
    ( ( ( sk213 @ v1_xboole_0 )
     != ( sk15 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3231,1236]) ).

thf(7411,plain,
    ( ( sk213 @ v1_xboole_0 )
   != ( sk15 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7410]) ).

thf(7414,plain,
    sk213 != sk15,
    inference(simp,[status(thm)],[7411]) ).

thf(422,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(3592,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)],[422]) ).

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(1846,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(29724,plain,
    ! [A: $i] :
      ( ( A != sk204 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,15720]) ).

thf(29725,plain,
    ! [A: $i] :
      ( ( A != sk204 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[29724]) ).

thf(29726,plain,
    ( ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ( sk204 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29725:[bind(A,$thf( sk204 ))]]) ).

thf(869,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ v12_lattices )
           => ( B @ ( A @ k23_filter_2 ) @ v12_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_2) ).

thf(5964,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ v12_lattices )
           => ( B @ ( A @ k23_filter_2 ) @ v12_lattices ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(12252,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7498]) ).

thf(12253,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12252]) ).

thf(12329,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk72 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12253]) ).

thf(947,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(6279,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)],[947]) ).

thf(500,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(3999,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)],[500]) ).

thf(308,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(2963,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)],[308]) ).

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(1286,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(757,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(5447,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)],[757]) ).

thf(2915,plain,
    sk187 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(4906,plain,
    sk329 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(7490,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)],[3080,7278]) ).

thf(7491,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)],[7490]) ).

thf(7492,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)],[7491:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15551,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7492,2266]) ).

thf(15552,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15551]) ).

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(1996,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(847,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(5872,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)],[847]) ).

thf(1024,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(6637,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)],[1024]) ).

thf(774,axiom,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(5524,plain,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(222,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(2391,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)],[222]) ).

thf(931,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(6203,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)],[931]) ).

thf(9571,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk293 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4327,3049]) ).

thf(9572,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk293 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9571]) ).

thf(9577,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk293 ),
    inference(simp,[status(thm)],[9572]) ).

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(1273,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(304,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(2941,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)],[304]) ).

thf(868,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [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(5960,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)],[868]) ).

thf(985,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(6469,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)],[985]) ).

thf(609,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(4577,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)],[609]) ).

thf(436,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(3686,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)],[436]) ).

thf(809,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( 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(5679,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)],[809]) ).

thf(1131,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)],[1129]) ).

thf(1135,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)],[1131]) ).

thf(280,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(2729,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)],[280]) ).

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(1648,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(303,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(2936,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)],[303]) ).

thf(6848,plain,
    ( ( ( sk215 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3043,3242]) ).

thf(6849,plain,
    ( ( sk215 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6848]) ).

thf(6854,plain,
    sk215 != k1_xboole_0,
    inference(simp,[status(thm)],[6849]) ).

thf(32344,plain,
    ! [A: $i] :
      ( ( A != sk215 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,6854]) ).

thf(32345,plain,
    ! [A: $i] :
      ( ( A != sk215 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[32344]) ).

thf(32346,plain,
    sk215 @ sk20 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[32345:[bind(A,$thf( sk215 ))]]) ).

thf(33807,plain,
    ! [A: $i] :
      ( ( ( sk215 @ sk20 @ 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)],[32346,1155]) ).

thf(33808,plain,
    ! [A: $i] :
      ( ( ( sk215 @ sk20 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[33807]) ).

thf(33809,plain,
    ( ( sk215 @ sk20 @ k1_relat_1 @ ( sk215 @ sk20 @ k9_relat_1 ) )
    = ( sk215 @ sk20 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[33808:[bind(A,$thf( sk215 @ sk20 ))]]) ).

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(1727,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(955,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( A @ v13_lattices )
           => ( B @ ( A @ k5_lattices @ ( A @ k22_filter_2 ) ) @ ( B @ ( A @ k18_filter_2 ) @ ( A @ u1_struct_0 @ r1_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_filter_2) ).

thf(6314,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)],[955]) ).

thf(2413,plain,
    sk119 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2411]) ).

thf(997,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(6507,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)],[997]) ).

thf(631,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(4708,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)],[631]) ).

thf(976,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(6437,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)],[976]) ).

thf(4685,plain,
    sk315 @ v14_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(209,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(2292,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)],[209]) ).

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(1698,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(248,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(2556,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)],[248]) ).

thf(205,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(2275,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)],[205]) ).

thf(4594,plain,
    sk310 @ v6_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(277,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(2717,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)],[277]) ).

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(1216,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(1217,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)],[1216]) ).

thf(1219,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)],[1217]) ).

thf(562,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(4340,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)],[562]) ).

thf(386,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(3375,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)],[386]) ).

thf(982,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(6454,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)],[982]) ).

thf(565,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(4359,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)],[565]) ).

thf(5525,plain,
    ! [A: $i] : ( A @ ( A @ sk388 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[5524]) ).

thf(368,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(3274,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)],[368]) ).

thf(12265,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7489]) ).

thf(12266,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12265]) ).

thf(12287,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk204 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12266]) ).

thf(591,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(4489,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)],[591]) ).

thf(895,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ! [E: $i] :
                      ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( C = F )
                              & ( B = E ) )
                           => ( ( ( C @ ( B @ ( A @ 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(6052,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)],[895]) ).

thf(1015,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(6598,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)],[1015]) ).

thf(793,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_0) ).

thf(5598,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(12820,plain,
    ! [A: $i] :
      ( ( ( A @ sk251 @ v1_xboole_0 )
       != ( sk15 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3748,1236]) ).

thf(12821,plain,
    ! [A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
     != ( sk15 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12820]) ).

thf(12827,plain,
    ! [A: $i] :
      ( ( A @ sk251 )
     != sk15 ),
    inference(simp,[status(thm)],[12821]) ).

thf(507,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( B @ ( A @ k23_filter_2 ) )
            = ( B @ ( A @ k10_filter_2 ) @ ( A @ k1_lattice2 @ k23_filter_2 ) @ ( A @ k1_lattice2 @ k24_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_2) ).

thf(4041,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( B @ ( A @ k23_filter_2 ) )
            = ( B @ ( A @ k10_filter_2 ) @ ( A @ k1_lattice2 @ k23_filter_2 ) @ ( A @ k1_lattice2 @ k24_filter_2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

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(3741,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(311,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(2970,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)],[311]) ).

thf(427,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(3636,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)],[427]) ).

thf(365,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).

thf(3255,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(555,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [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(4309,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)],[555]) ).

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(3758,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(522,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(4122,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)],[522]) ).

thf(837,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( 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(5831,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)],[837]) ).

thf(558,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(4328,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)],[558]) ).

thf(16983,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk353 @ ( A @ r2_hidden ) )
       != ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5062,2985]) ).

thf(16984,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk353 @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[16983]) ).

thf(17002,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk353 )
       != k1_xboole_0 )
      | ( A != B ) ),
    inference(simp,[status(thm)],[16984]) ).

thf(17009,plain,
    ! [A: $i] :
      ( ( A @ sk353 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[17002]) ).

thf(911,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(6108,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)],[911]) ).

thf(9591,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk72 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1979,4639]) ).

thf(9592,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk72 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9591]) ).

thf(9602,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk72 ),
    inference(simp,[status(thm)],[9592]) ).

thf(333,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(3086,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)],[333]) ).

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(1752,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(4677,plain,
    sk315 @ v17_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(801,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(5627,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)],[801]) ).

thf(940,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(6229,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)],[940]) ).

thf(797,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
               => ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattices) ).

thf(5612,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
               => ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(1393,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( B @ sk26 ) @ k1_relat_1 ) )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1388]) ).

thf(1402,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ sk26 ) @ k1_relat_1 )
        = B )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1393]) ).

thf(1403,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ sk26 ) @ k1_relat_1 )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[1402]) ).

thf(401,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(3458,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)],[401]) ).

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 @ 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(6407,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)],[975]) ).

thf(4590,plain,
    sk310 @ v4_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(12180,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7856]) ).

thf(12181,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12180]) ).

thf(12322,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk204 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12181]) ).

thf(271,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(2695,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)],[271]) ).

thf(1138,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(cnf,[status(esa)],[1137]) ).

thf(1139,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(lifteq,[status(thm)],[1138]) ).

thf(518,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(4112,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)],[518]) ).

thf(377,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(3330,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)],[377]) ).

thf(701,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_2 ) )
             => ! [D: $i] :
                  ( ( B @ ( D @ m1_filter_2 ) )
                 => ( ( ( C = D )
                      & ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
                        = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) ) )
                   => ( ( C @ ( A @ k8_filter_0 ) )
                      = ( D @ ( B @ k8_filter_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_2) ).

thf(5148,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_2 ) )
             => ! [D: $i] :
                  ( ( B @ ( D @ m1_filter_2 ) )
                 => ( ( ( C = D )
                      & ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
                        = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) ) )
                   => ( ( C @ ( A @ k8_filter_0 ) )
                      = ( D @ ( B @ k8_filter_0 ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(275,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(2706,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)],[275]) ).

thf(948,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(6281,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)],[948]) ).

thf(1003,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ 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(6525,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)],[1003]) ).

thf(5039,plain,
    sk348 @ v3_lattices,
    inference(cnfConj,[status(thm)],[5037]) ).

thf(608,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(4558,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)],[608]) ).

thf(339,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(3118,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)],[339]) ).

thf(681,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(5033,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)],[681]) ).

thf(198,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(2220,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)],[198]) ).

thf(969,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ ( A @ k20_filter_2 ) ) )
                = ( C @ ( B @ ( A @ a_3_0_filter_2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_2) ).

thf(6385,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)],[969]) ).

thf(515,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(4096,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)],[515]) ).

thf(296,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(2891,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)],[296]) ).

thf(679,axiom,
    ? [A: $i] : ( A @ l1_lattices ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).

thf(5010,plain,
    ? [A: $i] : ( A @ l1_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(5011,plain,
    sk345 @ l1_lattices,
    inference(cnf,[status(esa)],[5010]) ).

thf(4672,plain,
    sk315 @ v8_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(12810,plain,
    ! [A: $i] :
      ( ( ( A @ sk251 @ v1_xboole_0 )
       != ( sk215 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3748,3242]) ).

thf(12811,plain,
    ! [A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
     != ( sk215 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12810]) ).

thf(12830,plain,
    ! [A: $i] :
      ( ( A @ sk251 )
     != sk215 ),
    inference(simp,[status(thm)],[12811]) ).

thf(652,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(4822,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)],[652]) ).

thf(1058,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
      | ~ ( B @ ( A @ ( C @ sk4 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1054]) ).

thf(1107,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)],[1101]) ).

thf(406,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(3487,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)],[406]) ).

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(2055,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(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(2166,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(1088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
      | ( ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk7 ) ) ) )
      | ~ ( 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)],[1085]) ).

thf(1090,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 @ sk7 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk7 ) ) ) ) ),
    inference(lifteq,[status(thm)],[1088]) ).

thf(234,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(2457,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)],[234]) ).

thf(622,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(4640,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(3089,plain,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[3088]) ).

thf(3091,plain,
    k1_xboole_0 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3089]) ).

thf(6901,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)],[3091,1068]) ).

thf(6902,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)],[6901]) ).

thf(6903,plain,
    ! [A: $i] : ( k1_xboole_0 @ k1_relat_1 @ ( k1_xboole_0 @ k9_relat_1 ) @ ( A @ ( k1_xboole_0 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6902:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).

thf(19596,plain,
    k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ),
    inference(rewrite,[status(thm)],[6903,3046]) ).

thf(393,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(3416,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)],[393]) ).

thf(12822,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk251 @ v1_xboole_0 )
       != ( B @ k1_tarski @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3748,5293]) ).

thf(12823,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
     != ( B @ k1_tarski @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12822]) ).

thf(12825,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk251 )
     != ( B @ k1_tarski ) ),
    inference(simp,[status(thm)],[12823]) ).

thf(958,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(6334,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)],[958]) ).

thf(8981,plain,
    ! [A: $i] :
      ( ( ( sk139 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2541,7367]) ).

thf(8982,plain,
    ! [A: $i] :
      ( ( ( sk139 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8981]) ).

thf(8983,plain,
    ( ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8982:[bind(A,$thf( sk139 ))]]) ).

thf(15645,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8983]) ).

thf(15646,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15645]) ).

thf(15697,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk139 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15646]) ).

thf(15733,plain,
    ( ( sk139 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15697]) ).

thf(30668,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1042]) ).

thf(30669,plain,
    ( ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
    | ( sk2 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30668:[bind(A,$thf( sk2 ))]]) ).

thf(2474,plain,
    k13_nat_lat @ v5_lattices,
    inference(cnfConj,[status(thm)],[2467]) ).

thf(372,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(3302,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A
        = ( A @ a_1_0_domain_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(29844,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1041]) ).

thf(29845,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ( sk1 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29844:[bind(A,$thf( sk1 ))]]) ).

thf(4887,plain,
    sk328 @ v13_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(545,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(4245,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)],[545]) ).

thf(441,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(3719,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)],[441]) ).

thf(217,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(2358,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)],[217]) ).

thf(210,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(2319,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)],[210]) ).

thf(577,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(4433,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)],[577]) ).

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(1356,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(718,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(5212,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)],[718]) ).

thf(207,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(2284,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)],[207]) ).

thf(753,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k14_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_filter_2) ).

thf(5407,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k14_filter_2 ) @ m2_filter_2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(989,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(6478,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)],[989]) ).

thf(2359,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk111 ) @ v1_funct_1 )
      & ( A @ ( B @ sk111 ) @ v1_relat_1 )
      & ( B @ ( A @ ( A @ ( B @ sk111 ) @ m1_relset_1 ) ) ) ),
    inference(cnf,[status(esa)],[2358]) ).

thf(2361,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_relat_1 ),
    inference(cnfConj,[status(thm)],[2359]) ).

thf(3101,plain,
    k6_nat_lat @ v5_lattices,
    inference(cnfConj,[status(thm)],[3096]) ).

thf(846,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ v11_lattices )
           => ( B @ ( A @ k23_filter_2 ) @ v11_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_2) ).

thf(5870,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ v11_lattices )
           => ( B @ ( A @ k23_filter_2 ) @ v11_lattices ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(1395,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk26 ) @ v1_relat_1 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1388]) ).

thf(1407,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk26 ) @ v1_relat_1 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1395]) ).

thf(1408,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ sk26 ) @ v1_relat_1 ),
    inference(simp,[status(thm)],[1407]) ).

thf(954,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [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(6308,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)],[954]) ).

thf(806,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(5671,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)],[806]) ).

thf(364,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( B != k1_xboole_0 )
       => ! [E: $i] :
            ( ? [F: $i] :
                ( ( E
                  = ( F @ ( D @ k1_funct_1 ) ) )
                & ( C @ ( F @ r2_hidden ) )
                & ( A @ ( F @ r2_hidden ) ) )
           => ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).

thf(3251,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( B != k1_xboole_0 )
       => ! [E: $i] :
            ( ? [F: $i] :
                ( ( E
                  = ( F @ ( D @ k1_funct_1 ) ) )
                & ( C @ ( F @ r2_hidden ) )
                & ( A @ ( F @ r2_hidden ) ) )
           => ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(199,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(2229,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)],[199]) ).

thf(33767,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk215 @ sk20 @ 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)],[32346,1068]) ).

thf(33768,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk215 @ sk20 @ 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)],[33767]) ).

thf(33769,plain,
    ! [A: $i] : ( sk215 @ sk20 @ k1_relat_1 @ ( sk215 @ sk20 @ k9_relat_1 ) @ ( A @ ( sk215 @ sk20 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[33768:[bind(A,$thf( A )),bind(B,$thf( sk215 @ sk20 ))]]) ).

thf(41494,plain,
    ! [A: $i] : ( sk215 @ sk20 @ k2_relat_1 @ ( A @ ( sk215 @ sk20 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[33769,33809]) ).

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(2084,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(12231,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8989]) ).

thf(12232,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12231]) ).

thf(12297,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk204 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[12232]) ).

thf(2415,plain,
    sk119 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2411]) ).

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(1894,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(227,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).

thf(2422,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(977,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(6439,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)],[977]) ).

thf(6440,plain,
    ( ( k13_nat_lat @ l3_lattices )
    & ( k13_nat_lat @ v10_lattices )
    & ~ ( k13_nat_lat @ v3_struct_0 ) ),
    inference(cnf,[status(esa)],[6439]) ).

thf(6443,plain,
    k13_nat_lat @ l3_lattices,
    inference(cnfConj,[status(thm)],[6440]) ).

thf(282,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(2774,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)],[282]) ).

thf(936,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(6217,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)],[936]) ).

thf(6500,plain,
    sk462 @ v3_lattices,
    inference(cnfConj,[status(thm)],[6497]) ).

thf(435,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(3683,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)],[435]) ).

thf(413,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(3515,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)],[413]) ).

thf(298,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(2906,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)],[298]) ).

thf(929,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(6197,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)],[929]) ).

thf(5827,plain,
    k6_nat_lat @ l3_lattices,
    inference(cnfConj,[status(thm)],[5823]) ).

thf(8682,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk293 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4327,5293]) ).

thf(8683,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk293 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8682]) ).

thf(8688,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk293 ),
    inference(simp,[status(thm)],[8683]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [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(5853,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)],[844]) ).

thf(12194,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8018]) ).

thf(12195,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12194]) ).

thf(12316,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk313 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12195]) ).

thf(12354,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12316]) ).

thf(337,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(3106,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)],[337]) ).

thf(849,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(5880,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)],[849]) ).

thf(15592,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8018]) ).

thf(15593,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15592]) ).

thf(15703,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk313 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15593]) ).

thf(15740,plain,
    ( ( sk313 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15703]) ).

thf(4586,plain,
    sk310 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(8676,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3043,5293]) ).

thf(8677,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8676]) ).

thf(8689,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[8677]) ).

thf(31636,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_tarski ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,8689]) ).

thf(31637,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_tarski ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[31636]) ).

thf(31638,plain,
    ! [A: $i] : ( A @ k1_tarski @ sk20 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[31637:[bind(A,$thf( C @ k1_tarski )),bind(B,$thf( C ))]]) ).

thf(32883,plain,
    ! [A: $i] : ( A @ k1_tarski @ sk20 @ v1_relat_1 ),
    inference(simp,[status(thm)],[31638]) ).

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(2116,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(615,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(4616,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)],[615]) ).

thf(512,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(4073,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)],[512]) ).

thf(12749,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk72 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk72 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2081,9989]) ).

thf(12750,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk72 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk72 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12749]) ).

thf(12781,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( sk72 @ k2_relat_1 )
       != k1_xboole_0 )
      | ( ( sk72 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12750]) ).

thf(12791,plain,
    ( ( ( sk72 @ k2_relat_1 )
     != k1_xboole_0 )
    | ( ( sk72 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12781]) ).

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(1801,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(410,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(3500,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)],[410]) ).

thf(345,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ? [C: $i] :
            ( ( 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(3138,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)],[345]) ).

thf(532,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(4176,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)],[532]) ).

thf(921,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(6154,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)],[921]) ).

thf(813,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(5689,plain,
    f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(553,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( 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(4300,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)],[553]) ).

thf(569,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(4374,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)],[569]) ).

thf(351,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(3182,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(329,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(3066,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)],[329]) ).

thf(872,axiom,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).

thf(5971,plain,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(5972,plain,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[5971]) ).

thf(643,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(4773,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)],[643]) ).

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(1571,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(799,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( D = F )
                              & ( C = E ) )
                           => ( ( D @ ( C @ ( A @ r3_lattices ) ) )
                            <=> ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_filter_2) ).

thf(5616,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( B @ ( A @ k23_filter_2 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( D = F )
                              & ( C = E ) )
                           => ( ( ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ r3_lattices ) ) )
                               => ( D @ ( C @ ( A @ r3_lattices ) ) ) )
                              & ( ( D @ ( C @ ( A @ r3_lattices ) ) )
                               => ( F @ ( E @ ( B @ ( A @ k23_filter_2 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

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(1376,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(593,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(4509,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)],[593]) ).

thf(517,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(4107,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)],[517]) ).

thf(29743,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk81 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,15242]) ).

thf(29744,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk81 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[29743]) ).

thf(29745,plain,
    ! [A: $i] : ( A @ sk81 @ sk20 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[29744:[bind(A,$thf( C @ sk81 )),bind(B,$thf( C ))]]) ).

thf(32920,plain,
    ! [A: $i] : ( A @ sk81 @ sk20 @ v1_relat_1 ),
    inference(simp,[status(thm)],[29745]) ).

thf(570,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(4388,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)],[570]) ).

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(1172,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(1173,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)],[1172]) ).

thf(1175,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)],[1173]) ).

thf(3183,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[3182]) ).

thf(18277,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
    inference(rewrite,[status(thm)],[3183,2545]) ).

thf(537,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(4203,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)],[537]) ).

thf(620,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(4635,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)],[620]) ).

thf(576,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(4430,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)],[576]) ).

thf(3747,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk251 @ m1_subset_1 ) ),
    inference(cnfConj,[status(thm)],[3746]) ).

thf(572,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(4420,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)],[572]) ).

thf(4064,plain,
    ~ ( sk275 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4062]) ).

thf(14061,plain,
    ! [A: $i] :
      ( ( ( sk410 @ 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
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(paramod_ordered,[status(thm)],[5759,7314]) ).

thf(14062,plain,
    ! [A: $i] :
      ( ( ( sk410 @ 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 ) ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[14061]) ).

thf(14063,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk410 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk410 @ m2_relset_1 ) ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[14062:[bind(A,$thf( sk410 ))]]) ).

thf(317,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(3006,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)],[317]) ).

thf(7569,plain,
    ( ( ( sk293 @ v1_xboole_0 )
     != ( sk215 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4327,3242]) ).

thf(7570,plain,
    ( ( sk293 @ v1_xboole_0 )
   != ( sk215 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7569]) ).

thf(7575,plain,
    sk293 != sk215,
    inference(simp,[status(thm)],[7570]) ).

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(1177,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(15964,plain,
    ! [A: $i] :
      ( ( ( sk204 @ 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)],[3129,1155]) ).

thf(15965,plain,
    ! [A: $i] :
      ( ( ( sk204 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15964]) ).

thf(15966,plain,
    ( ( sk204 @ k1_relat_1 @ ( sk204 @ k9_relat_1 ) )
    = ( sk204 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15965:[bind(A,$thf( sk204 ))]]) ).

thf(2911,plain,
    sk187 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(965,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(6376,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)],[965]) ).

thf(6908,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk204 @ 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)],[3129,1068]) ).

thf(6909,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk204 @ 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)],[6908]) ).

thf(6910,plain,
    ! [A: $i] : ( sk204 @ k1_relat_1 @ ( sk204 @ k9_relat_1 ) @ ( A @ ( sk204 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6909:[bind(A,$thf( A )),bind(B,$thf( sk204 ))]]) ).

thf(21657,plain,
    ! [A: $i] : ( sk204 @ k2_relat_1 @ ( A @ ( sk204 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6910,15966]) ).

thf(7437,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk215 @ 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)],[3243,1068]) ).

thf(7438,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk215 @ 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)],[7437]) ).

thf(7439,plain,
    ! [A: $i] : ( sk215 @ k1_relat_1 @ ( sk215 @ k9_relat_1 ) @ ( A @ ( sk215 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[7438:[bind(A,$thf( A )),bind(B,$thf( sk215 ))]]) ).

thf(22106,plain,
    ! [A: $i] : ( sk215 @ k2_relat_1 @ ( A @ ( sk215 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[7439,15947]) ).

thf(516,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(4103,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)],[516]) ).

thf(4911,plain,
    sk329 @ v6_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(881,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [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(5994,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ 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)],[881]) ).

thf(203,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(2267,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)],[203]) ).

thf(4731,plain,
    sk317 @ v4_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(741,axiom,
    ( ! [A: $i] :
        ( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
       => ? [B: $i] :
            ( ( B @ ( A @ p1_s3_funct_2 ) )
            & ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
           => ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
        & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_2) ).

thf(5335,plain,
    ( ! [A: $i] :
        ( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
       => ? [B: $i] :
            ( ( B @ ( A @ p1_s3_funct_2 ) )
            & ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
           => ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
        & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(419,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(3572,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)],[419]) ).

thf(487,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(3932,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)],[487]) ).

thf(4897,plain,
    sk328 @ v6_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(581,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(4452,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)],[581]) ).

thf(370,axiom,
    k1_xboole_0 @ v1_xboole_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(3298,plain,
    k1_xboole_0 @ v1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(2542,plain,
    sk139 @ v2_funct_1,
    inference(cnfConj,[status(thm)],[2539]) ).

thf(710,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_lattice4 ) )
         => ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r1_tarski ) )
                 => ( B @ ( C @ ( A @ k2_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice4) ).

thf(5180,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_lattice4 ) )
         => ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r1_tarski ) )
                 => ( B @ ( C @ ( A @ k2_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(4726,plain,
    sk317 @ v8_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(263,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(2664,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)],[263]) ).

thf(206,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(2278,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)],[206]) ).

thf(678,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(5007,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)],[678]) ).

thf(4684,plain,
    sk315 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(30672,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1042]) ).

thf(30673,plain,
    ( ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
    | ( sk1 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30672:[bind(A,$thf( sk1 ))]]) ).

thf(1055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk4 ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ r2_hidden ) )
      | ( ( C @ k1_relat_1 )
       != A )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1054]) ).

thf(1060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk4 ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ r2_hidden ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 )
      | ( ( C @ k1_relat_1 )
       != A ) ),
    inference(lifteq,[status(thm)],[1055]) ).

thf(1061,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k1_relat_1 @ ( B @ sk4 ) ) )
      | ( B @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ ( B @ sk5 ) ) @ r2_hidden ) )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[1060]) ).

thf(12260,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8997]) ).

thf(12261,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12260]) ).

thf(12274,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk213 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[12261]) ).

thf(468,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(3838,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)],[468]) ).

thf(12757,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk139 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2081,11212]) ).

thf(12758,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk139 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk139 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12757]) ).

thf(12786,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( sk139 @ k2_relat_1 )
       != k1_xboole_0 )
      | ( ( sk139 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12758]) ).

thf(12797,plain,
    ( ( ( sk139 @ k2_relat_1 )
     != k1_xboole_0 )
    | ( ( sk139 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12786]) ).

thf(654,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(4827,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)],[654]) ).

thf(842,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_0) ).

thf(5849,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)],[842]) ).

thf(439,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(3706,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)],[439]) ).

thf(310,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(2967,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)],[310]) ).

thf(689,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(5089,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)],[689]) ).

thf(888,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( 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(6029,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)],[888]) ).

thf(934,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [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(6212,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)],[934]) ).

thf(988,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(6476,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)],[988]) ).

thf(33561,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk361 @ sk20 @ 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)],[29748,1068]) ).

thf(33562,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk361 @ sk20 @ 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)],[33561]) ).

thf(33563,plain,
    ! [A: $i] : ( sk361 @ sk20 @ k1_relat_1 @ ( sk361 @ sk20 @ k9_relat_1 ) @ ( A @ ( sk361 @ sk20 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[33562:[bind(A,$thf( A )),bind(B,$thf( sk361 @ sk20 ))]]) ).

thf(40073,plain,
    ! [A: $i] : ( sk361 @ sk20 @ k2_relat_1 @ ( A @ ( sk361 @ sk20 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[33563,33603]) ).

thf(1167,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)],[1165]) ).

thf(1170,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)],[1167]) ).

thf(1171,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)],[1170]) ).

thf(2418,plain,
    sk119 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2411]) ).

thf(657,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(4844,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)],[657]) ).

thf(5336,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( sk374 @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) )
        | ~ ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
        | ~ sk372 )
      & ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk374 @ m2_relset_1 ) ) )
        | ~ sk372 )
      & ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk374 @ v1_funct_2 ) ) )
        | ~ sk372 )
      & ( ( sk374 @ v1_funct_1 )
        | ~ sk372 )
      & ( sk372
        | ~ ( A @ ( sk373 @ p1_s3_funct_2 ) )
        | ~ ( f2_s3_funct_2 @ ( A @ m1_subset_1 ) ) )
      & ( sk372
        | ( f1_s3_funct_2 @ ( sk373 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[5335]) ).

thf(5340,plain,
    ( sk372
    | ( f1_s3_funct_2 @ ( sk373 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[5336]) ).

thf(279,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(2725,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)],[279]) ).

thf(223,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(2401,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)],[223]) ).

thf(2212,plain,
    sk95 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

thf(980,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(6449,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)],[980]) ).

thf(15573,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8568]) ).

thf(15574,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15573]) ).

thf(15691,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk72 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15574]) ).

thf(15725,plain,
    ( ( sk72 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15691]) ).

thf(720,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(5218,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)],[720]) ).

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

thf(1066,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)],[1065]) ).

thf(920,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( 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(6151,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)],[920]) ).

thf(568,axiom,
    ? [A: $i] : ( A @ l1_struct_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(4372,plain,
    ? [A: $i] : ( A @ l1_struct_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(4373,plain,
    sk297 @ l1_struct_0,
    inference(cnf,[status(esa)],[4372]) ).

thf(482,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(3917,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(15931,plain,
    ! [A: $i] :
      ( ( ( sk213 @ 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)],[3230,1155]) ).

thf(15932,plain,
    ! [A: $i] :
      ( ( ( sk213 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15931]) ).

thf(15933,plain,
    ( ( sk213 @ k1_relat_1 @ ( sk213 @ k9_relat_1 ) )
    = ( sk213 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15932:[bind(A,$thf( sk213 ))]]) ).

thf(9585,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk213 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3231,4639]) ).

thf(9586,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk213 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9585]) ).

thf(9601,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk213 ),
    inference(simp,[status(thm)],[9586]) ).

thf(24376,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 )
       != sk213 ) ),
    inference(paramod_ordered,[status(thm)],[2054,9601]) ).

thf(24377,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk213 ),
    inference(pattern_uni,[status(thm)],[24376:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(24397,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk213 ),
    inference(simp,[status(thm)],[24377]) ).

thf(6780,plain,
    ( ( ( sk153 @ v1_xboole_0 )
     != ( sk15 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2656,1236]) ).

thf(6781,plain,
    ( ( sk153 @ v1_xboole_0 )
   != ( sk15 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6780]) ).

thf(6783,plain,
    sk153 != sk15,
    inference(simp,[status(thm)],[6781]) ).

thf(727,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(5248,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)],[727]) ).

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 ) )
     => ( ( 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(3159,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)],[348]) ).

thf(219,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(2369,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)],[219]) ).

thf(566,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(4362,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)],[566]) ).

thf(491,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(3953,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)],[491]) ).

thf(875,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(5976,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)],[875]) ).

thf(925,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(6180,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)],[925]) ).

thf(950,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( 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(6293,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)],[950]) ).

thf(592,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(4497,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)],[592]) ).

thf(617,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(4626,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)],[617]) ).

thf(2207,plain,
    sk95 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

thf(738,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(5326,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(4890,plain,
    sk328 @ v10_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(398,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(3444,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)],[398]) ).

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(1809,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(4901,plain,
    sk329 @ v8_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(12186,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7862]) ).

thf(12187,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12186]) ).

thf(12288,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk213 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12187]) ).

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 ) )
     => ( ( 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(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 ) )
     => ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
        & ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(483,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(3921,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)],[483]) ).

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(1472,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(146,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(1958,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)],[146]) ).

thf(5753,plain,
    ( ( ( f3_s11_funct_2 @ ( sk410 @ ( 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)],[5752]) ).

thf(5763,plain,
    ( ( ( f3_s11_funct_2 @ ( sk410 @ ( 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)],[5753]) ).

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(2005,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(833,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ 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(5812,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( 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)],[833]) ).

thf(1076,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ ( D @ ( E @ sk6 ) ) ) ) @ 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)],[1075]) ).

thf(574,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(4426,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)],[574]) ).

thf(4907,plain,
    sk329 @ v9_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(778,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v3_filter_0 )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ ( E @ m1_filter_0 ) )
                     => ! [F: $i] :
                          ( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
                            & ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_filter_0) ).

thf(5538,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v3_filter_0 )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ ( E @ m1_filter_0 ) )
                     => ! [F: $i] :
                          ( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
                            & ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(2914,plain,
    ~ ( sk187 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2910]) ).

thf(12212,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7853]) ).

thf(12213,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12212]) ).

thf(12326,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk139 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12213]) ).

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(1662,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(526,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(4136,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)],[526]) ).

thf(1034,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(6672,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)],[1034]) ).

thf(1207,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)],[1206]) ).

thf(1208,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)],[1207]) ).

thf(4886,plain,
    sk328 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(315,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(2994,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)],[315]) ).

thf(38291,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)],[5265,1263]) ).

thf(38292,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)],[38291]) ).

thf(38337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[38292]) ).

thf(38350,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
     != ( B @ k1_tarski ) ),
    inference(simp,[status(thm)],[38337]) ).

thf(2471,plain,
    k13_nat_lat @ v10_lattices,
    inference(cnfConj,[status(thm)],[2467]) ).

thf(4735,plain,
    sk317 @ v7_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

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(1905,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(292,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(2878,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)],[292]) ).

thf(302,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(2927,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)],[302]) ).

thf(258,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(2629,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)],[258]) ).

thf(9589,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk293 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4327,4639]) ).

thf(9590,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk293 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9589]) ).

thf(9599,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk293 ),
    inference(simp,[status(thm)],[9590]) ).

thf(24368,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 )
       != sk293 ) ),
    inference(paramod_ordered,[status(thm)],[2054,9599]) ).

thf(24369,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk293 ),
    inference(pattern_uni,[status(thm)],[24368:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(24392,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk293 ),
    inference(simp,[status(thm)],[24369]) ).

thf(1144,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)],[1143]) ).

thf(1145,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)],[1144]) ).

thf(858,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(5916,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)],[858]) ).

thf(1012,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(6564,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)],[1012]) ).

thf(885,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(6008,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)],[885]) ).

thf(1032,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(6664,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)],[1032]) ).

thf(746,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ v11_lattices )
           => ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_0) ).

thf(5358,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ v11_lattices )
           => ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(1178,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)],[1177]) ).

thf(1179,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)],[1178]) ).

thf(1181,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)],[1179]) ).

thf(561,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(4336,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)],[561]) ).

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(1551,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(21678,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk204 @ k2_relat_1 @ ( A @ ( sk204 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21657,1099]) ).

thf(21679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk204 @ k2_relat_1 @ ( A @ ( sk204 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[21678]) ).

thf(21680,plain,
    ! [B: $i,A: $i] : ( sk204 @ k2_relat_1 @ ( A @ ( B @ ( sk204 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[21679:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk204 @ k9_relat_1 ) )),bind(C,$thf( sk204 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(21740,plain,
    ! [B: $i,A: $i] : ( sk204 @ k2_relat_1 @ ( A @ ( B @ ( sk204 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[21680]) ).

thf(675,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(4982,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)],[675]) ).

thf(4983,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk343 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
          = ( A @ f3_s12_funct_2 ) )
        | ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
        | ~ sk341 )
      & ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk343 @ m2_relset_1 ) ) )
        | ~ sk341 )
      & ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk343 @ v1_funct_2 ) ) )
        | ~ sk341 )
      & ( ( sk343 @ v1_funct_1 )
        | ~ sk341 )
      & ( sk341
        | ~ ( f2_s12_funct_2 @ ( sk342 @ f3_s12_funct_2 @ r2_hidden ) ) )
      & ( sk341
        | ( f1_s12_funct_2 @ ( sk342 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4982]) ).

thf(4986,plain,
    ( sk341
    | ( f1_s12_funct_2 @ ( sk342 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4983]) ).

thf(1009,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(6557,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)],[1009]) ).

thf(6641,plain,
    sk475 @ l3_lattices,
    inference(cnf,[status(esa)],[6640]) ).

thf(6011,plain,
    ( ~ ( sk423 @ v3_struct_0 )
    & ( sk423 @ l2_struct_0 ) ),
    inference(cnf,[status(esa)],[6010]) ).

thf(6012,plain,
    sk423 @ l2_struct_0,
    inference(cnfConj,[status(thm)],[6011]) ).

thf(505,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(4035,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)],[505]) ).

thf(733,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(5294,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)],[733]) ).

thf(481,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(3913,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)],[481]) ).

thf(469,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(3842,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)],[469]) ).

thf(262,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(2661,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)],[262]) ).

thf(357,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ ( A @ r1_relat_2 ) )
        <=> ! [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
             => ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).

thf(3214,plain,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( ! [C: $i] :
                ( ( B @ ( C @ r2_hidden ) )
               => ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) )
           => ( B @ ( A @ r1_relat_2 ) ) )
          & ( ( B @ ( A @ r1_relat_2 ) )
           => ! [C: $i] :
                ( ( B @ ( C @ r2_hidden ) )
               => ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(478,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(3904,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)],[478]) ).

thf(475,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(3872,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)],[475]) ).

thf(990,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
            = ( A @ k5_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattices) ).

thf(6481,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)],[990]) ).

thf(4593,plain,
    sk310 @ v12_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(29813,plain,
    ! [A: $i] :
      ( ( A != sk358 )
      | ( k1_xboole_0 @ l2_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,5173]) ).

thf(29814,plain,
    ( ( k1_xboole_0 @ l2_lattices )
    | ( sk358 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29813:[bind(A,$thf( sk358 ))]]) ).

thf(249,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(2567,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)],[249]) ).

thf(1013,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(6577,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)],[1013]) ).

thf(759,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
                <=> ! [D: $i] :
                      ( ( A @ ( D @ m1_subset_1 ) )
                     => ! [E: $i] :
                          ( ( A @ ( E @ m1_subset_1 ) )
                         => ! [F: $i] :
                              ( ( A @ ( F @ m1_subset_1 ) )
                             => ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                                = ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_binop_1) ).

thf(5452,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( ! [D: $i] :
                        ( ( A @ ( D @ m1_subset_1 ) )
                       => ! [E: $i] :
                            ( ( A @ ( E @ m1_subset_1 ) )
                           => ! [F: $i] :
                                ( ( A @ ( F @ m1_subset_1 ) )
                               => ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                                  = ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
                   => ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
                  & ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
                   => ! [D: $i] :
                        ( ( A @ ( D @ m1_subset_1 ) )
                       => ! [E: $i] :
                            ( ( A @ ( E @ m1_subset_1 ) )
                           => ! [F: $i] :
                                ( ( A @ ( F @ m1_subset_1 ) )
                               => ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                                  = ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(899,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(6069,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)],[899]) ).

thf(800,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(5624,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)],[800]) ).

thf(724,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(5229,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)],[724]) ).

thf(12225,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,7486]) ).

thf(12226,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12225]) ).

thf(12289,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk139 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12226]) ).

thf(7380,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk213 @ 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)],[3230,1068]) ).

thf(7381,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk213 @ 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)],[7380]) ).

thf(7382,plain,
    ! [A: $i] : ( sk213 @ k1_relat_1 @ ( sk213 @ k9_relat_1 ) @ ( A @ ( sk213 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[7381:[bind(A,$thf( A )),bind(B,$thf( sk213 ))]]) ).

thf(21743,plain,
    ! [A: $i] : ( sk213 @ k2_relat_1 @ ( A @ ( sk213 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[7382,15933]) ).

thf(913,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(6120,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)],[913]) ).

thf(29203,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk410 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk410 @ v1_partfun1 ) ) )
      | ~ $true
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(paramod_ordered,[status(thm)],[2266,14063]) ).

thf(29204,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk410 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk410 @ v1_partfun1 ) ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[29203]) ).

thf(29213,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk410 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk410 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[29204]) ).

thf(29229,plain,
    ( ( sk410 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk410 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[29213]) ).

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(1743,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(1394,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk26 ) @ v1_funct_1 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1388]) ).

thf(1399,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk26 ) @ v1_funct_1 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1394]) ).

thf(1400,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ sk26 ) @ v1_funct_1 ),
    inference(simp,[status(thm)],[1399]) ).

thf(332,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(3082,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)],[332]) ).

thf(1020,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(6621,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)],[1020]) ).

thf(4673,plain,
    sk315 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(32724,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1037]) ).

thf(32725,plain,
    ( ( k1_xboole_0 @ u1_struct_0 @ ( sk3 @ m1_subset_1 ) )
    | ( sk1 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[32724:[bind(A,$thf( sk1 ))]]) ).

thf(670,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(4950,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)],[670]) ).

thf(466,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_funct_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(3833,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_funct_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(431,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).

thf(3659,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(536,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(4200,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)],[536]) ).

thf(29764,plain,
    ! [A: $i] :
      ( ( A != sk187 )
      | ( k1_xboole_0 @ v3_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,2921]) ).

thf(29765,plain,
    ( ( k1_xboole_0 @ v3_lattices )
    | ( sk187 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29764:[bind(A,$thf( sk187 ))]]) ).

thf(15606,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7853]) ).

thf(15607,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15606]) ).

thf(15688,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk139 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15607]) ).

thf(15721,plain,
    ( ( sk139 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15688]) ).

thf(790,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(5592,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)],[790]) ).

thf(877,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(5980,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)],[877]) ).

thf(268,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(2678,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)],[268]) ).

thf(586,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(4469,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)],[586]) ).

thf(9575,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk153 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2656,3049]) ).

thf(9576,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk153 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9575]) ).

thf(9578,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk153 ),
    inference(simp,[status(thm)],[9576]) ).

thf(225,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(2407,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)],[225]) ).

thf(4894,plain,
    sk328 @ v8_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

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

thf(1230,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)],[1228]) ).

thf(288,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(2850,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)],[288]) ).

thf(19539,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk139 @ k2_relat_1 @ ( A @ ( sk139 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19518,1099]) ).

thf(19540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk139 @ k2_relat_1 @ ( A @ ( sk139 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[19539]) ).

thf(19541,plain,
    ! [B: $i,A: $i] : ( sk139 @ k2_relat_1 @ ( A @ ( B @ ( sk139 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[19540:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk139 @ k9_relat_1 ) )),bind(C,$thf( sk139 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(19584,plain,
    ! [B: $i,A: $i] : ( sk139 @ k2_relat_1 @ ( A @ ( B @ ( sk139 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[19541]) ).

thf(918,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(6146,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)],[918]) ).

thf(269,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(2689,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)],[269]) ).

thf(428,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(3642,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)],[428]) ).

thf(2920,plain,
    sk187 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(12812,plain,
    ! [A: $i] :
      ( ( ( A @ sk251 @ v1_xboole_0 )
       != ( sk361 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3748,5222]) ).

thf(12813,plain,
    ! [A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
     != ( sk361 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12812]) ).

thf(12826,plain,
    ! [A: $i] :
      ( ( A @ sk251 )
     != sk361 ),
    inference(simp,[status(thm)],[12813]) ).

thf(999,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(6513,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)],[999]) ).

thf(952,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(6298,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)],[952]) ).

thf(867,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(5955,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)],[867]) ).

thf(811,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(5684,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)],[811]) ).

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(2092,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(4905,plain,
    sk329 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(152,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(1987,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)],[152]) ).

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(1716,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(373,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(3305,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)],[373]) ).

thf(818,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(5731,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)],[818]) ).

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(1300,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(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(1637,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(8992,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3080,7367]) ).

thf(8993,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8992]) ).

thf(8994,plain,
    ( ( k1_xboole_0 @ v3_filter_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)],[8993:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15555,plain,
    ( ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8994,2266]) ).

thf(15556,plain,
    ( ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15555]) ).

thf(730,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(5276,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)],[730]) ).

thf(149,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(1980,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)],[149]) ).

thf(703,axiom,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
      & ( A @ k1_subset_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).

thf(5154,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
      & ( A @ k1_subset_1 @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(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(3774,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(563,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(4351,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)],[563]) ).

thf(923,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(6174,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)],[923]) ).

thf(702,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(5152,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)],[702]) ).

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(1658,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(273,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(2701,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)],[273]) ).

thf(297,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(2903,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)],[297]) ).

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(1679,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(392,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(3412,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)],[392]) ).

thf(645,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(4781,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)],[645]) ).

thf(637,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(4737,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)],[637]) ).

thf(29741,plain,
    ! [A: $i] :
      ( ( A != sk119 )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,2412]) ).

thf(29742,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ( sk119 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29741:[bind(A,$thf( sk119 ))]]) ).

thf(1218,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)],[1217]) ).

thf(758,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).

thf(5450,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(692,axiom,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).

thf(5106,plain,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(471,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(3853,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(2468,plain,
    k13_nat_lat @ v3_lattices,
    inference(cnfConj,[status(thm)],[2467]) ).

thf(1220,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)],[1217]) ).

thf(267,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(2675,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)],[267]) ).

thf(12176,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8568]) ).

thf(12177,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12176]) ).

thf(12328,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk72 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12177]) ).

thf(854,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(5902,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)],[854]) ).

thf(7947,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1081,7489]) ).

thf(7948,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7947]) ).

thf(7961,plain,
    ! [B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( B @ k1_relat_1 )
       != sk1 )
      | ( B != sk204 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7948]) ).

thf(7973,plain,
    ( ( ( sk204 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) )
    | ~ ( sk204 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[7961]) ).

thf(10589,plain,
    ( ( ( sk204 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7973,3129]) ).

thf(10590,plain,
    ( ( ( sk204 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[10589]) ).

thf(12773,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk204 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2081,10590]) ).

thf(12774,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk204 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12773]) ).

thf(12780,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( sk204 @ k2_relat_1 )
       != k1_xboole_0 )
      | ( ( sk204 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12774]) ).

thf(12790,plain,
    ( ( ( sk204 @ k2_relat_1 )
     != k1_xboole_0 )
    | ( ( sk204 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12780]) ).

thf(15674,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7489]) ).

thf(15675,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15674]) ).

thf(15699,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk204 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15675]) ).

thf(15736,plain,
    ( ( sk204 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15699]) ).

thf(492,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(3961,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)],[492]) ).

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(1372,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(937,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(6220,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)],[937]) ).

thf(1027,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(6650,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)],[1027]) ).

thf(437,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(3690,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)],[437]) ).

thf(3691,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)],[3690]) ).

thf(3692,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)],[3691]) ).

thf(3693,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ( A != B ) ),
    inference(cnfConj,[status(thm)],[3692]) ).

thf(3696,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ( A != B ) ),
    inference(lifteq,[status(thm)],[3693]) ).

thf(3697,plain,
    ! [A: $i] : ( A @ ( A @ r1_tarski ) ),
    inference(simp,[status(thm)],[3696]) ).

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(1898,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(6677,plain,
    ( ( ( sk72 @ v1_xboole_0 )
     != ( sk15 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1979,1236]) ).

thf(6678,plain,
    ( ( sk72 @ v1_xboole_0 )
   != ( sk15 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6677]) ).

thf(6679,plain,
    sk72 != sk15,
    inference(simp,[status(thm)],[6678]) ).

thf(286,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(2838,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)],[286]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(2113,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(30583,plain,
    ! [A: $i] :
      ( ( A != sk15 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,6856]) ).

thf(30584,plain,
    ! [A: $i] :
      ( ( A != sk15 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[30583]) ).

thf(30585,plain,
    sk15 @ sk20 @ v1_relat_1,
    inference(pattern_uni,[status(thm)],[30584:[bind(A,$thf( sk15 ))]]) ).

thf(33664,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk15 @ sk20 @ 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)],[30585,1068]) ).

thf(33665,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk15 @ sk20 @ 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)],[33664]) ).

thf(33666,plain,
    ! [A: $i] : ( sk15 @ sk20 @ k1_relat_1 @ ( sk15 @ sk20 @ k9_relat_1 ) @ ( A @ ( sk15 @ sk20 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[33665:[bind(A,$thf( A )),bind(B,$thf( sk15 @ sk20 ))]]) ).

thf(33704,plain,
    ! [A: $i] :
      ( ( ( sk15 @ sk20 @ 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)],[30585,1155]) ).

thf(33705,plain,
    ! [A: $i] :
      ( ( ( sk15 @ sk20 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[33704]) ).

thf(33706,plain,
    ( ( sk15 @ sk20 @ k1_relat_1 @ ( sk15 @ sk20 @ k9_relat_1 ) )
    = ( sk15 @ sk20 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[33705:[bind(A,$thf( sk15 @ sk20 ))]]) ).

thf(41318,plain,
    ! [A: $i] : ( sk15 @ sk20 @ k2_relat_1 @ ( A @ ( sk15 @ sk20 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[33666,33706]) ).

thf(722,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(5223,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)],[722]) ).

thf(341,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(3124,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)],[341]) ).

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(1536,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(6799,plain,
    ( ( ( sk361 @ v1_xboole_0 )
     != ( sk72 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1979,5222]) ).

thf(6800,plain,
    ( ( sk361 @ v1_xboole_0 )
   != ( sk72 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6799]) ).

thf(6803,plain,
    sk361 != sk72,
    inference(simp,[status(thm)],[6800]) ).

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(1702,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(220,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(2379,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)],[220]) ).

thf(674,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(4976,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)],[674]) ).

thf(24361,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 )
       != sk72 ) ),
    inference(paramod_ordered,[status(thm)],[2054,9602]) ).

thf(24362,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk72 ),
    inference(pattern_uni,[status(thm)],[24361:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(24389,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk72 ),
    inference(simp,[status(thm)],[24362]) ).

thf(882,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(5998,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)],[882]) ).

thf(726,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(5240,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)],[726]) ).

thf(1955,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    inference(cnf,[status(esa)],[1954]) ).

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(2145,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(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(1485,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(1048,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)],[1046]) ).

thf(1051,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)],[1048]) ).

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

thf(676,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(4991,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)],[676]) ).

thf(927,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( A @ ( 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(6193,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)],[927]) ).

thf(543,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(4235,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)],[543]) ).

thf(723,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(5226,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)],[723]) ).

thf(748,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
              <=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                  = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattices) ).

thf(5364,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                    = B )
                 => ( C @ ( B @ ( A @ r1_lattices ) ) ) )
                & ( ( C @ ( B @ ( A @ r1_lattices ) ) )
                 => ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                    = B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(305,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(2949,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)],[305]) ).

thf(792,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattices) ).

thf(5596,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(1004,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(6531,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)],[1004]) ).

thf(852,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(5895,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)],[852]) ).

thf(15117,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( A @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15098,1099]) ).

thf(15118,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( A @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15117]) ).

thf(15119,plain,
    ! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[15118:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f2_s4_funct_2 )),bind(D,$thf( D ))]]) ).

thf(15159,plain,
    ! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk313 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[15119]) ).

thf(13594,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)],[1957,2169]) ).

thf(13595,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
    inference(pattern_uni,[status(thm)],[13594:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(15601,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8554]) ).

thf(15602,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15601]) ).

thf(15695,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk313 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15602]) ).

thf(15731,plain,
    ( ( sk313 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15695]) ).

thf(38289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk81 @ ( A @ r2_hidden ) )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2131,1263]) ).

thf(38290,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk81 @ ( A @ r2_hidden ) )
     != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[38289]) ).

thf(38338,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk81 )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[38290]) ).

thf(38351,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
     != ( B @ sk81 ) ),
    inference(simp,[status(thm)],[38338]) ).

thf(4671,plain,
    sk315 @ v4_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(12806,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk251 @ v1_xboole_0 )
       != ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3748,3049]) ).

thf(12807,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk251 @ v1_xboole_0 )
     != ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12806]) ).

thf(12829,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk251 )
     != ( B @ ( B @ k1_funct_2 ) ) ),
    inference(simp,[status(thm)],[12807]) ).

thf(9381,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk213 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3231,2435]) ).

thf(9382,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk213 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9381]) ).

thf(9395,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk213 ),
    inference(simp,[status(thm)],[9382]) ).

thf(642,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(4770,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)],[642]) ).

thf(291,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(2870,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)],[291]) ).

thf(863,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(5934,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)],[863]) ).

thf(194,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(2187,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)],[194]) ).

thf(764,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
      <=> ? [F: $i,G: $i] :
            ( ( E @ ( G @ r2_hidden ) )
            & ( D @ ( F @ r2_hidden ) )
            & ( A
              = ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
            & ( C @ ( G @ m1_subset_1 ) )
            & ( B @ ( F @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).

thf(5485,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( ? [F: $i,G: $i] :
              ( ( E @ ( G @ r2_hidden ) )
              & ( D @ ( F @ r2_hidden ) )
              & ( A
                = ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
              & ( C @ ( G @ m1_subset_1 ) )
              & ( B @ ( F @ m1_subset_1 ) ) )
         => ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) ) )
        & ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
         => ? [F: $i,G: $i] :
              ( ( E @ ( G @ r2_hidden ) )
              & ( D @ ( F @ r2_hidden ) )
              & ( A
                = ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
              & ( C @ ( G @ m1_subset_1 ) )
              & ( B @ ( F @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(865,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(5939,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)],[865]) ).

thf(604,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(4548,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)],[604]) ).

thf(257,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(2626,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(17656,plain,
    ! [B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( B @ k1_zfmisc_1 ) )
      | ( ( A @ sk251 )
       != ( k1_xboole_0 @ k1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[1957,12831]) ).

thf(17657,plain,
    ! [A: $i] :
      ( ( A @ sk251 )
     != ( k1_xboole_0 @ k1_tarski ) ),
    inference(pattern_uni,[status(thm)],[17656:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).

thf(4727,plain,
    sk317 @ v10_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

thf(27605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ k2_tarski ) )
       != ( D @ ( C @ k2_tarski ) ) )
      | ( ( A @ k1_tarski )
       != ( B @ sk251 ) ) ),
    inference(paramod_ordered,[status(thm)],[4535,12824]) ).

thf(27606,plain,
    ! [B: $i,A: $i] :
      ( ( A @ k1_tarski )
     != ( B @ sk251 ) ),
    inference(pattern_uni,[status(thm)],[27605:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(979,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_nat_lat ) )
         => ! [C: $i] :
              ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_filter_2) ).

thf(6447,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_nat_lat ) )
         => ! [C: $i] :
              ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(421,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(3589,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)],[421]) ).

thf(821,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(5749,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)],[821]) ).

thf(335,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(3092,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)],[335]) ).

thf(4587,plain,
    sk310 @ v9_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(668,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(4945,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)],[668]) ).

thf(1180,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)],[1178]) ).

thf(15065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk313 @ k2_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15033,1113]) ).

thf(15066,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk313 @ k2_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15065]) ).

thf(15067,plain,
    ! [A: $i] : ( sk313 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[15066:[bind(A,$thf( sk313 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(15099,plain,
    ! [A: $i] : ( sk313 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[15067]) ).

thf(777,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_0) ).

thf(5536,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(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(1817,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(6013,plain,
    ~ ( sk423 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[6011]) ).

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(2078,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(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(1834,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(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(1913,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(7406,plain,
    ( ( ( sk215 @ v1_xboole_0 )
     != ( sk213 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3231,3242]) ).

thf(7407,plain,
    ( ( sk215 @ v1_xboole_0 )
   != ( sk213 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7406]) ).

thf(7412,plain,
    sk215 != sk213,
    inference(simp,[status(thm)],[7407]) ).

thf(11449,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk72 ) ),
    inference(paramod_ordered,[status(thm)],[1957,8527]) ).

thf(11450,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk72 ),
    inference(pattern_uni,[status(thm)],[11449:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(870,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(5966,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)],[870]) ).

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(1844,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(916,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(6137,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)],[916]) ).

thf(677,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(4997,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)],[677]) ).

thf(416,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(3548,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)],[416]) ).

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(1654,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(211,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(2325,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)],[211]) ).

thf(485,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(3928,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)],[485]) ).

thf(2209,plain,
    sk95 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

thf(1124,plain,
    ( ( k1_xboole_0 @ k1_relat_1 )
    = k1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1123]) ).

thf(1126,plain,
    ( ( k1_xboole_0 @ k1_relat_1 )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1124]) ).

thf(856,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(5907,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)],[856]) ).

thf(2919,plain,
    sk187 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(696,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(5124,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)],[696]) ).

thf(740,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v11_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ k4_lattices ) ) )
                        = ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_lattice2) ).

thf(5332,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v11_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ k4_lattices ) ) )
                        = ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(261,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(2658,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)],[261]) ).

thf(30952,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k4_tarski ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,9392]) ).

thf(30953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k4_tarski ) ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[30952]) ).

thf(30954,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk20 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[30953:[bind(A,$thf( E @ ( D @ k4_tarski ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).

thf(32784,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk20 @ v1_relat_1 ),
    inference(simp,[status(thm)],[30954]) ).

thf(686,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(5068,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)],[686]) ).

thf(712,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( B @ ( C @ ( A @ r1_lattices ) ) )
                  & ( C @ ( B @ ( A @ r1_lattices ) ) ) )
               => ( B = C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).

thf(5184,plain,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( B @ ( C @ ( A @ r1_lattices ) ) )
                  & ( C @ ( B @ ( A @ r1_lattices ) ) ) )
               => ( B = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(1104,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
      | ( ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
      | ( ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( 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)],[1101]) ).

thf(1108,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 @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
      | ( ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk10 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ),
    inference(lifteq,[status(thm)],[1104]) ).

thf(4730,plain,
    ~ ( sk317 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4723]) ).

thf(4678,plain,
    sk315 @ v10_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

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(1998,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(456,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(3797,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)],[456]) ).

thf(12254,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8565]) ).

thf(12255,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12254]) ).

thf(12302,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk213 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12255]) ).

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(1276,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(736,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ~ ( C @ ( D @ r2_hidden ) )
            & ( A = D )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).

thf(5315,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( ? [D: $i] :
              ( ~ ( C @ ( D @ r2_hidden ) )
              & ( A = D )
              & ( B @ ( D @ m1_subset_1 ) ) )
         => ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) ) )
        & ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
         => ? [D: $i] :
              ( ~ ( C @ ( D @ r2_hidden ) )
              & ( A = D )
              & ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(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(1326,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(662,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(4913,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)],[662]) ).

thf(313,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(2988,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)],[313]) ).

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(2098,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(440,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(3709,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)],[440]) ).

thf(627,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(4666,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)],[627]) ).

thf(4681,plain,
    sk315 @ v6_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(4683,plain,
    ~ ( sk315 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4669]) ).

thf(853,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(5899,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)],[853]) ).

thf(1019,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(6618,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)],[1019]) ).

thf(767,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ m2_lattice4 ) )
        & ~ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k22_filter_2) ).

thf(5505,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ m2_lattice4 ) )
        & ~ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ v1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(957,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(6322,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)],[957]) ).

thf(902,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(6077,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)],[902]) ).

thf(729,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(5272,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)],[729]) ).

thf(208,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(2290,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)],[208]) ).

thf(647,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(4791,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)],[647]) ).

thf(3104,plain,
    k6_nat_lat @ v9_lattices,
    inference(cnfConj,[status(thm)],[3096]) ).

thf(344,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(3136,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)],[344]) ).

thf(384,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(3368,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)],[384]) ).

thf(432,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(3662,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)],[432]) ).

thf(2416,plain,
    sk119 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2411]) ).

thf(4900,plain,
    sk329 @ v13_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

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(1558,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(547,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( 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(4261,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)],[547]) ).

thf(6340,plain,
    ( ( f2_s4_subset_1 = f3_s4_subset_1 )
    | ( sk450 @ p1_s4_subset_1 )
    | ( f3_s4_subset_1 @ ( sk450 @ r2_hidden ) )
    | sk448 ),
    inference(cnfConj,[status(thm)],[6339]) ).

thf(6354,plain,
    ( ( sk450 @ p1_s4_subset_1 )
    | ( f3_s4_subset_1 @ ( sk450 @ r2_hidden ) )
    | sk448
    | ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
    inference(lifteq,[status(thm)],[6340]) ).

thf(638,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(4745,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)],[638]) ).

thf(942,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(6257,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)],[942]) ).

thf(31453,plain,
    ! [A: $i] :
      ( ( A != sk3 )
      | ( k1_xboole_0 @ ( sk2 @ ( sk1 @ r3_lattices ) ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1043]) ).

thf(31454,plain,
    ( ( k1_xboole_0 @ ( sk2 @ ( sk1 @ r3_lattices ) ) )
    | ( sk3 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[31453:[bind(A,$thf( sk3 ))]]) ).

thf(839,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(5837,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)],[839]) ).

thf(754,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(5409,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)],[754]) ).

thf(1212,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ v3_binop_1 ) )
      | ( A @ ( A @ ( B @ sk13 ) @ 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)],[1210]) ).

thf(922,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [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(6166,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)],[922]) ).

thf(31451,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk3 @ ( k1_xboole_0 @ ( sk1 @ r3_lattices ) ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1043]) ).

thf(31452,plain,
    ( ( sk3 @ ( k1_xboole_0 @ ( sk1 @ r3_lattices ) ) )
    | ( sk2 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[31451:[bind(A,$thf( sk2 ))]]) ).

thf(39177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
       != ( C @ ( B @ k4_xboole_0 ) ) )
      | ( ( A @ ( C @ sk14 ) )
        = B ) ),
    inference(paramod_ordered,[status(thm)],[1139,39164]) ).

thf(39178,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ sk14 ) )
      = A ),
    inference(pattern_uni,[status(thm)],[39177:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(836,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(5828,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)],[836]) ).

thf(3176,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3173]) ).

thf(3180,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3176]) ).

thf(3181,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[3180]) ).

thf(2475,plain,
    k13_nat_lat @ v4_lattices,
    inference(cnfConj,[status(thm)],[2467]) ).

thf(613,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(4602,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)],[613]) ).

thf(375,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(3324,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)],[375]) ).

thf(625,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(4649,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)],[625]) ).

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 ) )
         => ( ( ( 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(6397,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)],[974]) ).

thf(673,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(4964,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)],[673]) ).

thf(2912,plain,
    sk187 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(991,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(6484,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)],[991]) ).

thf(9389,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk153 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2656,2435]) ).

thf(9390,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk153 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[9389]) ).

thf(9393,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk153 ),
    inference(simp,[status(thm)],[9390]) ).

thf(4591,plain,
    sk310 @ v10_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(640,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(4759,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)],[640]) ).

thf(21764,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk213 @ k2_relat_1 @ ( A @ ( sk213 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21743,1099]) ).

thf(21765,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk213 @ k2_relat_1 @ ( A @ ( sk213 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[21764]) ).

thf(21766,plain,
    ! [B: $i,A: $i] : ( sk213 @ k2_relat_1 @ ( A @ ( B @ ( sk213 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[21765:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk213 @ k9_relat_1 ) )),bind(C,$thf( sk213 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(21811,plain,
    ! [B: $i,A: $i] : ( sk213 @ k2_relat_1 @ ( A @ ( B @ ( sk213 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[21766]) ).

thf(893,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ 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(6045,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)],[893]) ).

thf(816,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(5699,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)],[816]) ).

thf(1001,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(6521,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)],[1001]) ).

thf(1077,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ ( C @ ( D @ ( E @ sk6 ) ) ) ) @ 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)],[1075]) ).

thf(2362,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_funct_1 ),
    inference(cnfConj,[status(thm)],[2359]) ).

thf(946,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(6277,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)],[946]) ).

thf(897,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(6062,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)],[897]) ).

thf(771,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).

thf(5517,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_lattices ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(429,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(3645,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)],[429]) ).

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(1444,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(978,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(6444,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)],[978]) ).

thf(984,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [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(6462,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)],[984]) ).

thf(6499,plain,
    ~ ( sk462 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[6497]) ).

thf(2627,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
    inference(cnf,[status(esa)],[2626]) ).

thf(2628,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) )
      = ( A @ k1_subset_1 ) ),
    inference(lifteq,[status(thm)],[2627]) ).

thf(38710,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k3_subset_1 ) )
      = k1_xboole_0 ),
    inference(rewrite,[status(thm)],[2628,2545,3014]) ).

thf(2421,plain,
    sk119 @ v1_lattice2,
    inference(cnfConj,[status(thm)],[2411]) ).

thf(659,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(4880,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)],[659]) ).

thf(15571,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8551]) ).

thf(15572,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15571]) ).

thf(15706,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk139 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15572]) ).

thf(15743,plain,
    ( ( sk139 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[15706]) ).

thf(4670,plain,
    sk315 @ v15_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(611,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(4596,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)],[611]) ).

thf(1016,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( 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(6600,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)],[1016]) ).

thf(713,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v7_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
                   => ( D @ ( C @ ( A @ k2_lattices ) ) @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattices) ).

thf(5187,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v7_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
                   => ( D @ ( C @ ( A @ k2_lattices ) ) @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(197,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(2218,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)],[197]) ).

thf(523,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(4125,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)],[523]) ).

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(1642,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(808,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(5677,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)],[808]) ).

thf(664,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(4917,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)],[664]) ).

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(2155,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(499,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(3997,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)],[499]) ).

thf(8128,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1083,7495]) ).

thf(8129,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk213 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8128]) ).

thf(8164,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 )
       != k1_xboole_0 )
      | ( A != sk1 )
      | ( B != sk213 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8129]) ).

thf(8180,plain,
    ( ( ( sk213 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk213 @ k1_relat_1 @ r1_tarski ) )
    | ~ ( sk213 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8164]) ).

thf(36032,plain,
    ( ( ( sk213 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk213 @ k1_relat_1 @ r1_tarski ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8180,3230]) ).

thf(36033,plain,
    ( ( ( sk213 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
    | ~ ( sk1 @ ( sk213 @ k1_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[36032]) ).

thf(36179,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk213 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk213 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2081,36033]) ).

thf(36180,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( sk1 @ ( sk213 @ k1_relat_1 @ r1_tarski ) ) )
      | ( ( sk213 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[36179]) ).

thf(36201,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( sk213 @ k1_relat_1 )
       != k1_xboole_0 )
      | ( ( sk213 @ k2_relat_1 )
       != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[36180]) ).

thf(36235,plain,
    ( ( ( sk213 @ k1_relat_1 )
     != k1_xboole_0 )
    | ( ( sk213 @ k2_relat_1 )
     != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v3_struct_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk213 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[36201]) ).

thf(635,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(4719,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)],[635]) ).

thf(241,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(2522,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)],[241]) ).

thf(3100,plain,
    k6_nat_lat @ v7_lattices,
    inference(cnfConj,[status(thm)],[3096]) ).

thf(30957,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1039]) ).

thf(30958,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ( sk1 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[30957:[bind(A,$thf( sk1 ))]]) ).

thf(745,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k16_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_filter_2) ).

thf(5356,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k16_filter_2 ) @ m1_filter_2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(983,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(6456,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)],[983]) ).

thf(12243,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8983]) ).

thf(12244,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk139 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12243]) ).

thf(12292,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk139 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk139 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[12244]) ).

thf(773,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ v14_lattices ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_0) ).

thf(5522,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ v14_lattices ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(379,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(3337,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)],[379]) ).

thf(12178,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,9000]) ).

thf(12179,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v3_filter_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12178]) ).

thf(12285,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk72 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[12179]) ).

thf(29776,plain,
    ! [A: $i] :
      ( ( A != sk329 )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,4904]) ).

thf(29777,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ( sk329 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29776:[bind(A,$thf( sk329 ))]]) ).

thf(993,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(6490,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)],[993]) ).

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(2050,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(794,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v3_filter_0 )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ! [G: $i] :
                              ( ( C @ ( G @ m1_filter_0 ) )
                             => ! [H: $i] :
                                  ( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
                                 => ! [I: $i] :
                                      ( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
                                     => ! [J: $i] :
                                          ( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
                                         => ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
                                                & ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                                             => ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                                            & ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
                                                & ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
                                             => ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_filter_0) ).

thf(5601,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v3_filter_0 )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ! [G: $i] :
                              ( ( C @ ( G @ m1_filter_0 ) )
                             => ! [H: $i] :
                                  ( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
                                 => ! [I: $i] :
                                      ( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
                                     => ! [J: $i] :
                                          ( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
                                         => ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
                                                & ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                                             => ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                                            & ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
                                                & ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
                                             => ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(409,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(3496,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)],[409]) ).

thf(4885,plain,
    sk328 @ v5_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(281,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(2768,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)],[281]) ).

thf(752,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(5398,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)],[752]) ).

thf(5754,plain,
    ( ( ( f4_s11_funct_2 @ ( sk410 @ ( 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)],[5752]) ).

thf(5760,plain,
    ( ( ( f4_s11_funct_2 @ ( sk410 @ ( 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)],[5754]) ).

thf(582,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(4455,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)],[582]) ).

thf(860,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(5926,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)],[860]) ).

thf(963,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(6366,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)],[963]) ).

thf(6778,plain,
    ( ( ( sk215 @ v1_xboole_0 )
     != ( sk153 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2656,3242]) ).

thf(6779,plain,
    ( ( sk215 @ v1_xboole_0 )
   != ( sk153 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6778]) ).

thf(6782,plain,
    sk215 != sk153,
    inference(simp,[status(thm)],[6779]) ).

thf(320,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(3015,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)],[320]) ).

thf(529,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(4146,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)],[529]) ).

thf(153,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(1989,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)],[153]) ).

thf(213,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(2334,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)],[213]) ).

thf(29758,plain,
    ! [A: $i] :
      ( ( A != sk317 )
      | ( k1_xboole_0 @ v9_lattices )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,4728]) ).

thf(29759,plain,
    ( ( k1_xboole_0 @ v9_lattices )
    | ( sk317 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[29758:[bind(A,$thf( sk317 ))]]) ).

thf(31227,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk353 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,17009]) ).

thf(31228,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk353 ) )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[31227]) ).

thf(31229,plain,
    ! [A: $i] : ( A @ sk353 @ sk20 @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[31228:[bind(A,$thf( C @ sk353 )),bind(B,$thf( C ))]]) ).

thf(32825,plain,
    ! [A: $i] : ( A @ sk353 @ sk20 @ v1_relat_1 ),
    inference(simp,[status(thm)],[31229]) ).

thf(274,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(2704,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)],[274]) ).

thf(996,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(6503,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)],[996]) ).

thf(782,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(5559,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)],[782]) ).

thf(497,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(3982,plain,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ k1_lattice2 @ l3_lattices )
        & ( A @ k1_lattice2 @ v3_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(462,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(3822,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)],[462]) ).

thf(346,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(3145,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)],[346]) ).

thf(4895,plain,
    sk328 @ v15_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(381,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(3347,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)],[381]) ).

thf(550,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(4286,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)],[550]) ).

thf(369,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(3277,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)],[369]) ).

thf(819,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(5741,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)],[819]) ).

thf(2417,plain,
    sk119 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2411]) ).

thf(2366,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk112 ) @ v1_relat_1 ),
    inference(cnfConj,[status(thm)],[2364]) ).

thf(307,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(2961,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)],[307]) ).

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(1288,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(1197,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)],[1196]) ).

thf(2913,plain,
    sk187 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2910]) ).

thf(967,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( A @ v13_lattices )
           => ( B @ ( A @ k23_filter_2 ) @ v13_lattices ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_filter_2) ).

thf(6380,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( A @ v13_lattices )
           => ( B @ ( A @ k23_filter_2 ) @ v13_lattices ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(789,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(5586,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)],[789]) ).

thf(845,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(5867,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)],[845]) ).

thf(12204,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8554]) ).

thf(12205,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12204]) ).

thf(12295,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk313 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12205]) ).

thf(12335,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12295]) ).

thf(579,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(4442,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)],[579]) ).

thf(284,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(2795,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)],[284]) ).

thf(719,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(5215,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)],[719]) ).

thf(4912,plain,
    sk329 @ v1_lattice2,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(972,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(6393,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)],[972]) ).

thf(12267,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4623,8557]) ).

thf(12268,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk313 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12267]) ).

thf(12320,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk313 != sk204 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12268]) ).

thf(15575,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,9000]) ).

thf(15576,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15575]) ).

thf(15704,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk72 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15576]) ).

thf(15741,plain,
    ( ( sk72 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15704]) ).

thf(434,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(3673,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)],[434]) ).

thf(945,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(6273,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)],[945]) ).

thf(283,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(2783,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)],[283]) ).

thf(737,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).

thf(5324,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(1092,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)],[1091]) ).

thf(1093,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)],[1092]) ).

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(2159,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(15640,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,8986]) ).

thf(15641,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk313 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15640]) ).

thf(15700,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk313 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15641]) ).

thf(15737,plain,
    ( ( sk313 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk313 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v3_filter_0 ) ),
    inference(simp,[status(thm)],[15700]) ).

thf(831,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(5806,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)],[831]) ).

thf(802,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(5637,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)],[802]) ).

thf(407,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(3489,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)],[407]) ).

thf(986,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(6471,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)],[986]) ).

thf(559,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(4330,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(672,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(4955,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)],[672]) ).

thf(1006,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(6548,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)],[1006]) ).

thf(18373,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( k1_xboole_0 @ k1_tarski @ ( A @ sk251 @ m1_subset_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[1957,3747]) ).

thf(18374,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ sk251 @ m1_subset_1 ),
    inference(pattern_uni,[status(thm)],[18373:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(31650,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ v3_filter_0 )
      | ( A @ sk20 @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1316,1044]) ).

thf(31651,plain,
    ( ( k1_xboole_0 @ v3_filter_0 )
    | ( sk1 @ sk20 @ v1_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[31650:[bind(A,$thf( sk1 ))]]) ).

thf(8684,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk72 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1979,5293]) ).

thf(8685,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk72 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8684]) ).

thf(8692,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk72 ),
    inference(simp,[status(thm)],[8685]) ).

thf(363,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
      <=> ( B
          = ( A @ k1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).

thf(3244,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( ( B
            = ( A @ k1_subset_1 ) )
         => ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) )
        & ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
         => ( B
            = ( A @ k1_subset_1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(658,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(4848,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)],[658]) ).

thf(717,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(5204,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)],[717]) ).

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(1829,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(956,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( B @ ( A @ 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(6316,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)],[956]) ).

thf(8054,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(paramod_ordered,[status(thm)],[1081,7856]) ).

thf(8055,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk204 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[8054]) ).

thf(8056,plain,
    ! [B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( B @ k1_relat_1 )
       != sk1 )
      | ( B != sk204 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ v1_relat_1 )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[8055]) ).

thf(8059,plain,
    ( ( ( sk204 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) )
    | ~ ( sk204 @ v1_relat_1 )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[8056]) ).

thf(11257,plain,
    ( ( ( sk204 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) )
    | ~ $true
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(rewrite,[status(thm)],[8059,3129]) ).

thf(11258,plain,
    ( ( ( sk204 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[11257]) ).

thf(12778,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk204 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ~ $true
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(paramod_ordered,[status(thm)],[2081,11258]) ).

thf(12779,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( k1_xboole_0 @ ( sk204 @ k2_relat_1 @ r1_tarski ) ) )
      | ( ( sk204 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12778]) ).

thf(12783,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( sk204 @ k2_relat_1 )
       != k1_xboole_0 )
      | ( ( sk204 @ k1_relat_1 )
       != sk1 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12779]) ).

thf(12793,plain,
    ( ( ( sk204 @ k2_relat_1 )
     != k1_xboole_0 )
    | ( ( sk204 @ k1_relat_1 )
     != sk1 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk204 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12783]) ).

thf(1151,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)],[1150]) ).

thf(1152,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)],[1151]) ).

thf(327,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(3057,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)],[327]) ).

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(1532,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(648,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(4799,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)],[648]) ).

thf(520,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(4118,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)],[520]) ).

thf(15638,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2266,7865]) ).

thf(15639,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk72 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[15638]) ).

thf(15696,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk72 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15639]) ).

thf(15732,plain,
    ( ( sk72 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk72 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[15696]) ).

thf(964,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(6373,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)],[964]) ).

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(3772,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(874,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(5975,plain,
    f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(932,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( 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(6205,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)],[932]) ).

thf(824,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(5768,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)],[824]) ).

thf(541,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(4229,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)],[541]) ).

thf(827,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(5774,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)],[827]) ).

thf(633,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(4713,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)],[633]) ).

thf(909,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(6104,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)],[909]) ).

thf(338,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(3113,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)],[338]) ).

thf(14680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( A @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[14657,1099]) ).

thf(14681,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( A @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14680]) ).

thf(14682,plain,
    ! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14681:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f1_s4_funct_2 )),bind(D,$thf( D ))]]) ).

thf(14727,plain,
    ! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk313 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14682]) ).

thf(761,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
      <=> ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).

thf(5473,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( ( B = C )
         => ( C @ ( B @ ( A @ r1_filter_2 ) ) ) )
        & ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
         => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(841,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(5845,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)],[841]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_lattice2) ).

thf(5344,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(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(2138,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(4674,plain,
    sk315 @ v9_lattices,
    inference(cnfConj,[status(thm)],[4669]) ).

thf(266,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(2672,plain,
    ! [A: $i,B: $i] :
      ( ( A @ v1_relat_1 )
     => ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(549,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(4274,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)],[549]) ).

thf(779,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( D @ ( C @ ( B @ r3_lattices ) ) )
            & ( A = D )
            & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).

thf(5542,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( ? [D: $i] :
              ( ( D @ ( C @ ( B @ r3_lattices ) ) )
              & ( A = D )
              & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) )
         => ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) ) )
        & ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
         => ? [D: $i] :
              ( ( D @ ( C @ ( B @ r3_lattices ) ) )
              & ( A = D )
              & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(4584,plain,
    sk310 @ v7_lattices,
    inference(cnfConj,[status(thm)],[4581]) ).

thf(4891,plain,
    sk328 @ v7_lattices,
    inference(cnfConj,[status(thm)],[4883]) ).

thf(371,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(3299,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)],[371]) ).

thf(2206,plain,
    sk95 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2203]) ).

thf(530,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ! [C: $i] :
                  ( ( 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(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] :
                  ( ( 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)],[530]) ).

thf(785,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(5569,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)],[785]) ).

thf(396,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(3432,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)],[396]) ).

thf(501,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(4002,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)],[501]) ).

thf(4734,plain,
    sk317 @ v6_lattices,
    inference(cnfConj,[status(thm)],[4723]) ).

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(3753,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(477,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(3901,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)],[477]) ).

thf(22128,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk215 @ k2_relat_1 @ ( A @ ( sk215 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22106,1099]) ).

thf(22129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk215 @ k2_relat_1 @ ( A @ ( sk215 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[22128]) ).

thf(22130,plain,
    ! [B: $i,A: $i] : ( sk215 @ k2_relat_1 @ ( A @ ( B @ ( sk215 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[22129:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk215 @ k9_relat_1 ) )),bind(C,$thf( sk215 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(22189,plain,
    ! [B: $i,A: $i] : ( sk215 @ k2_relat_1 @ ( A @ ( B @ ( sk215 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[22130]) ).

thf(490,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(3950,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)],[490]) ).

thf(644,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(4779,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)],[644]) ).

thf(734,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v15_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).

thf(5307,plain,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v15_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(293,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(2881,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)],[293]) ).

thf(879,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(5986,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)],[879]) ).

thf(735,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k4_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattices) ).

thf(5312,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k4_lattices ) ) )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(295,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(2887,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)],[295]) ).

thf(669,axiom,
    k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_nat_lat) ).

thf(4949,plain,
    k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(641,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(4767,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)],[641]) ).

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(1463,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(316,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(2998,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)],[316]) ).

thf(6716,plain,
    ( ( ( sk215 @ v1_xboole_0 )
     != ( sk72 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1979,3242]) ).

thf(6717,plain,
    ( ( sk215 @ v1_xboole_0 )
   != ( sk72 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6716]) ).

thf(6718,plain,
    sk215 != sk72,
    inference(simp,[status(thm)],[6717]) ).

thf(829,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(5788,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)],[829]) ).

thf(231,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(2438,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)],[231]) ).

thf(573,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(4423,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)],[573]) ).

thf(4908,plain,
    sk329 @ v7_lattices,
    inference(cnfConj,[status(thm)],[4899]) ).

thf(3313,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
      | ( A
       != ( C @ k1_tarski ) ) ),
    inference(cnfConj,[status(thm)],[3309]) ).

thf(3315,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
      | ( A
       != ( C @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[3313]) ).

thf(3316,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ k1_tarski @ r1_tarski ) ),
    inference(simp,[status(thm)],[3315]) ).

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(2170,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(917,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(6141,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)],[917]) ).

thf(890,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( 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(6035,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)],[890]) ).

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(1449,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(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(2087,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(584,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(4459,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)],[584]) ).

thf(2470,plain,
    k13_nat_lat @ v7_lattices,
    inference(cnfConj,[status(thm)],[2467]) ).

thf(15854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s11_funct_2 @ ( sk410 @ 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)],[14875,1099]) ).

thf(15855,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s11_funct_2 @ ( sk410 @ 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)],[15854]) ).

thf(15856,plain,
    ! [A: $i] :
      ( ( f1_s11_funct_2 @ ( A @ ( sk410 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[15855:[bind(A,$thf( sk410 @ k1_relat_1 )),bind(B,$thf( f1_s11_funct_2 )),bind(C,$thf( C ))]]) ).

thf(15899,plain,
    ! [A: $i] :
      ( ( f1_s11_funct_2 @ ( A @ ( sk410 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[15856]) ).

thf(906,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [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(6094,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)],[906]) ).

thf(787,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(5574,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)],[787]) ).

thf(420,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(3575,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)],[420]) ).

thf(47858,plain,
    $false,
    inference(e,[status(thm)],[4447,2094,15720,5329,1105,4729,2412,6855,1083,6074,6555,4728,6014,5385,5810,5659,1322,5509,5686,6085,5116,5561,4094,5918,1369,1190,33917,3345,4464,3008,2131,2109,4824,4909,2031,3930,30308,2921,15558,3979,6285,3397,15242,3830,2499,6042,4682,1956,5131,1549,1554,4904,1110,29812,1158,6177,5168,1068,2953,5173,1142,4623,4592,2363,1200,15098,2210,38726,5820,6106,39188,4515,3813,3230,3098,1073,6338,4711,3012,1205,4326,5265,2854,5237,6602,11440,32723,5614,6214,1041,4479,3017,6391,4090,1756,3044,38352,6655,3826,30671,3895,6640,15735,38844,8551,3049,3745,1137,3332,4647,3942,8568,4884,6359,2918,1164,3446,1233,6515,29740,9000,2476,2168,6551,3481,5782,6336,1063,1954,6804,3370,1196,2216,4142,1127,40238,2985,2082,2067,1254,1746,3103,2348,2723,15723,4266,3513,4679,3088,3777,1935,19518,3730,1645,5770,1601,1386,3466,7856,1724,1475,6306,1366,5874,6102,12324,9394,6182,2405,2667,3046,5759,5910,39055,2501,3485,11448,2654,4637,12351,1409,3204,5765,4439,4546,3976,9989,33110,2328,2916,3425,4896,1430,15033,1985,2039,6039,2698,3131,1298,4654,2444,2217,1826,6676,4130,1279,5130,5160,1455,3749,5182,3845,4023,1832,1191,6662,6006,1992,39617,24386,2466,5108,4428,3043,3855,5461,6130,1247,4622,5480,1494,4471,3231,1100,6071,5744,2420,7997,7862,6010,6049,3099,4353,5605,2169,1087,15727,5199,6149,15742,6626,4179,5193,1398,4830,4675,3470,5851,4551,3014,4141,14597,6098,4632,3835,1362,1963,3602,3557,2388,6487,2533,1232,3258,6382,6594,9580,15954,3788,4595,5792,5682,1946,4018,4600,4820,3702,4724,5135,5360,4556,2007,19206,6259,1415,6840,5892,4583,2027,6227,5526,3934,4903,5084,1811,12828,1040,1109,6657,4297,2469,4733,9225,6523,32982,2236,6534,1136,1864,4050,2122,3621,1978,2925,3973,12794,15554,8526,1383,4134,3357,3569,2540,8018,2034,6559,4115,5761,4686,3771,6562,2017,5834,1169,5353,3739,5370,19263,6498,4307,4038,3327,15738,3870,5045,7413,5572,5059,12330,24401,3986,5929,2367,2437,1928,6451,6631,4842,5220,1215,12824,6110,5772,1072,3036,1119,2424,2979,14658,8691,3756,4536,3243,4643,1201,29099,2965,8554,4892,4588,3906,1521,4628,4211,3492,3406,2205,3184,2586,2884,4483,3510,4065,5695,6474,3378,5012,5443,6064,5968,5291,6388,11456,1604,29843,2922,5174,3151,3097,39343,6856,1206,4604,4893,4323,31450,2204,5530,4589,2473,5751,2574,4888,1438,5839,5411,29757,3169,6296,3265,2646,1306,4531,1153,12333,4370,19329,4910,5519,1067,1736,4172,5281,4925,6092,1057,6200,1163,6652,4915,1223,1091,6000,6032,5349,16264,33603,3233,3207,4044,5049,2589,6079,2601,4016,2805,6605,1042,2541,1519,2596,3867,21646,4521,3816,2150,6496,5102,2414,5594,11212,6509,1238,2015,3307,5826,1837,4725,5690,1951,4553,1687,1656,3647,3408,3191,2464,1938,6629,5983,4140,2670,3810,7576,1920,4585,2433,2477,7314,4757,5177,5988,27621,4327,9391,5551,11452,5038,1159,4402,4942,5566,6060,1079,2213,3028,3926,3050,2345,1195,2211,3763,1128,7853,6666,5729,15724,4732,5936,4680,5515,4063,1106,15947,1983,15739,4668,6360,1360,2245,5189,3105,8530,1089,3909,5904,1234,1143,5609,5098,3122,2990,1534,5673,4512,2841,6195,1121,4486,1064,27314,5502,1111,2709,4789,4544,1856,2692,1498,4525,6235,1096,3102,4233,3963,3518,5583,4227,5978,2858,2537,3632,5889,15729,9603,3440,4219,7486,5497,3060,4817,4898,4676,1160,5080,12325,1182,2419,4191,5932,4333,5941,1329,4518,1082,4582,3179,6642,6363,2080,32721,2172,3428,1214,5662,3194,38359,6395,6501,15728,7577,3671,4457,4814,2472,9392,4621,1039,6271,1155,5387,4736,3242,1114,1451,1530,2598,5639,1974,6207,4717,4120,1263,6134,2450,2125,1099,1150,1249,2536,40462,1266,3354,2153,1231,5973,2355,1192,9581,1932,8690,1050,3390,7495,3819,4237,3222,4934,2497,2052,4902,14875,4953,12800,4259,1979,3074,4689,6224,12831,15940,4535,1202,3624,1563,6378,33109,5513,2617,5126,2529,2909,5170,3454,3824,5112,5557,14657,3802,8527,15042,3225,4288,1241,2546,4195,2208,8989,2043,4889,1712,7414,3592,1846,29726,5964,12329,6279,3999,2963,1286,3321,5447,1035,2915,4906,15552,1996,5872,6637,5524,2391,6203,9577,1273,2941,5960,6469,4577,3686,5679,1135,2729,1648,2936,33809,1727,6314,5483,2413,3130,6507,4708,6437,4685,1146,2292,1698,2556,2275,15976,5762,4594,2717,1219,4340,3375,6454,4359,5525,3274,12287,4489,6052,6598,5598,12827,4041,3741,2970,3636,3255,4309,3758,4122,5831,4328,17009,6108,3240,9602,2657,3086,1752,4677,5627,6229,5612,1403,3458,6407,32346,4590,12322,1226,2695,1256,1139,4112,3330,5148,2706,6281,6525,5039,4558,3118,5033,2220,6385,4096,2891,5011,3077,4672,12830,4822,1058,1107,3487,2055,2166,1090,2457,4640,19596,3416,12825,6334,15733,30669,3091,2474,3302,29845,4887,4245,7865,3719,2358,2319,4433,1356,1209,5212,2284,5222,5407,6478,2361,3101,5870,2538,1408,6308,5671,3251,2229,41494,2084,2214,12297,2415,1894,2422,6443,2774,6217,6500,3683,3515,2906,6197,5827,8688,5853,12354,3106,5880,15740,4586,32883,2116,4616,8986,4073,12791,1043,1801,3500,3138,4176,6154,5689,1122,4300,4374,3182,3066,5972,4773,1571,5616,1376,4509,4107,32920,4388,1175,18277,4203,4635,4430,3747,4420,4064,14063,8529,2410,3006,7575,1177,15966,2911,6376,1080,21657,22106,4882,4103,4911,5994,8983,2267,4731,5335,3572,3932,4897,4452,1149,3298,2542,5180,4726,2664,2278,5007,4684,30673,1061,12274,3838,12797,4827,5849,3706,2967,5089,6029,6212,6476,8689,40073,1171,2418,4844,5340,1198,2725,2401,2212,6449,15725,1044,5218,1066,21571,10549,6151,4373,7334,3917,15933,24397,6783,5248,3159,2369,4362,3953,5976,1113,6180,6293,4497,4626,39164,2207,5326,4890,3444,1809,4901,12288,2271,3921,1472,1958,5763,2005,5812,1076,2054,4426,4907,5538,2914,12326,1662,4136,6672,1208,4886,4580,2994,38350,2471,4735,1905,3981,2878,1081,2927,2629,9639,2202,24392,1145,5916,6564,6008,6664,5358,4722,1181,4336,1551,21740,4986,6557,6641,6012,5822,4035,5294,3913,3842,2661,3214,3904,3228,3872,6481,4593,29814,2567,6577,5452,6069,5624,5229,12289,21743,6120,26784,1156,29229,1743,1400,26793,3082,6621,4673,32725,4950,3833,3659,5484,4200,29765,3129,15721,5592,5980,2678,4469,9578,2407,4894,1230,2850,19584,6146,2689,3642,2920,9599,1038,12826,6513,6298,2656,3080,5955,1053,5684,2092,4905,1987,1716,3305,5731,1300,1637,15556,5276,1980,5154,3774,3127,8528,4351,6174,5152,1658,2701,2545,2903,4982,1679,3412,4781,4737,29742,1218,5450,5106,3095,3853,2468,1220,5062,2675,12328,5902,12790,1221,15736,3961,1372,7498,6220,6650,3697,1898,6679,2838,2113,41318,5223,3124,1536,6803,1702,2379,4976,24389,2543,5998,5240,1955,2145,1485,1052,4991,6193,4235,5226,1094,1140,5364,2949,8565,5596,6531,2266,5895,15159,13595,15731,38351,4671,12829,9601,9395,4770,2870,5934,2187,5485,2435,4639,5939,4548,2626,1316,1084,17657,4727,27606,6447,3589,5749,3092,4587,4945,1180,15099,5536,1817,6013,3171,2078,1834,1913,7412,3533,11450,5966,1844,6137,4997,3548,28933,1654,2325,3928,1216,2209,1126,5907,2919,5124,5332,2658,32784,5068,4061,5184,1108,4730,4678,1998,3797,12302,1276,5315,1326,4913,2988,2098,3709,4666,4681,4683,5899,3748,5010,6618,5505,6322,6077,5272,2290,4791,3104,3136,3368,3662,2416,4900,1558,4261,6354,4745,6257,2081,8997,31454,5837,5409,1212,6166,31452,4619,1045,39178,5828,3181,2475,4602,3324,4649,6854,6397,4964,2912,6484,9393,4591,4759,21811,6045,5040,5699,6521,1077,2362,6277,6062,5517,1893,33706,3645,1444,6444,2917,4372,6462,6499,38710,1161,2421,4880,15743,4670,1097,4596,3521,10590,6600,5187,2218,4125,1642,5677,4917,1957,5129,2155,5971,3232,3997,6439,9579,36235,4719,2522,3100,30958,7489,5356,6456,12292,5522,3337,12285,1148,29777,6490,2050,5601,3496,4885,2768,3690,5398,5760,4455,5926,6366,6782,3015,4146,1989,2334,29759,32825,8557,2704,6503,5559,3982,3822,3145,4895,3347,4286,3277,1172,5741,36033,2417,2366,7278,2961,1288,1197,2913,6380,5586,5867,5251,1891,5036,12335,4442,2795,5215,4912,6393,12320,15741,30585,3673,6273,2783,5324,1093,2159,15737,5806,5637,3489,6471,4330,4955,6548,9600,18374,1120,31651,8692,3244,1236,2127,4848,5204,1829,1977,6316,3543,12793,11258,1152,3057,1532,4799,2265,4118,15732,6373,3772,1976,5975,6205,5768,4229,5774,4713,4936,6104,3113,29748,14727,5473,5845,5344,2138,4674,5172,2672,7367,4274,5542,4584,4891,3299,2206,4161,5569,3432,4002,4734,3753,4533,3901,22189,3950,4779,5307,2881,5986,5312,2887,4949,4767,1463,2998,6718,5788,2436,2438,1037,4423,4908,3316,2170,6141,6035,1449,2087,5293,4459,3047,2470,15899,1069,6094,5574,3575]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LAT335+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
% 0.12/0.39  % Computer : n019.cluster.edu
% 0.12/0.39  % Model    : x86_64 x86_64
% 0.12/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39  % Memory   : 8046.5625MB
% 0.12/0.39  % OS       : Linux 6.8.0-71-generic
% 0.12/0.39  % CPULimit : 300
% 0.12/0.39  % WCLimit  : 300
% 0.12/0.39  % DateTime : Fri Sep 25 21:00:35 UTC 2026
% 0.12/0.39  % CPUTime  : 
% 0.12/0.39  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 3.25/1.68  % [INFO] 	 Parsing done (695ms). 
% 3.68/1.70  % [INFO] 	 Running in sequential loop mode. 
% 4.36/2.09  % [INFO] 	 eprover registered as external prover. 
% 4.36/2.09  % [INFO] 	 Scanning for conjecture ... 
% 5.56/2.42  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3017 axioms. Running axiom selection ... 
% 8.10/3.34  % [INFO] 	 Axiom selection finished. Selected 1032 axioms (removed 1985 axioms). 
% 10.73/4.17  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 10.92/4.24  % [INFO] 	 Type checking passed. 
% 10.92/4.24  % [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 ... 
% 163.11/48.63  % External prover 'e' found a proof!
% 163.11/48.64  % [INFO] 	 Killing All external provers ... 
% 163.11/48.64  % Time passed: 48101ms (effective reasoning time: 46930ms)
% 163.11/48.64  % 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)>
% 163.11/48.65  % Axioms used in derivation (1032): t31_lattice2, d14_filter_2, t7_filter_0, dt_k4_filter_2, t1_filter_2, t45_lattice4, t2_filter_0, t21_zfmisc_1, t11_filter_2, t13_relset_1, dt_k7_filter_0, rc1_lattice2, d1_lattices, t119_funct_2, t158_relat_1, t17_lattice4, dt_k9_filter_2, t50_lattice4, redefinition_m2_relset_1, fraenkel_a_1_0_domain_1, t51_partfun1, t24_filter_0, t10_lattice2, d13_filter_0, t38_filter_2, fraenkel_a_3_2_domain_1, cc5_lattice2, t31_filter_0, t37_lattice2, t78_filter_0, t43_lattice2, dt_m1_lattice4, fc1_zfmisc_1, t35_subset_1, t135_zfmisc_1, t25_relset_1, t30_relat_1, d4_funct_1, t20_lattice4, t39_lattices, t76_lattice2, d10_lattices, t20_zfmisc_1, d1_tarski, dt_k2_lattice2, d20_binop_1, t66_funct_2, t62_filter_0, t66_partfun1, dt_k1_filter_2, t80_filter_0, t53_subset_1, t44_filter_2, d6_filter_0, d5_relat_1, t109_xboole_1, redefinition_k16_filter_2, t25_lattice2, d10_binop_1, t10_filter_2, t36_lattice4, t19_filter_2, t34_filter_2, t29_filter_0, fc2_filter_0, t81_filter_0, t24_lattice4, d13_lattices, cc3_lattice2, d14_binop_1, dt_k9_domain_1, d6_lattice2, t7_subset_1, t30_lattice2, t32_funct_2, d11_binop_1, t2_realset1, t3_xboole_1, d4_lattice4, t3_realset1, d3_subset_1, fc1_xboole_0, rc12_lattices, dt_k7_domain_1, t34_xboole_1, t29_lattice2, t59_filter_2, d1_lattice2, t56_partfun1, t63_filter_2, t59_partfun1, s12_funct_2, t43_lattices, s3_funct_2, t28_filter_2, t42_filter_0, cc6_lattices, t57_lattice2, t33_lattice2, t16_funct_2, d16_lattices, t113_zfmisc_1, t67_lattice2, t7_lattice2, t48_domain_1, t111_zfmisc_1, dt_k2_subset_1, t8_subset_1, t80_lattice2, t9_filter_2, existence_l1_lattices, t32_lattice4, d5_tarski, t15_funct_1, dt_k11_domain_1, t26_lattices, fc4_relat_1, t19_lattices, t4_ordinal1, t1_subset, dt_k1_lattice4, t147_relat_1, t10_partfun1, t47_lattice2, d5_xboole_0, t70_filter_2, t4_lattice4, t9_lattice2, fc4_subset_1, t12_filter_2, t168_funct_2, t10_relset_1, dt_k15_filter_2, fc3_relat_1, d8_funct_1, t69_filter_0, t57_filter_2, t144_relat_1, t57_domain_1, existence_l3_lattices, dt_k6_nat_lat, t39_filter_2, t53_lattices, dt_k3_funct_2, dt_k5_lattices, t7_funct_2, t87_filter_0, fc4_lattice2, t42_zfmisc_1, t21_lattice2, t14_binop_1, dt_k1_subset_1, t19_relat_1, dt_k16_filter_2, t28_binop_1, dt_k13_domain_1, fc1_lattice2, dt_g2_struct_0, t72_lattice2, t117_zfmisc_1, t32_relat_1, dt_k4_subset_1, t83_filter_0, t35_lattice4, t55_filter_2, t23_filter_0, redefinition_k12_filter_2, t16_lattice4, abstractness_v2_struct_0, t46_lattice4, dt_m2_nat_lat, d7_binop_1, existence_m3_lattice4, existence_m1_struct_0, dt_k3_lattice4, t35_zfmisc_1, t18_filter_0, rc2_struct_0, dt_k1_lattice2, t65_partfun1, t44_funct_2, fraenkel_a_2_0_lattice4, t117_funct_1, d10_filter_0, cc4_lattice2, dt_k1_struct_0, t26_lattice4, cc2_lattice2, t85_filter_0, dt_m1_realset1, t110_zfmisc_1, t103_zfmisc_1, dt_k19_filter_2, dt_u2_struct_0, t63_partfun1, t15_relset_1, t14_filter_0, fraenkel_a_2_0_filter_0, rc2_partfun1, t18_relat_1, fc1_filter_0, t48_filter_0, d9_lattice4, t49_funct_2, t41_lattice2, t64_filter_2, t70_zfmisc_1, t69_zfmisc_1, cc4_lattices, redefinition_k11_filter_0, fc2_filter_2, rc3_funct_1, fraenkel_a_3_3_domain_1, l70_filter_2, t68_filter_2, t50_funct_2, dt_k5_filter_0, dt_k3_filter_0, d1_struct_0, t27_zfmisc_1, t37_xboole_1, t41_zfmisc_1, fc2_lattice2, dt_m2_relset_1, cc1_relat_1, dt_k7_funct_2, dt_k5_filter_2, t59_lattice2, t70_partfun1, fc3_lattice2, t26_filter_0, t56_relat_1, t83_lattice2, t17_funct_1, t21_filter_2, t43_filter_2, redefinition_k2_funct_2, t2_funct_1, t36_subset_1, t29_partfun1, t33_lattice4, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, t32_filter_0, commutativity_k7_domain_1, t46_lattice2, fraenkel_a_2_0_domain_1, d2_tarski, dt_k2_binop_1, involutiveness_k3_subset_1, rc1_funct_1, t53_filter_0, d5_lattices, 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, t71_filter_2, 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, t31_partfun1, dt_k7_lattices, t3_funct_2, rc2_subset_1, existence_l2_lattices, l59_filter_2, t75_filter_2, t27_relset_1, t52_domain_1, t118_zfmisc_1, t55_partfun1, s4_subset_1, t8_funct_2, t118_funct_2, t29_lattice4, t76_nat_lat, t14_relset_1, t39_lattice4, t16_relset_1, t38_lattice4, dt_k11_filter_2, d15_filter_2, d13_relat_1, t74_filter_2, t28_lattice2, t164_funct_2, d15_lattice4, fc2_funct_2, t6_boole, t12_funct_1, dt_k6_subset_1, t10_relat_1, d1_relat_1, t59_filter_0, t1_xboole_1, t26_relset_1, t64_partfun1, t47_lattice4, d5_filter_2, existence_l2_struct_0, t32_lattices, t19_filter_0, t44_lattice4, t49_filter_0, t5_subset, t17_filter_2, redefinition_k12_filter_0, t29_relat_1, d14_lattice4, cc6_lattice2, t50_filter_2, t77_funct_2, t59_domain_1, t34_filter_0, d4_filter_2, t5_lattice4, t54_filter_2, t22_lattices, t32_partfun1, d6_tarski, t4_relat_1, t26_binop_1, t28_subset_1, d12_lattices, d17_lattice4, fc3_subset_1, t128_zfmisc_1, t39_partfun1, t75_zfmisc_1, redefinition_k4_filter_2, t8_lattice4, rc1_filter_0, d2_realset1, d16_filter_2, t51_filter_2, fc2_subset_1, t45_funct_2, d9_filter_2, t25_zfmisc_1, d4_relat_1, d7_lattices, t6_lattice2, t23_binop_1, t150_relat_1, existence_m1_relset_1, t1_zfmisc_1, dt_m2_filter_2, t47_filter_2, t50_lattices, fc4_filter_2, s8_domain_1, dt_l3_lattices, t48_lattice2, t30_filter_2, d16_nat_lat, t79_zfmisc_1, t12_lattice2, t5_funct_2, dt_k8_funct_2, d12_lattice4, t16_filter_2, t167_funct_2, dt_m1_struct_0, t17_lattices, t11_funct_2, t65_filter_2, t40_funct_2, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t24_binop_1, t27_lattice4, t4_filter_0, t89_filter_0, dt_l2_lattices, redefinition_k7_domain_1, t40_filter_0, d3_filter_2, d12_filter_2, t72_partfun1, t8_funct_1, t2_tarski, t16_funct_1, t28_zfmisc_1, t72_zfmisc_1, t82_funct_2, dt_k4_filter_0, t33_xboole_1, s9_domain_1, t84_lattice2, t75_lattice2, t67_filter_2, t47_lattices, d7_filter_2, d20_lattices, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t38_filter_0, d3_lattices, t77_filter_2, t23_zfmisc_1, t34_lattice4, cc5_lattices, t4_subset, t38_subset_1, d18_lattices, t169_funct_2, t44_lattices, dt_k2_funct_1, cc1_funct_2, t39_subset_1, d8_filter_0, t56_lattice2, t52_subset_1, t60_filter_0, t5_ordinal1, rc13_lattices, t4_boole, t71_lattice2, d2_funct_2, t22_lattice2, t8_filter_2, t70_lattice2, dt_k8_domain_1, dt_k17_filter_2, fc3_filter_2, t15_lattice4, t74_zfmisc_1, t32_xboole_1, t61_filter_2, dt_k8_filter_0, t14_funct_1, t5_filter_2, t9_zfmisc_1, d7_filter_0, existence_m3_realset1, t56_subset_1, dt_k1_domain_1, t17_funct_2, t85_lattice2, redefinition_k14_filter_2, t75_filter_0, t13_lattice2, fc1_realset1, t25_filter_2, t132_funct_2, t45_lattices, t49_lattice4, t51_funct_2, d12_binop_1, t21_lattices, t12_zfmisc_1, existence_m2_realset1, fc5_filter_2, d2_lattice4, t38_lattice2, t139_zfmisc_1, t16_lattice2, cc1_funct_1, t4_funct_2, redefinition_k1_filter_2, d10_lattice4, s11_funct_2, d3_relat_2, s2_domain_1, rc3_struct_0, t3_ordinal1, t9_domain_1, d6_filter_2, t25_lattices, t7_boole, dt_k14_filter_2, dt_k5_lattice4, t11_binop_1, t55_filter_0, t143_relat_1, d2_subset_1, t27_lattice2, commutativity_k4_lattices, redefinition_k9_filter_2, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, rc2_lattice2, commutativity_k2_struct_0, t7_filter_2, t23_filter_2, dt_k6_domain_1, t157_funct_1, t31_lattice4, fc5_lattice2, d17_lattices, dt_k2_partfun1, rc2_funct_1, t158_funct_2, dt_k9_filter_0, t90_filter_0, redefinition_k15_filter_2, t4_subset_1, redefinition_k1_domain_1, rc1_funct_2, l48_filter_2, t26_zfmisc_1, t6_filter_2, t69_partfun1, t7_ordinal1, dt_k10_filter_2, t9_funct_2, t31_funct_2, rc1_subset_1, t48_lattice4, t68_filter_0, fc6_lattice2, t8_lattice2, t18_lattices, cc1_lattices, t5_filter_0, t64_zfmisc_1, fc5_relat_1, t30_filter_0, t40_lattice4, t13_filter_2, redefinition_r3_lattices, t40_lattices, t4_filter_2, t113_funct_2, t71_partfun1, d21_lattices, t41_lattices, t159_funct_2, t116_zfmisc_1, d4_lattices, existence_m1_filter_0, dt_k3_lattice2, t78_filter_2, t2_lattice2, redefinition_m1_filter_2, dt_k2_struct_0, t49_lattices, t14_funct_2, t27_binop_1, t48_lattices, dt_k2_lattice4, t9_filter_0, t65_funct_1, t40_filter_2, fc1_nat_lat, fraenkel_a_3_1_domain_1, t60_funct_2, t7_lattice4, t36_filter_2, cc2_funct_1, t5_realset1, s4_funct_2, t41_lattice4, rc9_lattices, dt_k7_filter_2, d2_zfmisc_1, cc1_filter_0, t169_partfun1, fraenkel_a_2_1_lattice4, t26_lattice2, dt_k24_filter_2, t17_lattice2, t18_funct_1, 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, t118_funct_1, d9_binop_1, t19_lattice2, t146_relat_1, t35_xboole_1, t49_domain_1, d17_binop_1, dt_k2_filter_0, dt_k2_funct_2, d2_filter_0, rc1_nat_lat, t5_lattice2, free_g2_struct_0, t44_filter_0, t73_filter_2, dt_k20_filter_2, t17_relset_1, cc3_lattices, d5_subset_1, t99_partfun1, t107_zfmisc_1, t9_realset1, t121_funct_2, t114_zfmisc_1, dt_k23_filter_2, t58_partfun1, d1_zfmisc_1, t27_filter_0, t15_filter_2, t11_lattice4, rc2_relat_1, t36_lattice2, existence_m2_relset_1, d4_binop_1, t64_filter_0, t38_zfmisc_1, t75_nat_lat, t9_lattice4, t69_enumset1, t82_lattice2, t22_zfmisc_1, t14_filter_2, d1_filter_0, redefinition_k7_filter_0, t76_filter_2, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, t62_lattice2, t39_filter_0, t74_lattice2, t11_filter_0, t29_filter_2, existence_m2_lattice4, t23_lattice4, d4_lattice2, t116_funct_2, t69_filter_2, fraenkel_a_3_6_domain_1, t168_partfun1, s14_funct_2, t51_filter_0, t14_lattice4, t37_lattice4, redefinition_k2_binop_1, t74_filter_0, 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, t72_filter_2, 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
% 163.11/48.65  % No. of inferences in proof: 3358
% 163.11/48.65  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 48101 ms resp. 46930 ms w/o parsing
% 169.63/49.92  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 169.63/49.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------